diff --git a/.gitmodules b/.gitmodules index cb86c78b46bdff327233025966aff72d29689346..cb766b513364c6baf7795156248b958c1f61669f 100644 --- a/.gitmodules +++ b/.gitmodules @@ -3,3 +3,8 @@ path = docs/tutorial url = git@gitlab.nektar.info:nektar/tutorial ignore = all +[submodule "docs/developer-guide"] + branch = master + path = docs/developer-guide + url = git@gitlab.nektar.info:nektar/developer-guide + ignore = all diff --git a/CHANGELOG.md b/CHANGELOG.md index 4ead3eeb88c6acbdca168a1e03b340d40fe4986b..bf565655d08b048112de1c14be4d58b773455a6b 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -1,6 +1,21 @@ Changelog ========= +v4.5.0 +------ +**NekMesh**: +- Add periodic boundary condition meshing in 2D (!733) +- Adjust boundary layer thickness in corners in 2D (!739) +- Rework meshing control so that if possible viewable meshes will be dumped + when some part of the system fails (!756) +- Add manifold meshing option (!756) + +**Documentation**: +- Added the developer-guide repository as a submodule (!751) + +**Library** +- Remove the duplicate output of errorutil (!756) + v4.4.0 ------ **Library**: @@ -100,9 +115,9 @@ v4.4.0 - Change variable names in mcf file to make more sense (!736) - Fix issues in varopti module so that in can be compiled without meshgen on (!736) -- Replace LAPACK Eigenvalue calculation with handwritten function in +- Replace LAPACK Eigenvalue calculation with handwritten function in varopti (!738) -- Improved node-colouring algorithm for better load-balancing +- Improved node-colouring algorithm for better load-balancing in varopti (!738) - Simplified calculation of the energy functional in varopti for improved performance (!738) diff --git a/VERSION b/VERSION index fdc6698807a92654177d5679fe2de81be0c17dd4..a84947d6ffe7bdf361dfd679a8e931b44f0e9001 100644 --- a/VERSION +++ b/VERSION @@ -1 +1 @@ -4.4.0 +4.5.0 diff --git a/docs/CMakeLists.txt b/docs/CMakeLists.txt index 25a41388486594e1577e0874d288ba79194d769a..c13b168ce38baeee88368932ed79fa8245562204 100644 --- a/docs/CMakeLists.txt +++ b/docs/CMakeLists.txt @@ -1,5 +1,8 @@ ADD_SUBDIRECTORY(user-guide) -ADD_SUBDIRECTORY(developer-guide) + +IF (EXISTS ${CMAKE_CURRENT_SOURCE_DIR}/developer-guide/CMakeLists.txt) + ADD_SUBDIRECTORY(developer-guide) +ENDIF () IF (EXISTS ${CMAKE_CURRENT_SOURCE_DIR}/tutorial/CMakeLists.txt) ADD_SUBDIRECTORY(tutorial) diff --git a/docs/developer-guide b/docs/developer-guide new file mode 160000 index 0000000000000000000000000000000000000000..e128cfaffbbd37c734a667cdc2a07b6f06291615 --- /dev/null +++ b/docs/developer-guide @@ -0,0 +1 @@ +Subproject commit e128cfaffbbd37c734a667cdc2a07b6f06291615 diff --git a/docs/developer-guide/CMakeLists.txt b/docs/developer-guide/CMakeLists.txt deleted file mode 100644 index b679a6bc11fdcc67a82ccf4b668010711c0072a4..0000000000000000000000000000000000000000 --- a/docs/developer-guide/CMakeLists.txt +++ /dev/null @@ -1,43 +0,0 @@ -SET(DEVGUIDESRC ${CMAKE_CURRENT_SOURCE_DIR}) -SET(DEVGUIDE ${CMAKE_BINARY_DIR}/docs/developer-guide) - -FILE(MAKE_DIRECTORY ${DEVGUIDE}/html) - -FIND_PROGRAM(HTLATEX htlatex) -ADD_CUSTOM_TARGET(developer-guide-html - export TEXINPUTS=${CMAKE_SOURCE_DIR}//:${DEVGUIDESRC}//: && - ${HTLATEX} ${DEVGUIDESRC}/developer-guide.tex - "${DEVGUIDESRC}/styling.cfg,html,3,next,NoFonts" - WORKING_DIRECTORY ${DEVGUIDE}/html -) - -# If tex4ht successful, create img dir and copy images across -FILE(GLOB_RECURSE imgfiles "img/*.png" "img/*.jpg" "*/img/*.png" "*/img/*.jpg") -ADD_CUSTOM_COMMAND(TARGET developer-guide-html - POST_BUILD COMMAND ${CMAKE_COMMAND} -E make_directory ${DEVGUIDE}/html/img) -FOREACH(img ${imgfiles}) - ADD_CUSTOM_COMMAND(TARGET developer-guide-html - POST_BUILD COMMAND ${CMAKE_COMMAND} -E copy ${img} ${DEVGUIDE}/html/img) -ENDFOREACH() - -FILE(GLOB_RECURSE pdffiles "*/img/*.pdf") -FIND_PROGRAM(CONVERT convert) -FOREACH(pdf ${pdffiles}) - GET_FILENAME_COMPONENT(BASENAME ${pdf} NAME_WE) - ADD_CUSTOM_COMMAND(TARGET developer-guide-html - POST_BUILD COMMAND - ${CONVERT} ${pdf} ${DEVGUIDE}/html/img/${BASENAME}.png) -ENDFOREACH() - -FIND_PROGRAM(PDFLATEX pdflatex) -FIND_PROGRAM(BIBTEX bibtex) -FIND_PROGRAM(MAKEINDEX makeindex) -ADD_CUSTOM_TARGET(developer-guide-pdf - export TEXINPUTS=${CMAKE_SOURCE_DIR}//: && - ${PDFLATEX} --output-directory ${DEVGUIDE} ${DEVGUIDESRC}/developer-guide.tex - COMMAND TEXMFOUTPUT=${DEVGUIDE} ${BIBTEX} ${DEVGUIDE}/developer-guide.aux - COMMAND TEXMFOUTPUT=${DEVGUIDE} ${MAKEINDEX} ${DEVGUIDE}/developer-guide.idx - COMMAND export TEXINPUTS=${CMAKE_SOURCE_DIR}//: && - ${PDFLATEX} --output-directory ${DEVGUIDE} ${DEVGUIDESRC}/developer-guide.tex - WORKING_DIRECTORY ${DEVGUIDESRC} -) diff --git a/docs/developer-guide/coding-standard/coding-standard.tex b/docs/developer-guide/coding-standard/coding-standard.tex deleted file mode 100644 index 71d8d4c6785ed570735598ed974ed2cdb67274f6..0000000000000000000000000000000000000000 --- a/docs/developer-guide/coding-standard/coding-standard.tex +++ /dev/null @@ -1,145 +0,0 @@ -\chapter{Coding Standard} - -The purpose of this page is to detail the coding standards of the project which -all contributers are requested to follow. - -This page describes the coding style standard for C++. A coding style standard -defines the visual layout of source code. Presenting source code in a uniform -fashion facilitates the use of code by different developers. In addition, -following a standard prevents certain types of coding errors. - -All of the items below, unless otherwise noted, are guidelines. They are -recommendations about how to lay out a given block of code. Use common sense and -provide comments to describe any deviation from the standard. Sometimes, -violating a guideline may actually improve readability. - -If you are working with code that does not follow the standard, bring the code -up-to-date or follow the existing style. Don’t mix styles. - -\section{Code Layout} - -The aim here is to maximise readability on all platforms and editors. -\begin{itemize} -\item Code width of 80 characters maximum - hard-wrap longer lines. -\item Use sensible wrapping for long statements in a way which maximises -readability. -\item Do not put multiple statements on the same line. -\item Do not declare multiple variables on the same line. -\item Provide a default value on all variable declarations. -\item Enclose every program block (if, else, for, while, etc) in braces, even if -empty or just a single line. -\item Opening braces (\{) should be on their own line. -\item Braces at same indentation as preceeding statement. -\item One class per .cpp and .h file only, unless nested. -\item Define member functions in the .cpp file in the same order as defined in -the .h file. -\item Templated classes defined and implemented in a single .hpp file. -\item Do not put inline functions in the header file unless the function is -trivial (e.g. accessor, empty destructor), or profiling explicitly suggests to. -\item Inline functions should be declared within the class declaration but -defined outside the class declaration at the bottom of the header file. -\begin{notebox} -Virtual and inline are mutually exclusive. Virtual functions should therefore be -implemented in the .cpp file. -\end{notebox} -\end{itemize} - - -\section{Space} - -Adding an appropriate amount of white space enhances readability. Too much white -space, on the other hand, detracts from that readability. - -\begin{itemize} -\item Indent using a four-space tab. Consistent tab spacing is necessary to -maintain formatting. Note that this means when a tab is pressed, four physical spaces are -inserted into the source instead. -\item Put a blank line at the end of a public/protected/private block. -\item Put a blank line at the end of every file. -\item Put a space after every keyword (if, while, for, etc.). -\item Put a space after every comma, unless the comma is at the end of the line. -\item Do not put a space before the opening parenthesis of an argument list to a -function. -\item Declare pointers and references with the * or \& symbol next to the -declarator, not the type; e.g., Object *object. Do not put multiple variables in the same -declaration. -\item Place a space on both sides of a binary operator. -\item Do not use a space to separate a unary operator from its operand. -\item Place open and close braces on their own line. No executable statements -should appear on the line with the brace, but comments are allowed. Indent opening -braces at the same level as the statement above and indent the closing brace at -the same level as the corresponding opening brace. -\item Indent all statements following an open brace by one tab. Developer Studio -puts any specifier terminated with a colon at the same indentation level as the -enclosing brace. Examples of such specifiers include case statements, access -specifiers (public, private, protected), and goto labels. This is not acceptable -and should be manually corrected so that all statements appearing within a block -and delineated by braces are indented. -\item Break a line into multiple lines when it becomes too long to read. Use at -least two tabs to start the new line, so it does not look like the start of a -block. -\item Follow C++ style comments with one space. It is also preferable to -consider any text that follows C++ style comments as a sentence and to begin this text -with a capital letter. This helps to distinguish the line from a continuation of -a previous line; i.e., \inlsh{// This is my comment.} -\item As a general rule, don’t keep commented out source code in the final -baselined product. Such code leads the reader to believe there was uncertainty -in the code as it currently exists. -\item Place the \# of a preprocessor directive at column one. An exception is -the use of nested ifdefs where the bodies only contain other preprocessor directives. -Add tabs to enhance readability: -\begin{lstlisting}[style=C++Style] -void foo() { - for(int i = 0; i < 10; ++i) - { -#ifdef BAR - do_something(); -#endif - for_loop_code(); - } -} -\end{lstlisting} -\item Use tabular white space if it enhances -readability. -\item Use only one return statement. Structure the code so that only one return -statement is necessary. -\end{itemize} - -\section{Naming Conventions} - -Keep variable and function names meaningful but concise. -\begin{itemize} -\item Begin variable names with lower-case letter. -\item Begin function names and class names with upper-case letter. -\item All function, class and variable names should be written in CamelCase, -e.g. \inlsh{MyClass, DoFunction() or myVariableName}. -\item All preprocessor definitions written in UPPER\_CASE with words separated -by underscores, e.g. USE\_SPECIFIC\_FEATURE. -\item All member variables prefixed with m\_. -\item All constants prefixed with a k. -\item All function parameters prefixed with a p. -\item All enumerations prefixed with an e. -\item Do not use leading underscores. -\end{itemize} - -\section{Namespaces} - -The top-level namespace is "Nektar". All code should reside in this namespace or -a sub-space of this. - -\begin{itemize} -\item Namespaces correspond to code structure. -\item Namespaces should be kept to a minimum to simplify the interface to their -contents. -\end{itemize} - -\section{Documentation} -\begin{itemize} -\item Briefs for classes, functions and types in header files using -\inlsh{///} notation. -\item Full documentation with implementation using \inlsh{/** ... *\/} -notation. -\item Use @ symbol for @class, @param, @returns, etc for ease of identification. -\item Any separate documentation pages not directly associated with a portion of -the code should be in a separate file in /docs/html/doxygen. -\end{itemize} diff --git a/docs/developer-guide/core-concepts/core-concepts.tex b/docs/developer-guide/core-concepts/core-concepts.tex deleted file mode 100644 index fd876236d1c4837be5de6d924241806596a067a5..0000000000000000000000000000000000000000 --- a/docs/developer-guide/core-concepts/core-concepts.tex +++ /dev/null @@ -1,354 +0,0 @@ -\chapter{Core Concepts} - -This section describes some of the key concepts which are useful when developing -code within the Nektar++ framework. - -\section{Factory method pattern} -The factory method pattern is used extensively throughout Nektar++ as a -mechanism to instantiate objects. It provides the following benefits: -\begin{itemize} -\item Encourages modularisation of code such that conceptually related -algorithms are grouped together -\item Structuring of code such that different implementations of the same -concept are encapsulated and share a common interface -\item Users of a factory-instantiated modules need only be concerned with the - interface and not the details of underlying implementations -\item Simplifies debugging since code relating to a specific implementation - resides in a single class -\item The code is naturally decoupled to reduce header-file dependencies and - improves compile times -\item Enables implementations (e.g. relating to third-party libraries) to be - disabled through the build process (CMake) by not compiling a specific - implementation, rather than scattering preprocessing statements throughout the - code -\end{itemize} - -For conceptual details see the Wikipedia page. -%\url{http://en.wikipedia.org/wiki/Factory_pattern}. - -\subsection{Using NekFactory} -The templated NekFactory class implements the factory pattern in Nektar++. -There are two distinct aspects to creating a factory-instantiated collection of -classes: defining the public interface, and registering specific -implementations. Both of these involve adding standard boilerplate code. It is -assumed that we are writing a code which implements a particular concept or -functionality within the code, for which there are multiple implementations. The -reasons for multiple implementations may be very low level such as alternative -algorithms for solving a linear system, or high level, such as selecting from a -range of PDEs to solve. - -\subsubsection{Creating an interface (base class)} -A base class must be defined which prescribes an implementation-independent -interface. In Nektar++, the template method pattern is used, requiring public -interface functions to be defined which call private virtual implementation -methods. The latter will be overridden in the specific implementation classes. -In the base class these virtual methods should be defined as pure virtual, since -there is no implementation and we will not be instantiating this base class -explicitly. - -As an example we will create a factory for instantiating different -implementations of some concept \inlsh{MyConcept}, defined in -\inlsh{MyConcept.h} and \inlsh{MyConcept.cpp}. First in \inlsh{MyConcept.h}, -we need to include the NekFactory header - -\begin{lstlisting}[style=C++Style] -#include -\end{lstlisting} - -The following code should then be included just before the base class -declaration (in the same namespace as the class): - -\begin{lstlisting}[style=C++Style] -class MyConcept - -// Datatype for the MyConcept factory -typedef LibUtilities::NekFactory< std::string, MyConcept, - ParamType1, - ParamType2 > MyConceptFactory; -MyConceptFactory& GetMyConceptFactory(); -\end{lstlisting} - -The template parameters define the datatype of the key used to retrieve a -particular implementation (usually a string, enum or custom class such as -\inlsh{MyConceptKey}, the base class (in our case \inlsh{MyConcept} and a list -of zero or more parameters which are taken by the constructors of all -implementations of the type \inlsh{MyConcept} (in our case we have two). Note -that all implementations must take the same parameter list in their constructors. - -The normal definition of our base class then follows: - -\begin{lstlisting}[style=C++Style] -class MyConcept -{ - public: - MyConcept(ParamType1 p1, ParamType2 p2); - ... -}; -\end{lstlisting} - -We must also define a shared pointer for our base class for use later -\begin{lstlisting}[style=C++Style] -typedef boost::shared_ptr MyConceptShPtr; -\end{lstlisting} - -\subsubsection{Creating a specific implementation (derived class)} -A class is defined for each specific implementation of a concept. It is these -specific implementations which are instantiated by the factory. - -In our example we will have an implementations called \inlsh{MyConceptImpl1} -defined in \inlsh{MyConceptImpl1.h} and \inlsh{MyConceptImpl1.cpp}. In the -header file we include the base class header file - -\begin{lstlisting}[style=C++Style] -#include -\end{lstlisting} - -We then define the derived class as normal: - -\begin{lstlisting}[style=C++Style] -class MyConceptImpl1 : public MyConcept -{ -... -}; -\end{lstlisting} - -In order for the factory to work, it must know -\begin{itemize} -\item that {{{MyConceptImpl1}}} exists, and -\item how to create it. -\end{itemize} - -To allow the factory to create instances of our class we define a function in -our class: -\begin{lstlisting}[style=C++Style] -/// Creates an instance of this class -static MyConceptSharedPtr create( - ParamType1 p1, - ParamType2 p2) -{ - return MemoryManager::AllocateSharedPtr(p1, p2); -} -\end{lstlisting} -This function simply creates an instance of \inlsh{MyConceptImpl1} using the -supplied parameters. It must be \inlsh{static} because we are not operating on -an existing instance and it should return a base class shared pointer (rather -than a \inlsh{MyConceptImpl1} shared pointer), since the point of the factory -is that the calling code does not know about specific implementations. - -The last task is to register our implementation with the factory. This is done -using the \inlsh{RegisterCreatorFunction} member function of the factory. -However, we wish this to happen as early on as possible (so we can use the -factory straight away) and without needing to explicitly call the function for -every implementation at the beginning of our program (since this would again -defeat the point of a factory)! The solution is to use the function to -initialise a static variable: it will be executed prior to the start of the -\inlsh{main()} routine, and can be located within the very class it is -registering, satisfying our code decoupling requirements. - -In \inlsh{MyConceptImpl1.h} we define a static variable with the same datatype -as the key used in our factory (in our case \inlsh{std::string}) -\begin{lstlisting}[style=C++Style] -static std::string className; -\end{lstlisting} -The above variable can be \inlsh{private} since it is typically never actually -used within the code. We then initialise it in \inlsh{MyConceptImpl1.cpp} - -\begin{lstlisting}[style=C++Style] -string MyConceptImpl1::className - = GetMyConceptFactory().RegisterCreatorFunction( - "Impl1", - MyConceptImpl1::create, - "First implementation of my concept."); -\end{lstlisting} -The first parameter specifies the value of the key which should be used to -select this implementation. The second parameter is a function pointer to our -static function used to instantiate our class. The third parameter provides a -description which can be printed when listing the available MyConcept -implementations. - -\subsection{Instantiating classes} -To create instances of MyConcept implementations elsewhere in the code, we must -first include the ''base class'' header file -\begin{lstlisting}[style=C++Style] -#include -\end{lstlisting} -Note we do not include the header files for the specific MyConcept -implementations anywhere in the code (apart from \inlsh{MyConceptImpl1.cpp}). -If we modify the implementation, only the implementation itself requires -recompiling and the executable relinking. - -We create an instance by retrieving the \inlsh{MyConceptFactory} and call the -\inlsh{CreateInstance} member function of the factory: -\begin{lstlisting}[style=C++Style] -ParamType p1 = ...; -ParamType p2 = ...; -MyConceptShPtr p = GetMyConceptFactory().CreateInstance( "Impl1", p1, p2 ); -\end{lstlisting} - -Note that the class is used through the pointer \inlsh{p}, which is of type -\inlsh{MyConceptShPtr}, allowing the use of any of the public interface -functions in the base class (and therefore the specific implementations behind them) to be -called, but not directly any functions declared solely in a specific -implementation. - - -\section{NekArray} -An Array is a thin wrapper around native arrays. Arrays provide all the -functionality of native arrays, with the additional benefits of automatic use of -the Nektar++ memory pool, automatic memory allocation and deallocation, bounds -checking in debug mode, and easier to use multi-dimensional arrays. - -Arrays are templated to allow compile-time customization of its dimensionality -and data type. - -Parameters: -\begin{itemize} -\item \inltt{Dim} Must be a type with a static unsigned integer called -\inltt{Value} that specifies the array's dimensionality. For example -\begin{lstlisting}[style=C++Style] -struct TenD { - static unsigned int Value = 10; -}; -\end{lstlisting} -\item \inltt{DataType} The type of data to store in the array. -\end{itemize} - -It is often useful to create a class member Array that is shared with users of -the object without letting the users modify the array. To allow this behavior, -Array inherits from Array. The following -example shows what is possible using this approach: -\begin{lstlisting}[style=C++Style] - class Sample { - public: - Array& getData() const { return m_data; } - void getData(Array& out) const { out = m_data; } - - private: - Array m_data; - }; -\end{lstlisting} -In this example, each instance of Sample contains an array. The getData -method gives the user access to the array values, but does not allow -modification of those values. - -\subsection{Efficiency Considerations} - -Tracking memory so it is deallocated only when no more Arrays reference it does -introduce overhead when copying and assigning Arrays. In most cases this loss of -efficiency is not noticeable. There are some cases, however, where it can cause -a significant performance penalty (such as in tight inner loops). If needed, -Arrays allow access to the C-style array through the \texttt{Array::data} member -function. - - -\section{Threading} -\begin{notebox} -Threading is not currently included in the main code distribution. However, this -hybrid MPI/pthread functionality should be available within the next few months. -\end{notebox} - -We investigated adding threaded parallelism to the already MPI parallel -Nektar++. MPI parallelism has multiple processes that exchange data using -network or network-like communications. Each process retains its own memory -space and cannot affect any other process’s memory space except through the MPI -API. A thread, on the other hand, is a separately scheduled set of instructions -that still resides within a single process’s memory space. Therefore threads -can communicate with one another simply by directly altering the process’s -memory space. The project's goal was to attempt to utilise this difference to -speed up communications in parallel code. - -A design decision was made to add threading in an implementation independent -fashion. This was achieved by using the standard factory methods which -instantiate an abstract thread manager, which is then implemented by a concrete -class. For the reference implementation it was decided to use the Boost library -rather than native p-threads because Nektar++ already depends on the Boost -libraries, and Boost implements threading in terms of p-threads anyway. - -It was decided that the best approach would be to use a thread pool. This -resulted in the abstract classes ThreadManager and ThreadJob. ThreadManager is -a singleton class and provides an interface for the Nektar++ programmer to -start, control, and interact with threads. ThreadJob has only one method, the -virtual method run(). Subclasses of ThreadJob must override run() and provide a -suitable constructor. Instances of these subclasses are then handed to the -ThreadManager which dispatches them to the running threads. Many thousands of -ThreadJobs may be queued up with the ThreadManager and strategies may be -selected by which the running threads take jobs from the queue. Synchronisation -methods are also provided within the ThreadManager such as wait(), which waits -for the thread queue to become empty, and hold(), which pauses a thread that -calls it until all the threads have called hold(). The API was thoroughly -documented in Nektar++’s existing Javadoc style. - -Classes were then written for a concrete implementation of ThreadManager using -the Boost library. Boost has the advantage of being available on all Nektar++’s -supported platforms. It would not be difficult, however, to implement -ThreadManager using some other functionality, such as native p-threads. - -Two approaches to utilising these thread classes were then investigated. The -bottom-up approach identifies likely regions of the code for parallelisation, -usually loops around a simple and independent operation. The top-down approach -seeks to run as much of the code as is possible within a threaded environment. - -The former approach was investigated first due to its ease of implementation. -The operation chosen was the multiplication of a very large sparse block -diagonal matrix with a vector, where the matrix is stored as its many smaller -sub matrices. The original algorithm iterated over the sub matrices multiplying -each by the vector and accumulating the result. The new parallel algorithm -sends ThreadJobs consisting of batches of sub matrices to the thread pool. The -worker threads pick up the ThreadJobs and iterate over the sub matrices in the -job accumulating the result in a thread specific result vector. This latter -detail helps to avoid the problem of cache ping-pong which is where multiple -threads try to write to the same memory location, repeatedly invalidating one -another's caches. - -Clearly this approach will work best when the sub matrices are large and there -are many of them . However, even for test cases that would be considered large -it became clear that the code was still spending too much time in its scalar -regions. - -This led to the investigation of the top-down approach. Here the intent is to -run as much of the code as possible in multiple threads. This is a much more -complicated approach as it requires that the overall problem can be partitioned -suitably, that a mechanism be available to exchange data between the threads, -and that any code using shared resources be thread safe. As Nektar++ already -has MPI parallelism the first two requirements (data partitioning and exchange) -are already largely met. However since MPI parallelism is implemented by having -multiple independent processes that do not share memory space, global data in -the Nektar++ code, such as class static members or singleton instances, are now -vulnerable to change by all the threads running in a process. - -To Nektar++’s communication class, Comm, was added a new class, ThreadedComm. -This class encapsulates a Comm object and provides extra functionality without -altering the API of Comm (this is the Decorator pattern). To the rest of the -Nektar++ library this Comm object behaves the same whether it is a purely MPI -Comm object or a hybrid threading plus MPI object. The existing data -partitioning code can be used with very little modification and the parts of the -Nektar++ library that exchange data are unchanged. When a call is made to -exchange data with other workers ThreadedComm first has the master thread on -each process (i.e. the first thread) use the encapsulated Comm object (typically -an MPI object) to exchange the necessary data between the other processes, and -then exchanges data with the local threads using direct memory to memory copies. - -As an example: take the situation where there are two processes A and B, -possibly running on different computers, each with two threads 1 and 2. A -typical data exchange in Nektar++ uses the Comm method AllToAll(...) in which -each worker sends data to each of the other workers. Thread A1 will send data -from itself and thread A2 via the embedded MPI Comm to thread B1, receiving in -turn data from threads B1 and B2. Each thread will then pick up the data it -needs from the master thread on its process using direct memory to memory -copies. Compared to the situation where there are four MPI processes the number -of communications that actually pass over the network is reduced. Even MPI -implementations that are clever enough to recognise when processes are on the -same host must make a system call to transfer data between processes. - -The code was then audited for situations where threads would be attempting to -modify global data. Where possible such situations were refactored so that each -thread has a copy of the global data. Where the original design of Nektar++ did -not permit this access to global data was mediated through locking and -synchronisation. This latter approach is not favoured except for global data -that is used infrequently because locking reduces concurrency. - -The code has been tested and Imperial College cluster cx1 and has shown good -scaling. However it is not yet clear that the threading approach outperforms -the MPI approach; it is possible that the speedups gained through avoiding -network operations are lost due to locking and synchronisation issues. These -losses could be mitigated through more in-depth refactoring of Nektar++. \ No newline at end of file diff --git a/docs/developer-guide/data-structures-algorithms/connectivity.tex b/docs/developer-guide/data-structures-algorithms/connectivity.tex deleted file mode 100644 index fc7bf9ad755459a48db8fc45979ceb0106227d81..0000000000000000000000000000000000000000 --- a/docs/developer-guide/data-structures-algorithms/connectivity.tex +++ /dev/null @@ -1,289 +0,0 @@ -\section{Connectivity} -The typical elemental decomposition of the spectral/hp element method requires a -global assembly process when considering multi-elemental problems. This global -assembly will ensure some level of connectivity between adjacent elements sucht -that there is some form of continuity across element boundaries in the global -solution. In this section, we will merely focus on the classical Galerkin -method, where global continuity is typically imposed by making the approximation -$C^0$ continuous. - -\subsection{Connectivity in two dimensions} - -As explained in \cite{KaSh05}, the global assembly process involves the -transformation from local degrees of freedom to global degrees of freedom -(DOF). This transformation is typically done by a mapping array which relates -the numbering of the local (= elemental) DOF's to the numbering of the global -DOF's. To understand how this transformation is set up in Nektar++ one should -understand the following: -\begin{itemize} -\item \textbf{Starting point} - - The starting point is the initial numbering of the elemental expansion modes. - This corresponds to the order in which the different local expansion modes - are listed in the coefficient array \texttt{m\_coeffs} of the elemental - (local or standard) expansion. The specific order in which the different elemental - expansion modes appear is motivated by the compatability with the - sum-factorisation technique. This also implies that this ordering is fixed - and should not be changed by the user. Hence, this unchangeable initial local - numbering will serve as starting input for the connectivity. - -\item \textbf{end point} - - Obviously, we are working towards the numbering of the global DOF's. This - global ordering should: - \begin{itemize} - \item reflect the chosen continuity approach (standard $C^0$ Galerkin in our case) - \item (optionally) have some optimal ordering (where optimality can - be defined in different ways, e.g. minimal bandwith) - \end{itemize} -\end{itemize} - -All intermittent steps from starting point to end point can basically be chosen -freely but they should allow for an efficient construction of the global -numbering system starting from the elemental ordering of the local degrees of -freedom. Currently, Nektar++ provides a number of tools and routines in the -different sublibraries which can be employed to set up the mapping from local to -global DOF's. These tools will be listed below, but first the connectivity -strategies for both modal and nodal expansions will be explained. Note that all -explanations below are focussed on quadrilateral elements. However, the general -idea equally holds for triangles. - -\subsection{Connectivity strategies} - -For a better understanding of the described strategies, one should first -understand how Nektar++ deals with the basic geometric concepts such as edges -and (2D) elements. - -In Nektar++, a (2D) element is typically defined by a set of edges. In the input -.xml files, this should be done as (for a quadrilateral element): -\begin{lstlisting}[style=XMLStyle] - e0 e1 e2 e3 -\end{lstlisting} -where \inltt{e0} to \inltt{e3} correspond to the mesh ID's of the different -edges. -It is important to know that in Nektar++, the convention is that these edges -should be ordered counterclokwise (Note that this order also corresponds to the -order in which the edges are passed to the constructors of the 2D geometries). -In addition, note that we will refer to edge \inltt{e0} as the edge with local -(elemental) edge ID equal to 0, to edge \inltt{e1} as local edge with ID 1, to -edge \inltt{e2} as local edge with ID equal 2 and to edge \inltt{e3} as local -edge with ID 3. -Furthermore, one should note that the local coordinate system is orientated such -that the first coordinate axis is aligned with edge 0 and 2 (local edge ID), and -the second coordinate axis is aligned with edge 1 and 3. The direction of these -coordinate axis is such that it points in counterclockwise direction for edges 0 -and 1, and in clockwise direction for edge 2 and 3. - -Another important feature in the connectivity strategy is the concept of edge -orientation. For a better understanding, consider the input format of an edge as -used in the input .xml files which contain the information about the mesh. An -edge is defined as: -\begin{lstlisting}[style=XMLStyle] - v0 v1 -\end{lstlisting} -where \inltt{v0} and \inltt{v1} are the ID's of the two vertices that define -the edge (Note that these vertices are passed in the same order to the constructor -of the edge). Now, the orientation of an edge of a two-dimensional element (i.e. -quadrilateral or triangle) is defined as: -\begin{itemize} -\item Forward if the vertex with ID \inltt{v0} comes before the vertex with ID -\inltt{v1} when considering the vertices the vertices of the element in a -counterclockwise direction -\item Backward otherwise. -\end{itemize} - -This has the following implications: -\begin{itemize} -\item The common edge of two adjacent elements has always a forward orientation -for one of the elements it belongs to and a backward orientation for the other. -\item The orientation of an edge is only relevant when considering -two-dimensional elements. It is a property which is not only inherent to the edge itself, but - depends on the element it belongs to. (This also means that a segment does not - have an orientation) -\end{itemize} - -\subsubsection{Modal expansions} - -We will follow the basic principles of the connectivity strategy as explained in -Section 4.2.1.1 of \cite{KaSh05} (such as the hierarchic ordering of the edge -modes). However, we do not follow the strategy described to negate the odd modes -of an intersecting edge of two adjacent elements if the local coordinate systems -have an opposite direction. The explained strategy involves checking the -direction of the local coordinate systems of the neighbouring elements. However, -for a simpler automatic procedure to identify which edges need to have odd mode -negated, we would like to have an approach which can be applied to the elements -individually, without information being coupled between neighbouring elements. -This can be accomplished in the following way. Note that this approach is based -on the earlier observation that the intersecting edge of two elements always has -opposite orientation. Proper connectivity can now be guaranteed if: -\begin{itemize} -\item forward oriented edges always have a counterclockwise local coordinate -axis -\item backward oriented edges always have a clockwise local coordinate axis. -\end{itemize} - -Both the local coordinate axis along an intersecting edge will then point in the -same direction. Obviously, these conditions will not be fulfilled by default. -But in order to do so, the direction of the local coordinate axis should be -reversed in following situations: -\begin{lstlisting}[style=C++Style] - if ((LocalEdgeId == 0)||(LocalEdgeId == 1)) { - if( EdgeOrientation == Backward ) { - change orientation of local coordinate axis - } - } - - if ((LocalEdgeId == 2)||(LocalEdgeId == 3)) { - if( EdgeOrientation == Forward ) { - change orientation of local coordinate axis - } - } -\end{lstlisting} -This algorithm above is based on the earlier observation that the local -coordinate axis automatically point in counterclockwise direction for edges 0 -and 1 and in clockwise direction for the other edges. As explained in \cite{KaSh05} -the change in local coordinate axis can actually be done by reversing the sigqn -of the odd modes. This is implemented by means of an additional sign vector. - -\subsubsection{Nodal expansions} - -For the nodal expansions, we will use the connectivity strategy as explained in -Section 4.2.1.1 of \cite{KaSh05}. However, we will clarify this strategy from a -Nektar++ point of view. As pointed out in \cite{KaSh05}, the nodal edge modes -can be identified with the physical location of the nodal points. In order to ensure -proper connectivity between elements the egde modes with the same nodal location -should be matched. This will be accomplished if both the sets of local edge -modes along the intersection edge of two elements are numbered in the same -direction. And as the intersecting edge of two elements always has opposite -direction, this can be guaranteed if: -\begin{itemize} -\item the local numbering of the edge modes is counterclockwise for forward - oriented edges -\item the local numbering of the edge modes is clockwise for backward oriented -edges. -\end{itemize} - -This will ensure that the numbering of the global DOF's on an edge is in the -same direction as the tow subsets of local DOF's on the intersecting edge. - -\subsection{Implementation} -The main entity for the transformation from local DOF's to global DOF's (in 2D) -is the LocalToGlobalMap2D class. This class basically is the abstraction of the -mapping array map[e][i] as introduced in section 4.2.1 of \cite{KaSh05}. This -mapping array is contained in the class' main data member, -LocalToGlobalMap2D::m\_locToContMap. Let us recall what this mapping array -\begin{lstlisting} - map[e][i] = globalID -\end{lstlisting} -actually represents: -\begin{itemize} -\item e corresponds to the e th element -\item i corresponds to the i th expansion -mode within element e. This index i in this map array corresponds to the index of - the coefficient array m\_coeffs. -\item globalID represents the ID of the corresponding global degree of freedom. -\end{itemize} - -However, rather than this two-dimensional structure of the mapping array,\\ -\texttt{LocalToGlobalMap2D::m\_locToContMap} stores the mapping array as a -one-dimensional array which is the concatenation of the different elemental -mapping arrays map[e]. This mapping array can then be used to assemble the -global system out of the local entries, or to do any other transformation -between local and global degrees of freedom (Note that other mapping arrays such -as the boundary mapping bmap[e][i] or the sign vector sign[e][i] which might be -required are also contained in the LocalToGlobalMap2D class). - -For a better appreciation of the implementation of the connectivity in Nektar++, -it might be useful to consider how this mapping array is actually being -constructed (or filled). To understand this, first consider the following: -\begin{itemize} -\item The initial local elemental numbering (referred to as starting point in -the beginning of this document) is not suitable to set up the mapping. In no way - does it correspond to the local numbering required for a proper connectivity as - elaborated in Section 4.2.1 of \cite{KaSh05}. Hence, this initial ordering - asuch cannot be used to implement the connectivity strategies explained above. As a - result, additional routines (see here), which account for some kind of - reordering of the local numbering will be required in order to construct the - mapping array properly. -\item Although the different edge modes can be thought of as to include both -the vertex mode, we will make a clear distinction between them in the - implementation. In other words, the vertex modes will be treated separately - from the other modes on an edge as they are conceptually different from an - connectivity point of view. We will refer to these remaining modes as interior - edge modes. -\end{itemize} - -The fill-in of the mapping array can than be summarised by the following part of -(simplified) code: -\begin{lstlisting}[style=C++Style] - for(e = 0; e < Number_Of_2D_Elements; e++) { - for(i = 0; i < Number_Of_Vertices_Of_Element_e; i++) { - offsetValue = ... - map[e][GetVertexMap(i)] = offsetValue; - } - - for(i = 0; i < Number_Of_Edges_Of_Element_e; i++) { - localNumbering = GetEdgeInteriorMap(i); offsetValue = ... - for(j = 0; j < Number_Of_InteriorEdgeModes_Of_Edge_i; j++) { - map[e][localNumbering(j)] = offsetValue + j; - } - } - } -\end{lstlisting} - -In this document, we will not cover how the calculate the offsetValue which: -\begin{itemize} -\item for the vertices, corresponds to the global ID of the specific vertex -\item for the edges, corresponds to the starting value of the global numbering on the - concerned edge -\end{itemize} - -However, we would like to focus on the routines GetVertexMap() and -GetEdgeInteriorMap(), 2 functions which somehow reorder the initial local -numbering in order to be compatible with the connectivity strategy. - -\subsubsection{GetVertexMap()} - -Given the local vertex id (i.e. 0,1,2 or 3 for a quadrilateral element), it -returns the position of the corresponding vertex mode in the elemental -coefficient array StdRegions::StdExpansion::m\_coeffs. By using this function as -in the code above, it is ensured that the global ID of the vertex is entered in -the correct position in the mapping array. - -\subsubsection{GetEdgeInteriorMap()} - -Like the previous routine, this function is also defined for all two dimensional -expanions in the StdRegions::StdExpansion class tree. This is actually the most -important function to ensure proper connectivity between neigbouring elements. -It is a function which reorders the numbering of local DOF's according to the -connectivity strategy. As input this function takes: -\begin{itemize} -\item the local edge ID of the edge to be considered -\item the orientation of this edge. -\end{itemize} - -As output, it returns the local ordering of the requested (interior) edge modes. -This is contained - in an array of size N-2, where N is the number of expansion modes in the - relevant direction. The entries in this array represent the position of the - corresponding interior edge mode in the elemental coefficient array - StdRegions::StdExpansion::m\_coeffs. - -Rather than the actual values of the local numbering, it is the ordering of -local edge modes which is of importance for the connectivity. That is why it is -important how the different interior edge modes are sorted in the returned -array. This should be such that for both the elements which are connected by the -intersecting edge, the local (interior) edge modes are iterated in the same -order. This will guarantee a correct global numbering scheme when employing the -algorithm shown above. This proper connectivity can be ensured if the function -GetEdgeInteriorMap: - -\begin{itemize} -\item for modal expansions: returns the edge interior modes in hierarchical -order (i.e. the lowest polynomial order mode first), -\item for nodal expansions: returns the edge interior modes in: - \begin{itemize} - \item counterclockwise order for forward oriented edges - \item clockwise order for backward oriented edges. - \end{itemize} -\end{itemize} diff --git a/docs/developer-guide/data-structures-algorithms/data-structures-algorithms.tex b/docs/developer-guide/data-structures-algorithms/data-structures-algorithms.tex deleted file mode 100644 index ea1e4e22a640cb72d919e240d077896e0c16b1ed..0000000000000000000000000000000000000000 --- a/docs/developer-guide/data-structures-algorithms/data-structures-algorithms.tex +++ /dev/null @@ -1,8 +0,0 @@ -\chapter{Data Structures and Algorithms} -\label{ch:data} - -\input{connectivity} - -\input{time-integration} - -\input{preconditioners} \ No newline at end of file diff --git a/docs/developer-guide/data-structures-algorithms/preconditioners.tex b/docs/developer-guide/data-structures-algorithms/preconditioners.tex deleted file mode 100644 index 7834c599657ea23c8ac84836524bef8d860cd87a..0000000000000000000000000000000000000000 --- a/docs/developer-guide/data-structures-algorithms/preconditioners.tex +++ /dev/null @@ -1,385 +0,0 @@ -\section{Preconditioners} -\label{sec:precon} - -Most of the solvers in \nekpp, including the incompressible Navier-Stokes -equations, rely on the solution of a Helmholtz equation, -% -\begin{equation} - \nabla^{2}u(\mathbf{x})+\lambda u(\mathbf{x})=f(\mathbf{x}), - \label{eq:precon:helm} -\end{equation} -% -an elliptic boundary value problem, at every time-step, where $u$ is defined on -a domain $\Omega$ of $N_{\mathrm{el}}$ non-overlapping elements. In this -section, we outline the preconditioners which are implemented in \nekpp. Whilst -some of the preconditioners are generic, many are especially designed for the -\emph{modified} basis only. - -\subsection{Mathematical formulation} - -The standard spectral/$hp$ approach to discretise \eqref{eq:precon:helm} starts -with an expansion in terms of the elemental modes: -% -\begin{equation} - u^{\delta}(\mathbf{x})=\sum_{n=0}^{N_{\mathrm{dof}}-1}\hat{u}_n - \Phi_n(\mathbf{x})=\sum_{e=1}^{{N_{\mathrm{el}}}} - \sum_{n=0}^{N^{e}_m-1}\hat{u}_n^e\phi_n^e(\mathbf{x}) - \label{eq:precon:disc} -\end{equation} -% -where $N_{\mathrm{el}}$ is the number of elements, $N^{e}_m$ is the number of -local expansion modes within the element $\Omega^e$, $\phi_n^e(\mathbf{x})$ is -the $n^{\mathrm{th}}$ local expansion mode within the element $\Omega^e$, -$\hat{u}_n^e$ is the $n^{\mathrm{th}}$ local expansion coefficient within the -element $\Omega^e$. Approximating our solution by~\eqref{eq:precon:disc}, we -adopt a Galerkin discretisation of equation~\eqref{eq:precon:helm} where for an -appropriate test space $V^\delta$ we find an approximate solution -$\mathbf{u}^{\delta} \in V^{\delta}$ such that -% -\[ -\mathcal L \left({v, u}\right) = \int_{\Omega}\nabla v^{\delta} \cdot \nabla -u^{\delta} + \lambda v^{\delta} u^{\delta} d \mathbf{x} = \int_{\Omega} -v^{\delta} f d\mathbf{x} \quad \forall v^{\delta} \in V^{\delta} -\] -% -This can be formulated in matrix terms as -% -\[ -\mathbf{H}\hat{\mathbf{u}} = \mathbf{f} -\] -% -where $\mathbf{H}$ represents the Helmholtz matrix, $\hat{\mathbf{u}}$ are the -unknown global coefficients and $\mathbf{f}$ the inner product the expansion -basis with the forcing function. - -\subsubsection{$C^0$ formulation} - -We first consider the $C^0$ (i.e. continuous Galerkin) formulation. The -spectral/$hp$ expansion basis is obtained by considering interior modes, which -have support in the interior of the element, separately from boundary modes -which are non-zero on the boundary of the element. We align the boundary modes -across the interface of the elements to obtain a continuous global solution. The -boundary modes can be further decomposed into vertex, edge and face modes, -defined as follows: - -\begin{itemize} - \item vertex modes have support on a single vertex and the three adjacent - edges and faces as well as the interior of the element; - \item edge modes have support on a single edge and two adjacent faces as well - as the interior of the element; - \item face modes have support on a single face and the interior of the - element. -\end{itemize} - -When the discretisation is continuous, this strong coupling between vertices, -edges and faces leads to a matrix of high condition number $\kappa$. Our aim is -to reduce this condition number by applying specialised -preconditioners. Utilising the above mentioned decomposition, we can write the -matrix equation as: -% -\[ -\left[\begin{array}{cc} - \mathbf{H}_{bb} & \mathbf{H}_{bi}\\ - \mathbf{H}_{ib} & \mathbf{H}_{ii} - \end{array}\right] -\left[ \begin{array}{c} -\hat{\mathbf{u}}_{b}\\ -\hat{\mathbf{u}}_{i}\\ -\end{array}\right] = -\left[ \begin{array}{c} -\hat{\mathbf{f}}_{b}\\ -\hat{\mathbf{f}}_{i}\\ -\end{array}\right] -\] -% -where the subscripts $b$ and $i$ denote the boundary and interior degrees of -freedom respectively. This system then can be statically condensed allowing us -to solve for the boundary and interior degrees of freedom in a decoupled -manor. The statically condensed matrix is given by -% -\[ -\left[\begin{array}{cc} - \mathbf{H}_{bb}-\mathbf{H}_{bi} \mathbf{H}_{ii}^{-1} \mathbf{H}_{ib} & 0\\ - \mathbf{H}_{ib} & \mathbf{H}_{ii} - \end{array}\right] -\left[ \begin{array}{c} -\hat{\mathbf{u}}_{b}\\ -\hat{\mathbf{u}}_{i}\\ -\end{array}\right] = -\left[ \begin{array}{c} -\hat{\mathbf{f}}_{b}-\mathbf{H}_{bi} \mathbf{H}_{ii}^{-1}\hat{\mathbf{f}}_{i}\\ -\hat{\mathbf{f}}_{i}\\ -\end{array}\right] -\] -% -This is highly advantageous since by definition of our interior expansion this -vanishes on the boundary, and so $\mathbf{H}_{ii}$ is block diagonal and thus -can be easily inverted. The above sub-structuring has reduced our problem to -solving the boundary problem: -% -\[ -\mathbf{S}_{1}\hat{\mathbf{u}} = \hat{\mathbf{f}}_{1} -\] -% -where -$\mathbf{S_{1}}=\mathbf{H}_{bb}-\mathbf{H}_{bi} \mathbf{H}_{ii}^{-1} -\mathbf{H}_{ib}$ -and -$\hat{\mathbf{f}}_{1}=\hat{\mathbf{f}}_{b}-\mathbf{H}_{bi} -\mathbf{H}_{ii}^{-1}\hat{\mathbf{f}}_{i}$. -Although this new system typically has better convergence properties (i.e lower -$\kappa$), the system is still ill-conditioned, leading to a convergence rate of -the conjugate gradient (CG) routine that is prohibitively slow. For this reason -we need to precondition $\mathbf{S}_1$. To do this we solve an equivalent -system of the form: -% -\[ -\mathbf{M}^{-1}\left(\mathbf{S}_{1} \hat{\mathbf{u}} - \hat{\mathbf{f}}_{1} \right) = 0 -\] -% -where the preconditioning matrix $\mathbf{M}$ is such that -$\kappa\left(\mathbf{M}^{-1} \mathbf{S}_{1}\right)$ is less than -$\kappa\left(\mathbf{S}_{1}\right)$ and speeds up the convergence rate. Within -the conjugate gradient routine the same preconditioner $\mathbf{M}$ is applied -to the residual vector $\hat{\mathbf{r}}_{k+1}$ of the CG routine every -iteration: -% -\[ -\hat{\mathbf{z}}_{k+1}=\mathbf{M}^{-1}\hat{\mathbf{r}}_{k+1}. -\] -% - -\subsubsection{HDG formulation} - -When utilising a hybridizable discontinuous Galerkin formulation, we perform a -static condensation approach but in a discontinuous framework, which for brevity -we omit here. However, we still obtain a matrix equation of the form -% -\[ -\mathbf{\Lambda}\hat{\mathbf{u}} = \hat{\mathbf{f}}. -\] -% -where $\mathbf{\Lambda}$ represents an operator which projects the solution of -each face back onto the three-dimensional element or edge onto the -two-dimensional element. In this setting then, $\hat{\mathbf{f}}$ consists of -degrees of freedom for each egde (in 2D) or face (in 3D). The overall system -does not, therefore, results in a weaker coupling between degrees of freedom, -but at the expense of a larger matrix system. - -\subsection{Preconditioners} - -Within the \nekpp framework a number of preconditioners are available to speed -up the convergence rate of the conjugate gradient routine. The table below -summarises each method, the dimensions of elements which are supported, and also -the discretisation type support which can either be continuous (CG) or -discontinuous (hybridizable DG). - -\begin{center} - \begin{tabular}{lll} - \toprule - \textbf{Name} & \textbf{Dimensions} & \textbf{Discretisations} \\ - \midrule - \inltt{Null} & All & All \\ - \inltt{Diagonal} & All & All \\ - \inltt{FullLinearSpace} & 2/3D & CG \\ - \inltt{LowEnergyBlock} & 3D & CG \\ - \inltt{Block} & 2/3D & All \\ - \midrule - \inltt{FullLinearSpaceWithDiagonal} & All & CG \\ - \inltt{FullLinearSpaceWithLowEnergyBlock} & 2/3D & CG \\ - \inltt{FullLinearSpaceWithBlock} & 2/3D & CG \\ - \bottomrule - \end{tabular} -\end{center} - -The default is the \inltt{Diagonal} preconditioner. The above preconditioners -are specified through the \inltt{Preconditioner} option of the -\inltt{SOLVERINFO} section in the session file. For example, to enable -\inltt{FullLinearSpace} one can use: - -\begin{lstlisting}[style=XMLStyle] - -\end{lstlisting} - -Alternatively one can have more control over different preconditioners for each -solution field by using the \inltt{GlobalSysSoln} section. For more details, -consult the user guide. The following sections specify the details for each -method. - -\subsubsection{Diagonal} - -Diagonal (or Jacobi) preconditioning is amongst the simplest preconditioning -strategies. In this scheme one takes the global matrix $\mathbf{H} = (h_{ij})$ -and computes the diagonal terms $h_{ii}$. The preconditioner is then formed as a -diagonal matrix $\mathbf{M}^{-1} = (h_{ii}^{-1})$. - -\subsubsection{Linear space} - -The linear space (or coarse space) of the matrix system is that containing -degrees of freedom corresponding only to the vertex modes in the high-order -system. Preconditioning of this space is achieved by forming the matrix -corresponding to the coarse space and inverting it, so that -% -\[ -\mathbf{M}^{-1} = (\mathbf{S}^{-1}_{1})_{vv} -\] -% -Since the mesh associated with higher order methods is relatively coarse -compared with traditional finite element discretisations, the linear space can -usually be directly inverted without memory issues. However such a methodology -can be prohibitive on large parallel systems, due to a bottleneck in -communication. - -In \nekpp the inversion of the linear space present is handled using the -$XX^{T}$ library. $XX^{T}$ is a parallel direct solver for problems of the form -$\mathbf{A}\hat{\mathbf{x}} = \hat{\mathbf{b}}$ based around a sparse -factorisation of the inverse of $\mathbf{A}$. To precondition utilising this -methodology the linear sub-space is gathered from the expansion and the -preconditioned residual within the CG routine is determined by solving -% -\[ -(\mathbf{S}_{1})_{vv}\hat{\mathbf{z}}=\hat{\mathbf{r}} -\] -% -The preconditioned residual $\hat{\mathbf{z}}$ is then scattered back to the -respective location in the global degrees of freedom. - -\subsubsection{Block} - -Block preconditioning of the $C^0$ continuous system is defined by the -following: -% -\[ -\mathbf{M}^{-1}=\left[ \begin{array}{ccc} -(\mathbf{S}^{-1}_{1})_{vv} & 0 & 0 \\ -0 & (\mathbf{S}^{-1}_{1})_{eb} & 0\\ -0 & 0 & (\mathbf{S}^{-1}_{1})_{ef}\\ - \end{array} \right] -\] -% -where $\mathrm{diag}[(\mathbf{S}_{1})_{vv}]$ is the diagonal of the vertex -modes, $(\mathbf{S}_{1})_{eb}$ and $(\mathbf{S}_{1})_{fb}$ are block diagonal -matrices corresponding to coupling of an edge (or face) with itself i.e ignoring -the coupling to other edges and faces. This preconditioner is best suited for -two dimensional problems. - -In the HDG system, we take the block corresponding to each face and invert -it. Each of these inverse blocks then forms one of the diagonal components of -the block matrix $\mathbf{M}^{-1}$. - -\subsection{Low energy} - -Low energy basis preconditioning follows the methodology proposed by Sherwin \& -Casarin. In this method a new basis is numerically constructed from the original -basis which allows the Schur complement matrix to be preconditioned using a -block preconditioner. The method is outlined briefly in the following. - -Elementally the local approximation $\mathbf{u}^{\delta}$ can be expressed as -different expansions lying in the same discrete space $V^{\delta}$ -% -\[ -\mathbf{u}^{\delta}(\mathbf{x})=\sum_{i}^{\dim(V^{\delta})}\hat{u}_{1i}\phi_{1i}(x) -= \sum_{i}^{\dim(V^{\delta})}\hat{u}_{2i}\phi_{2j}(x) -\] -% -Since both expansions lie in the same space it's possible to express one basis -in terms of the other via a transformation, i.e. -% -\[ -\phi_{2}=\mathbf{C}\phi_{1} \implies \hat{\mathbf{u}}_{1}=C^{T}\hat{\mathbf{u}}_{2} -\] -% -Applying this to the Helmholtz operator it is possible to show that, -% -\[ -\mathbf{H}_{2}=\mathbf{C}\mathbf{H}_{1}\mathbf{C}^{T} -\] -% -For sub-structured matrices ($\mathbf{S}$) the transformation matrix -($\mathbf{C}$) becomes: -% -\[ -\mathbf{C}=\left[ \begin{array}{cc} -\mathbf{R} & 0\\ -0 & \mathbf{I} - \end{array} \right] -\] -% -Hence the transformation in terms of the Schur complement matrices is: -% -\[ -\mathbf{S}_{2}=\mathbf{R}\mathbf{S}_{1}\mathbf{R}^{T} -\] -% -Typically the choice of expansion basis $\phi_{1}$ can lead to a Helmholtz -matrix that has undesirable properties i.e poor condition number. By choosing a -suitable transformation matrix $\mathbf{C}$ it is possible to construct a new -basis, numerically, that is amenable to block diagonal preconditioning. -% -\[ -\mathbf{S}_{1}=\left[ \begin{array}{ccc} -\mathbf{S}_{vv} & \mathbf{S}_{ve} & \mathbf{S}_{vf}\\ -\mathbf{S}^{T}_{ve}& \mathbf{S}_{ee} & \mathbf{S}_{ef} \\ -\mathbf{S}^{T}_{vf} & \mathbf{S}^{T}_{ef} & \mathbf{S}_{ff} \end{array} \right] =\left[ \begin{array}{cc} -\mathbf{S}_{vv} & \mathbf{S}_{v,ef} \\ -\mathbf{S}^{T}_{v,ef} & \mathbf{S}_{ef,ef} \end{array} \right] -\] -% -Applying the transformation -$\mathbf{S}_{2}=\mathbf{R} \mathbf{S}_{1} \mathbf{R}^{T}$ leads to the following -matrix -% -\[ -\mathbf{S}_{2}=\left[ \begin{array}{cc} -\mathbf{S}_{vv}+\mathbf{R}_{v}\mathbf{S}^{T}_{v,ef}+\mathbf{S}_{v,ef}\mathbf{R}^{T}_{v}+\mathbf{R}_{v}\mathbf{S}_{ef,ef}\mathbf{R}^{T}_{v} & [\mathbf{S}_{v,ef}+\mathbf{R}_{v}\mathbf{S}_{ef,ef}]\mathbf{A}^{T} \\ -\mathbf{A}[\mathbf{S}^{T}_{v,ef}+\mathbf{S}_{ef,ef}\mathbf{R}^{T}_{v}] & \mathbf{A}\mathbf{S}_{ef,ef}\mathbf{A}^{T} \end{array} \right] -\] -% -where $\mathbf{A}\mathbf{S}_{ef,ef}\mathbf{A}^{T}$ is given by -% -\[ -\mathbf{A}\mathbf{S}_{ef,ef}\mathbf{A}^{T}=\left[ \begin{array}{cc} -\mathbf{S}_{ee}+\mathbf{R}_{ef}\mathbf{S}^{T}_{ef}+\mathbf{S}_{ef}\mathbf{R}^{T}_{ef}+\mathbf{R}_{ef}\mathbf{S}_{ff}\mathbf{R}^{T}_{ef} & \mathbf{S}_{ef}+\mathbf{R}_{ef}\mathbf{S}_{ff}\\ -\mathbf{S}^{T}_{ef}+\mathbf{S}_{ff}\mathbf{R}^{T}_{ef} & \mathbf{S}_{ff} - \end{array} \right] -\] -% -To orthogonalise the vertex-edge and vertex-face modes, it can be seen from the -above that -% -\[ -\mathbf{R}^{T}_{ef}=-\mathbf{S}^{-1}_{ff}\mathbf{S}^{T}_{ef} -\] -% -and for the edge-face modes: -% -\[ -\mathbf{R}^{T}_{v}=-\mathbf{S}^{-1}_{ef,ef}\mathbf{S}^{T}_{v,ef} -\] -% -Here it is important to consider the form of the expansion basis since the -presence of $\mathbf{S}^{-1}_{ff}$ will lead to a new basis which has support on -all other faces; this is problematic when creating a $C^{0}$ continuous global -basis. To circumvent this problem when forming the new basis, the decoupling is -only performed between a specific edge and the two adjacent faces in a symmetric -standard region. Since the decoupling is performed in a rotationally symmetric -standard region the basis does not take into account the Jacobian mapping -between the local element and global coordinates, hence the final expansion will -not be completely orthogonal. - -The low energy basis creates a Schur complement matrix that although it is not -completely orthogonal can be spectrally approximated by its block diagonal -contribution. The final form of the preconditioner is: -% -\[ -\mathbf{M}^{-1}=\left[ \begin{array}{ccc} -\mathrm{diag}[(\mathbf{S}_{2})_{vv}] & 0 & 0 \\ -0 & (\mathbf{S}_{2})_{eb} & 0\\ -0 & 0 & (\mathbf{S}_{2})_{fb}\\ - \end{array} \right]^{-1} -\] -% -where $\mathrm{diag}[(\mathbf{S}_{2})_{vv}]$ is the diagonal of the vertex -modes, $(\mathbf{S}_{2})_{eb}$ and $(\mathbf{S}_{2})_{fb}$ are block diagonal -matrices corresponding to coupling of an edge (or face) with itself i.e ignoring -the coupling to other edges and faces. diff --git a/docs/developer-guide/data-structures-algorithms/time-integration.tex b/docs/developer-guide/data-structures-algorithms/time-integration.tex deleted file mode 100644 index fc653ec7ca4664f8e96390c8dc04c1951cc531ee..0000000000000000000000000000000000000000 --- a/docs/developer-guide/data-structures-algorithms/time-integration.tex +++ /dev/null @@ -1,908 +0,0 @@ -\section{Time integration} -This page discusses the implementation of time-integration in Nektar++. - -\subsection{General Linear Methods} -General linear methods (GLMs) can be considered as the generalization of a broad -range of different numerical methods for ordinary differential equations. They -were introduced by Butcher and they provide a unified formulation for -traditional methods such as the Runge-Kutta methods and the linear multi-step -methods. From an implementation point of view, this means that all these -numerical methods can be abstracted in a similar way. As this allows a high -level of generality, it is chosen in Nektar++ to cast all time integration -schemes in the framework of general linear methods. - -For background information about general linear methods, please consult -\cite{Bu06} - -\subsection{Introduction} -The standard initial value problem can written in the form -\begin{align*} -\frac{d\boldsymbol{y}}{dt} = \boldsymbol{f}(t,\boldsymbol{y}),\quad -\boldsymbol{y}(t_0)=\boldsymbol{y}_0 -\end{align*} -where $\boldsymbol{y}$ is a vector containing the variable (or an -array of array contianing the variables). - -In the formulation of general linear methods, it is more convenient to consider -the ODE in autonomous form, i.e. -\begin{align*} -\frac{d\boldsymbol{\hat{y}}}{dt}=\boldsymbol{\hat{f}}(\boldsymbol{\hat{y}}),\quad -\boldsymbol{\hat{y}}(t_0)= \boldsymbol{\hat{y}}_0. -\end{align*} - -\subsection{Formulation} -Suppose the governing differential equation is given in autonomous form, the -$n^{th}$ step of the GLM comprising -\begin{itemize} -\item $r$ steps (as in a multi-step method) -\item $s$ stages (as in a Runge-Kutta method) -\end{itemize} -is formulated as: -\begin{align*} -\boldsymbol{Y}_i &= \Delta -t\sum_{j=0}^{s-1}a_{ij}\boldsymbol{F}_j+\sum_{j=0}^{r-1}u_{ij}\boldsymbol{\hat{y}}_{j}^{[n-1]}, -\qquad i=0,1,\ldots,s-1 \\ -\boldsymbol{\hat{y}}_{i}^{[n]}&=\Delta -t\sum_{j=0}^{s-1}b_{ij}\boldsymbol{F}_j+\sum_{j=0}^{r-1}v_{ij} -\boldsymbol{\hat{y}}_{j}^{[n-1]}, \qquad i=0,1,\ldots,r-1 -\end{align*} -where $\boldsymbol{Y}_i$ are referred to as the stage values and -$\boldsymbol{F}_j$ as the stage derivatives. Both quantities are -related by the differential equation: -\begin{align*} -\boldsymbol{F}_i = \boldsymbol{\hat{f}}(\boldsymbol{Y}_i). -\end{align*} - -The matrices $A=[a_{ij}]$, $U=[u_{ij}]$, -$B=[b_{ij}]$, $V=[v_{ij}]$ are characteristic of a -specific method. Each scheme can then be uniquely defined by a partioned -$(s+r)\times(s+r)$ matrix -\begin{align*} -\left[ -\begin{array}{cc} - A & U\\ - B & V \end{array}\right] -\end{align*} - - -\subsection{Matrix notation} -Adopting the notation: -\begin{align*} -\boldsymbol{\hat{y}}^{[n-1]}= \left[\begin{array}{c} -\boldsymbol{\hat{y}}^{[n-1]}_0\\ -\boldsymbol{\hat{y}}^{[n-1]}_1\\ -\vdots\\ -\boldsymbol{\hat{y}}^{[n-1]}_{r-1} -\end{array}\right],\quad \boldsymbol{\hat{y}}^{[n]}= \left[\begin{array}{c} -\boldsymbol{\hat{y}}^{[n]}_0\\ -\boldsymbol{\hat{y}}^{[n]}_1\\ -\vdots\\ -\boldsymbol{\hat{y}}^{[n]}_{r-1} -\end{array}\right],\quad \boldsymbol{Y}= \left[\begin{array}{c} -\boldsymbol{Y}_0\\ -\boldsymbol{Y}_1\\ -\vdots\\ -\boldsymbol{Y}_{s-1} -\end{array}\right],\quad \boldsymbol{F}= \left[\begin{array}{c} -\boldsymbol{F}_0\\ -\boldsymbol{F}_1\\ -\vdots\\ -\boldsymbol{F}_{s-1} -\end{array}\right]\quad -\end{align*} -the general linear method can be written more compactly in the following form: -\begin{align*} -\left[ \begin{array}{c} \boldsymbol{Y}\\ -\boldsymbol{\hat{y}}^{[n]} -\end{array}\right] = \left[ \begin{array}{cc} A\otimes I_N & U\otimes I_N \\ -B\otimes I_N & V\otimes I_N \end{array}\right] \left[ \begin{array}{c} \Delta -t\boldsymbol{F}\\ -\boldsymbol{\hat{y}}^{[n-1]} -\end{array}\right] -\end{align*} -where $I_N$ is the identity matrix of dimension $N\times N$. - - -\subsection{General Linear Methods in Nektar++} -Although the GLM is essentially presented for ODE's in its autonomous form, in -Nektar++ it will be used to solve ODE's formulated in non-autonomous form. -Given the ODE, -\begin{align*} -\frac{d\boldsymbol{y}}{dt}=\boldsymbol{f}(t,\boldsymbol{y}),\quad -\boldsymbol{y}(t_0)=\boldsymbol{y}_0 -\end{align*} -a single step of GLM can then be evaluated in the following way: -\begin{itemize} -\item \textbf{input} - -$\boldsymbol{y}^{[n-1]}$, \emph{i.e.} the $r$ - subvectors comprising $\boldsymbol{y}^{[n-1]}_i$ - - $t^{[n-1]}$, \emph{i.e.} the equivalent of - $\boldsymbol{y}^{[n-1]}$ for the time variable $t$. - -\item \textbf{step 1}: The stage values $\boldsymbol{Y}_i$, -$\boldsymbol{T}_i$ and the stage derivatives -$\boldsymbol{F}_i$ are calculated through the relations: -\begin{enumerate} -\item $\boldsymbol{Y}_i = \Delta - t\sum_{j=0}^{s-1}a_{ij}\boldsymbol{F}_j+\sum_{j=0}^{r-1}u_{ij}\boldsymbol{y}_{j}^{[n-1]}, - \qquad i=0,1,\ldots,s-1$ -\item $T_i\ =\ \Delta - t\sum_{j=0}^{s-1}a_{ij}+\sum_{j=0}^{r-1}u_{ij}t_{j}^{[n-1]}, \qquad - i=0,1,\ldots,s-1$ -\item $\boldsymbol{F}_i\ =\ - f(T_i,\boldsymbol{Y}_i), \qquad i=0,1,\ldots,s-1$ -\end{enumerate} - -\item \textbf{step 2}: The approximation at the new time level -$\boldsymbol{y}^{[n]}$ is calculated as a linear combination of the -stage derivatives $\boldsymbol{F}_i$ and the input vector -$\boldsymbol{y}^{[n-1]}$. In addition, the time vector -$t^{[n]}$ is also updated - -\begin{enumerate} -\item $\boldsymbol{y}_{i}^{[n]} = \Delta - t\sum_{j=0}^{s-1}b_{ij}\boldsymbol{F}_j+\sum_{j=0}^{r-1}v_{ij}\boldsymbol{y}_{j}^{[n-1]}, - \qquad i=0,1,\ldots,r-1$ -\item $t_{i}^{[n]}\ =\ \Delta - t\sum_{j=0}^{s-1}b_{ij}+\sum_{j=0}^{r-1}v_{ij}t_{j}^{[n-1]}, \qquad - i=0,1,\ldots,r-1$ -\end{enumerate} - -\item \textbf{output} -\begin{enumerate} -\item $\boldsymbol{y}^{[n]}$, i.e. the $r$ subvectors - comprising $\boldsymbol{y}^{[n]}_i$. - $\boldsymbol{y}^{[n]}_0$ corresponds to the actual approximation - at the new time level. -\item $t^{[n]}$ where $t^{[n]}_0$ is equal to the new time - level $t+\Delta t$. -\end{enumerate} -\end{itemize} - -For a detailed describtion of the formulation and a deeper insight of the -numerical method see \cite{VoEsBoChKi11}. - - -\subsection{Types of time Integration Schemes} -Nektar++ contains various classes and methods which implement the concept of -GLMs. This toolbox is capable of numerically solving the generalised ODE using a -broad range of different time-stepping methods. We distinguish the following -types of general linear methods: -\begin{itemize} -\item \textbf{Formally Explicit Methods}: These types of methods are -considered explicit from an ODE point of view. They are characterised by a lower - triangular coefficient matrix $A$, ''i.e.'' $a_{ij} = 0$ - for $j\geq i$. To avoid confusion, we make a further distinction: - \begin{itemize} - \item \textbf{direct explicit method}: Only forward operators are required. - \item \textbf{indirect explicit method}: The inverse operator is required. - \end{itemize} - \item \textbf{Diagonally Implicit Methods}: Compared to explicit methods, - the coefficient matrix $A$ has now non-zero entries on the diagonal. - This means that each stage value depend on the stage derivative at the same - stage, requiring an implicit step. However, the calculation of the different - stage values is still uncoupled. Best known are the DIRK schemes. - \item \textbf{IMEX schemes}: These schemes support the concept of being able - to split right hand forcing term into an explicit and implicit component. This is - useful in advection diffusion type problems where the advection is handled - explicity and the diffusion is handled implicit. - \item \textbf{Fully Implicit Methods Methods}: The coefficient matrix has a - non-zero upper triangular part. The calculation of all stages values is fully coupled. -\end{itemize} - -The aim in Nektar++ is to fully support the first three types of GLMs. -Fully implicit methods are currently not implemented. - -\subsection{Usage} -The goal of abstracting the concept of general linear methods is to provide -users with a single interface for time-stepping, independent of the chosen -method. The classes tree allows the user to numerically integrate ODE's using -high-order complex schemes, as if it was done using the Forward-Euler method. -Switching between time-stepping schemes is as easy as changing a parameter in an -input file. - -In the already implemented solvers the time-integration schemes have been set up -according to the nature of the equations. -For example the incompressible Navier-Stokes equations solver allows the use of -three different Implicit-Explicit time-schemes if solving the equations with a -splitting-scheme. -This is because this kind of scheme has an explicit and an implicit operator -that combined solve the ODE's system. - -Once aware of the problem's nature and implementation, the user can easily -switch between some (depending on the problem) of the following -time-integration schemes: - -\begin{center} -\footnotesize -\begin{tabular}{p{4cm}p{10cm}} -\toprule -AdamsBashforthOrder1 & Adams-Bashforth Forward multi-step scheme of order 1\\ -AdamsBashforthOrder2 & Adams-Bashforth Forward multi-step scheme of order 2\\ -AdamsBashforthOrder3 & Adams-Bashforth Forward multi-step scheme of order 3\\ -AdamsMoultonOrder1 & Adams-Moulton Forward multi-step scheme of order 1\\ -AdamsMoultonOrder2 & Adams-Moulton Forward multi-step scheme of order 2\\ -BDFImplicitOrder2 & BDF multi-step scheme of order 2 (implicit)\\ -ClassicalRungeKutta4 & Runge-Kutta multi-stage scheme 4th order explicit\\ -RungeKutta2\_ModifiedEuler & Runge-Kutta multi-stage scheme 2nd order explicit\\ -RungeKutta2\_ImprovedEuler & Runge-Kutta multi-stage scheme 2nd order explicit\\ -ForwardEuler & Forward-Euler scheme\\ -BackwardEuler & Backward Euler scheme\\ -IMEXOrder1 & IMEX 1st order scheme using Euler Backwards Euler - Forwards \\ -IMEXOrder2 & IMEX 2nd order scheme using Backward Different Formula \& - Extrapolation\\ -IMEXOrder3 & IMEX 3rd order scheme using Backward Different Formula \& - Extrapolation\\ -Midpoint & Midpoint method\\ -DIRKOrder2 & Diagonally Implicit Runge-Kutta scheme of order 2\\ -DIRKOrder3 & Diagonally Implicit Runge-Kutta scheme of order 3\\ -CNAB & Crank-Nicolson-Adams-Bashforth Order 2 (CNAB)\\ -IMEXGear & IMEX Gear Order 2\\ -MCNAB & Modified Crank-Nicolson-Adams-Bashforth Order 2 (MCNAB)\\ -IMEXdirk\_1\_1\_1 & Forward-Backward Euler IMEX DIRK(1,1,1)\\ -IMEXdirk\_1\_2\_1 & Forward-Backward Euler IMEX DIRK(1,2,1)\\ -IMEXdirk\_1\_2\_2 & Implicit-Explicit Midpoint IMEX DIRK(1,2,2)\\ -IMEXdirk\_2\_2\_2 & L-stable, two stage, second order IMEX DIRK(2,2,2)\\ -IMEXdirk\_2\_3\_2 & L-stable, three stage, third order IMEX DIRK(3,4,3)\\ -IMEXdirk\_2\_3\_3 & L-stable, two stage, third order IMEX DIRK(2,3,3)\\ -IMEXdirk\_3\_4\_3 & L-stable, three stage, third order IMEX DIRK(3,4,3)\\ -IMEXdirk\_4\_4\_3 & L-stable, four stage, third order IMEX DIRK(4,4,3)\\ -\bottomrule -\end{tabular} -\end{center} - -Nektar++ input file for your problem will ask you just the string corresponding -the time-stepping scheme you want to use (between quotation marks in the -previous list), and few parameters to define your integration in time (time-step -and number of steps or final time). For example:\\ -\begin{lstlisting}[style=XMLStyle] - - - - - - - - - -

TimeStep = 0.001

-

NumSteps = 1000

-

Kinvis = 1

- -\end{lstlisting} - - -\subsection{Implementation of a time-dependent problem} -In order to implement a new solver which takes advantage of the time-integration -class in Nektar++, two main ingredients are required: -\begin{itemize} -\item A main files in which the time-integration of you ODE's system is -initialized and performed. -\item A class representing the spatial discretization of your problem, which -reduces your system of PDE's to a system of ODE's. -\end{itemize} - -Your pseudo-main file, where you actually loop over the time steps, will look -like -\begin{lstlisting}[style=C++Style] -NekDouble timestep = 0.1; -NekDouble time = 0.0; -int NumSteps = 1000; - -YourClass solver(Input); - -LibUtilities::TimeIntegrationMethod TIME_SCHEME; -LibUtilities::TimeIntegrationSchemeOperators ODE; - -ODE.DefineOdeRhs(&YourClass::YourExplicitOperatorFunction,solver); -ODE.DefineProjection(&YourClass::YourProjectionFunction,solver); -ODE.DefineImplicitSolve(&YourClass::YourImplicitOperatorFunction,solver); - -Array IntScheme; - -LibUtilities::TimeIntegrationSolutionSharedPtr ode_solution; - -Array > U; - -TIME_SCHEME = LibUtilities::eForwardEuler; -int numMultiSteps=1; -IntScheme = Array(numMultiSteps); -LibUtilities::TimeIntegrationSchemeKey IntKey(TIME_SCHEME); -IntScheme[0] = LibUtilities::TimeIntegrationSchemeManager()[IntKey]; -ode_solution = IntScheme[0]->InitializeScheme(timestep,U,time,ODE); - -for(int n = 0; n < NumSteps; ++n) { - U = IntScheme[0]->TimeIntegrate(timestep,ode_solution,ODE); -} -\end{lstlisting} - -We can distinguish three different sections in the code above - -\subsubsection{Definitions} -\begin{lstlisting}[style=C++Style] -NekDouble timestep = 0.1; -NekDouble time = 0.0; -int NumSteps = 1000; - -YourClass equation(Input); - -LibUtilities::TimeIntegrationMethod TIME_SCHEME; -LibUtilities::TimeIntegrationSchemeOperators ODE; - -ODE.DefineOdeRhs(&YourClass::YourExplicitOperatorFunction,equation); -ODE.DefineProjection(&YourClass::YourProjectionFunction, equation); -ODE.DefineImplicitSolve(&YourClass::YourImplicitOperatorFunction, equation); -\end{lstlisting} -In this section you define the basic parameters (like time-step, initial time, -etc.) and the time-integration objects. -The operators are not all required, it depends on the nature of your problem and -on the type of time integration schemes you want to use. In this case, the -problem has been set up to work just with Forward-Euler, then for sure you will -not need the implicit operator. -An object named \texttt{equation} has been initialized, is an object of type -\texttt{YourClass}, where your spatial discretization and the functions which -actually represent your operators are implemented. An example of this class will -be shown later in this page. - -\subsubsection{Initialisations} -\begin{lstlisting}[style=C++Style] -Array IntScheme; - -LibUtilities::TimeIntegrationSolutionSharedPtr ode_solution; - -Array > U; - -TIME_SCHEME = LibUtilities::eForwardEuler; -int numMultiSteps=1; -IntScheme = Array(numMultiSteps); -LibUtilities::TimeIntegrationSchemeKey IntKey(TIME_SCHEME); -IntScheme[0] = LibUtilities::TimeIntegrationSchemeManager()[IntKey]; -ode_solution = IntScheme[0]->InitializeScheme(timestep,U,time,ODE); -\end{lstlisting} -The second part consists in the scheme initialization. In this example we set up -just Forward-Euler, but we can set up more then one time-integration scheme and -quickly switch between them from the input file. -Forward-Euler does not require any other scheme for the start-up procedure. High -order multi-step schemes may need lower-order schemes for the start up. - -\subsubsection{Integration} -\begin{lstlisting}[style=C++Style] -for(int n = 0; n < NumSteps; ++n) { - U = IntScheme[0]->TimeIntegrate(timestep,ode_solution,ODE); -} -\end{lstlisting} -The last step is the typical time-loop, where you iterate in time to get -your new solution at each time-level. -The solution at time $t^{n+1}$ is stored into vector \texttt{U} (you need -to properly initialize this vector). -\texttt{U} is an Array of Arrays, where the first dimension corresponds to -the number of variables (eg. u,v,w) and the second dimension corresponds to the -variables size (e.g. the number of modes or the number of physical points). - -The variable \texttt{ODE} is an object which contains the methods. A class -representing a PDE equation (or a system of equations) must have a series of -functions representing the implicit/explicit part of the method, which -represents the reduction of the PDE's to a system of ODE's. -The spatial discretization and the definition of this method should be -implemented in \texttt{YourClass}. -\texttt{\&YourClass::YourExplicitOperatorFunction} is a functor, i.e. a pointer -to a function where the method is implemented. \texttt{equation} is a pointer -to the object, i.e. the class, where the function/method is implemented. -Here a pseudo-example of the .h file of your hypothetical class representing the -set of equations. -The implementation of the functions is meant to be in the related .cpp file. - -\begin{lstlisting}[style=C++Style] -class YourCalss -{ -public: - YourClass(INPUT); - - ~YourClass(void); - - void YourExplicitOperatorFunction( - const Array > & inarray, - Array > & outarray, - const NekDouble time); - - void YourProjectionFunction( - const Array > & inarray, - Array > & outarray, const - NekDouble time); - - void YourImplicitOperatorFunction( - const Array > & inarray, - Array > & outarray, const - NekDouble time, - const NekDouble lambda); - - void InternalMethod1(...); - - NekDouble internalvariale1; - -protected: - ... - -private: - ... -}; -\end{lstlisting} - - -\subsection{Strongly imposed essential boundary conditions} -Dirichlet boundary conditions can be strongly imposed by lifting the known -Dirichlet solution. -This is equivalent to decompose the approximate solution $y$ into an -known part, $y^{\mathcal{D}}$, which satisfies the Dirichlet boundary -conditions, and an unknown part, $y^{\mathcal{H}}$, which is zero on -the Dirichlet boundaries, i.e. -\begin{align*} -y = y^{\mathcal{D}} + y^{\mathcal{H}} -\end{align*} - -In a Finite Element discretisation, this corresponds to splitting the solution -vector of coefficients $\boldsymbol{y}$ into the known Dirichlet -degrees of freedom $\boldsymbol{y}^{\mathcal{D}}$ and the unknown -homogeneous degrees of freedom $\boldsymbol{y}^{\mathcal{H}}$. -Ordering the known coefficients first, this corresponds to: -\begin{align*} -\boldsymbol{y} = \left[ \begin{array}{c} -\boldsymbol{y}^{\mathcal{D}} \\ -\boldsymbol{y}^{\mathcal{H}} \end{array} \right] -\end{align*} - -The generalised formulation of the general linear method (i.e. the introduction -of a left hand side operator) allows for an easier treatment of these types of -boundary conditions. To better appreciate this, consider the equation for the -stage values for an explicit general linear method where both the left and right -hand side operator are linear operators, i.e. they can be represented by a -matrix. -\begin{align*} -\boldsymbol{M}\boldsymbol{Y}_i = \Delta -t\sum_{j=0}^{i-1}a_{ij}\boldsymbol{L}\boldsymbol{Y}_j+\sum_{j=0}^{r-1}u_{ij}\boldsymbol{y}_{j}^{[n-1]}, -\qquad i=0,1,\ldots,s-1 -\end{align*} - -In case of a lifted known solution, this can be written as: -\begin{align*} -\left[ \begin{array}{cc} -\boldsymbol{M}^{\mathcal{DD}} & \boldsymbol{M}^{\mathcal{DH}} \\ -\boldsymbol{M}^{\mathcal{HD}} & \boldsymbol{M}^{\mathcal{HH}} \end{array} \right] -\left[ \begin{array}{c} -\boldsymbol{Y}^{\mathcal{D}}_i \\ -\boldsymbol{Y}^{\mathcal{H}}_i \end{array} \right] -= \Delta t\sum_{j=0}^{i-1}a_{ij} -\left[ \begin{array}{cc} -\boldsymbol{L}^{\mathcal{DD}} & \boldsymbol{L}^{\mathcal{DH}} \\ -\boldsymbol{L}^{\mathcal{HD}} & \boldsymbol{L}^{\mathcal{HH}} \end{array} \right] -\left[ \begin{array}{c} -\boldsymbol{Y}^{\mathcal{D}}_j \\ -\boldsymbol{Y}^{\mathcal{H}}_j \end{array} \right] -+\sum_{j=0}^{r-1}u_{ij} -\left[ \begin{array}{c} -\boldsymbol{y}^{\mathcal{D}[n-1]}_j \\ -\boldsymbol{y}^{\mathcal{H}[n-1]}_j \end{array} \right],\\ -\qquad i=0,1,\ldots,s-1 -\end{align*} - -In order to calculate the stage values correctly, the explicit operator -should now be implemented to do the following: -\begin{align*} -\left[ \begin{array}{c} -\boldsymbol{b}^{\mathcal{D}} \\ -\boldsymbol{b}^{\mathcal{H}} \end{array} \right] -= -\left[ \begin{array}{cc} -\boldsymbol{L}^{\mathcal{DD}} & \boldsymbol{L}^{\mathcal{DH}} \\ -\boldsymbol{L}^{\mathcal{HD}} & \boldsymbol{L}^{\mathcal{HH}} \end{array} \right] -\left[ \begin{array}{c} -\boldsymbol{y}^{\mathcal{D}} \\ -\boldsymbol{y}^{\mathcal{H}} \end{array} \right] -\end{align*} - -Note that only the homogeneous part $\boldsymbol{b}^{\mathcal{H}}$ will be used -to calculate the stage values. This means essentially that only the bottom part -of the operation above, i.e. -$\boldsymbol{L}^{\mathcal{HD}}\boldsymbol{y}^{\mathcal{D}} + -\boldsymbol{L}^{\mathcal{HH}}\boldsymbol{y}^{\mathcal{H}}$ is required. However, -sometimes it might be more convenient to use/implement routines for the explicit -operator that also calculate $\boldsymbol{b}^{\mathcal{D}}$.\\ - -An implicit method should solve the system: -\begin{align*} -\left(\left[ \begin{array}{cc} -\boldsymbol{M}^{\mathcal{DD}} & \boldsymbol{M}^{\mathcal{DH}} \\ -\boldsymbol{M}^{\mathcal{HD}} & \boldsymbol{M}^{\mathcal{HH}} \end{array} \right] -- \lambda \left[ \begin{array}{cc} -\boldsymbol{L}^{\mathcal{DD}} & \boldsymbol{L}^{\mathcal{DH}} \\ -\boldsymbol{L}^{\mathcal{HD}} & \boldsymbol{L}^{\mathcal{HH}} \end{array} \right]\right) -\left[ \begin{array}{c} -\boldsymbol{y}^{\mathcal{D}} \\ -\boldsymbol{y}^{\mathcal{H}} \end{array} \right] -= -\left[ \begin{array}{cc} -\boldsymbol{H}^{\mathcal{DD}} & \boldsymbol{H}^{\mathcal{DH}} \\ -\boldsymbol{H}^{\mathcal{HD}} & \boldsymbol{H}^{\mathcal{HH}} \end{array} \right] -\left[ \begin{array}{c} -\boldsymbol{y}^{\mathcal{D}} \\ -\boldsymbol{y}^{\mathcal{H}} \end{array} \right] -= -\left[ \begin{array}{c} -\boldsymbol{b}^{\mathcal{D}} \\ -\boldsymbol{b}^{\mathcal{H}} \end{array} \right] -\end{align*} - -for the unknown vector $\boldsymbol{y}$. This can be done in three steps: -\begin{itemize} -\item Set the known solution $\boldsymbol{y}^{\mathcal{D}}$ -\item Calculate the modified right hand side term - $\boldsymbol{b}^{\mathcal{H}} - - \boldsymbol{H}^{\mathcal{HD}}\boldsymbol{y}^{\mathcal{D}}$ -\item Solve the system below for the unknown - $\boldsymbol{y}^{\mathcal{H}}$, i.e. - $\boldsymbol{H}^{\mathcal{HH}}\boldsymbol{y}^{\mathcal{H}} = - \boldsymbol{b}^{\mathcal{H}} - - \boldsymbol{H}^{\mathcal{HD}}\boldsymbol{y}^{\mathcal{D}}$ -\end{itemize} - -\subsection{How to add a new time-stepping method} - -To add a new time integration scheme, follow the steps below: -\begin{itemize} -\item Choose a name for the method and add it to the -\texttt{TimeIntegrationMethod} enum list. -\item Populate the switch statement in the \texttt{TimeIntegrationScheme} -constructor with the coefficients of the new method. -\item Use ( or modify) the function \texttt{InitializeScheme} to select (or -implement) a proper initialisation strategy for the method. -\item Add documentation for the method (especially indicating what the auxiliary - parameters of the input and output vectors of the multi-step method represent) -\end{itemize} - -\subsection{Examples of already implemented time stepping schemes} - -Here we show some examples time-stepping shemes implemented in Nektar++, to give an idea of what is required -to add one of them. - -\subsubsection{Forward Euler} -\begin{align*} -\left[\begin{array}{c|c} -A & U \\ -\hline -B & V -\end{array}\right] = -\left[\begin{array}{c|c} -0 & 1 \\ -\hline -1 & 1 -\end{array}\right],\qquad -\boldsymbol{y}^{[n]}= -\left[\begin{array}{c} -\boldsymbol{y}^{[n]}_0 -\end{array}\right]= -\left[\begin{array}{c} -\boldsymbol{m}\left(t^n,\boldsymbol{y}^{n}\right) -\end{array}\right] -\end{align*} - -\subsubsection{Backward Euler} -\begin{align*} -\left[\begin{array}{c|c} -A & U \\ -\hline - B & V -\end{array}\right] = -\left[\begin{array}{c|c} -1 & 1 \\ -\hline -1 & 1 -\end{array}\right],\qquad -\boldsymbol{y}^{[n]}= -\left[\begin{array}{c} -\boldsymbol{y}^{[n]}_0 -\end{array}\right]= -\left[\begin{array}{c} -\boldsymbol{m}\left(t^n,\boldsymbol{y}^{n}\right) -\end{array}\right] -\end{align*} - -\subsubsection{2nd order Adams Bashforth} -\begin{align*} -\left[\begin{array}{c|c} -A & U \\ -\hline -B & V -\end{array}\right] = -\left[\begin{array}{c|cc} -0 & 1 & 0 \\ -\hline -\frac{3}{2} & 1 & \frac{-1}{2} \\ -1 & 0 & 0 -\end{array}\right],\qquad -\boldsymbol{y}^{[n]}= -\left[\begin{array}{c} -\boldsymbol{y}^{[n]}_0\\ -\boldsymbol{y}^{[n]}_1\\ -\end{array}\right]= -\left[\begin{array}{c} -\boldsymbol{m}\left(t^n,\boldsymbol{y}^{n}\right)\\ -\Delta t \boldsymbol{l}(t^{n-1},\boldsymbol{y}^{n-1}) -\end{array}\right] -\end{align*} - -\subsubsection{1st order IMEX Euler backwards/ Euler Forwards} -\begin{align*} -\left[ \begin{array}{cc|c} -A^{\mathrm{IM}} & A^{\mathrm{EM}} & U \\ -\hline -B^{\mathrm{IM}} & B^{\mathrm{EM}} & V -\end{array} \right ] = -\left[\begin{array}{cc|c} -\left [ \begin{array}{c} 1 \end{array} \right ] & \left [ \begin{array}{c} 0 \end{array} \right ] & -\left [ \begin{array}{cc} 1 & 1 \end{array} \right ] \\ -\hline -\left [ \begin{array}{c} 1 \\ 0 \end{array} \right ] & \left [ \begin{array}{c} 0 \\ 1 \end{array} \right ]& -\left [ \begin{array}{cc} 1 & 1 \\ 0 & 0 \end{array} \right ] -\end{array}\right] \quad \mathrm{with}\quad -\boldsymbol{y}^{[n]}= -\left[\begin{array}{c} -\boldsymbol{y}^{[n]}_0\\ -\boldsymbol{y}^{[n]}_1 -\end{array}\right]= -\left[\begin{array}{c} -\boldsymbol{m}\left(t^n,\boldsymbol{y}^{n}\right)\\ -\Delta t \boldsymbol{l}\left ( t^n, \boldsymbol{y}^{n}\right) -\end{array}\right] -\end{align*} - -\subsubsection{2nd order IMEX Backward Different Formula \& Extrapolation} -\begin{align*} -\left[ \begin{array}{cc|c} -A^{\mathrm{IM}} & A^{\mathrm{EM}} & U \\ -\hline -B^{\mathrm{IM}} & B^{\mathrm{EM}} & V -\end{array} \right ] = -\left[\begin{array}{cc|c} -\left [ \begin{array}{c} \frac{2}{3} \end{array} \right ] & \left [ \begin{array}{c} 0 \end{array} \right ] & -\left [ \begin{array}{cccc} \frac{4}{3} & -\frac{1}{3} & \frac{4}{3} & -\frac{2}{3} \end{array} \right ] \\ -\hline -\left [ \begin{array}{c} \frac{2}{3} \\ 0 \\ 0 \\ 0 \end{array} \right ] & \left [ \begin{array}{c} 0 \\0 \\ 1 \\ 0 \end{array} \right ]& -\left [ \begin{array}{cccc} \frac{4}{3} & -\frac{1}{3} & \frac{4}{3} & -\frac{2}{3} \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\\ 0 & 0 & 1 & 0 \end{array} \right ] -\end{array}\right] -\end{align*} -with -\begin{align*} -\boldsymbol{y}^{[n]}= -\left[\begin{array}{c} -\boldsymbol{y}^{[n]}_0\\ -\boldsymbol{y}^{[n]}_1 \\ -\boldsymbol{y}^{[n]}_2 \\ -\boldsymbol{y}^{[n]}_3 -\end{array}\right]= -\left[\begin{array}{l} -\boldsymbol{m}\left(t^n,\boldsymbol{y}^{n}\right)\\ -\boldsymbol{m}\left(t^{n-1},\boldsymbol{y}^{n-1}\right)\\ -\Delta t \boldsymbol{l}\left ( t^n, \boldsymbol{y}^{n}\right)\\ -\Delta t \boldsymbol{l}\left ( t^{n-1}, \boldsymbol{y}^{n-1}\right) -\end{array}\right] -\end{align*} - -\begin{notebox} -The first two rows are normalised so the coefficient on -$\boldsymbol{y}_n^{[n+1]}$ is one. In the standard formulation it is $3/2$. -\end{notebox} - -\subsubsection{3rdorder IMEX Backward Different Formula \& Extrapolation} -\begin{align*} - \left[ \begin{array}{cc|c} - A^{\mathrm{IM}} & A^{\mathrm{EM}} & U \\ - \hline - B^{\mathrm{IM}} & B^{\mathrm{EM}} & V - \end{array} \right ] = - \left[\begin{array}{cc|c} - \left [ \begin{array}{c} \frac{6}{11} \end{array} \right ] & \left [ \begin{array}{c} 0 \end{array} \right ] & - \left [ \begin{array}{cccccc} \frac{18}{11} & -\frac{9}{11} & \frac{2}{11} & \frac{18}{11} & -\frac{18}{11} & \frac{6}{11} \end{array} \right ] \\ - \hline - \left [ \begin{array}{c} \frac{6}{11}\\ 0 \\ 0 \\ 0 \\0 \\0 \end{array} \right ] & \left [ \begin{array}{c} 0 \\0 \\ 0 \\ 1 \\ 0 \\ 0 \end{array} \right ]& - \left [ \begin{array}{cccccc} \frac{18}{11} & -\frac{9}{11} & \frac{2}{11} & \frac{18}{11} & -\frac{18}{11} & \frac{6}{11} \\ 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 \end{array} \right ] - \end{array}\right] -\end{align*} -with -\begin{align*} - \boldsymbol{y}^{[n]}= - \left[\begin{array}{l} - \boldsymbol{y}^{[n]}_0 \\ - \boldsymbol{y}^{[n]}_1 \\ - \boldsymbol{y}^{[n]}_2 \\ - \boldsymbol{y}^{[n]}_3 \\ - \boldsymbol{y}^{[n]}_4 \\ - \boldsymbol{y}^{[n]}_5 - \end{array}\right]= - \left[\begin{array}{l} - \boldsymbol{m}\left(t^n,\boldsymbol{y}^{n}\right)\\ - \boldsymbol{m}\left(t^{n-1},\boldsymbol{y}^{n-1}\right)\\ - \boldsymbol{m}\left(t^{n-2},\boldsymbol{y}^{n-2}\right)\\ - \Delta t \boldsymbol{l}\left ( t^n, \boldsymbol{y}^{n}\right)\\ - \Delta t \boldsymbol{l}\left ( t^{n-1}, \boldsymbol{y}^{n-1}\right)\\ - \Delta t \boldsymbol{l}\left ( t^{n-2}, \boldsymbol{y}^{n-2}\right) - \end{array}\right] -\end{align*} - -\begin{notebox} -The first two rows are normalised so the coefficient on -$\boldsymbol{y}_n^{[n+1]}$ is one. In the standard formulation it is $11/6$. -\end{notebox} - -\subsubsection{2nd order Adams Moulton} -\begin{align*} - \left[\begin{array}{c|c} - A & U \\ - \hline - B & V - \end{array}\right] = - \left[\begin{array}{c|cc} - \frac{1}{2} & 1 & \frac{1}{2} \\ - \hline - \frac{1}{2} & 1 & \frac{1}{2} \\ - 1 & 0 & 0 - \end{array}\right],\qquad - \boldsymbol{y}^{[n]}= - \left[\begin{array}{c} - \boldsymbol{y}^{[n]}_0\\ - \boldsymbol{y}^{[n]}_1\\ - \end{array}\right]= - \left[\begin{array}{c} - \boldsymbol{m}\left(t^n,\boldsymbol{y}^{n}\right)\\ - \Delta t \boldsymbol{l}(t^{n},\boldsymbol{y}^{n}) - \end{array}\right] -\end{align*} - -\subsubsection{Midpoint method} -\begin{align*} - \left[\begin{array}{c|c} - A & U \\ - \hline - B & V - \end{array}\right] = - \left[\begin{array}{cc|c} - 0 & 0 & 1 \\ - \frac{1}{2} & 0 & 1 \\ - \hline - 0 & 1 & 1 - \end{array}\right],\qquad - \boldsymbol{y}^{[n]}= - \left[\begin{array}{c} - \boldsymbol{y}^{[n]}_0 - \end{array}\right]= - \left[\begin{array}{c} - \boldsymbol{m}\left(t^n,\boldsymbol{y}^{n}\right) - \end{array}\right] -\end{align*} - -\subsubsection{RK4: the standard fourth order Runge-Kutta scheme} -\begin{align*} - \left[\begin{array}{c|c} - A & U \\ - \hline - B & V - \end{array}\right] = - \left[\begin{array}{cccc|c} - 0 & 0 & 0 & 0 & 1 \\ - \frac{1}{2} & 0 & 0 & 0 & 1 \\ - 0 & \frac{1}{2} & 0 & 0 & 1 \\ - 0 & 0 & 1 & 0 & 1 \\ - \hline - \frac{1}{6} & \frac{1}{3} & \frac{1}{3} & \frac{1}{6} & 1 - \end{array}\right],\qquad - \boldsymbol{y}^{[n]}= - \left[\begin{array}{c} - \boldsymbol{y}^{[n]}_0 - \end{array}\right]= - \left[\begin{array}{c} - \boldsymbol{m}\left(t^n,\boldsymbol{y}^{n}\right) - \end{array}\right] -\end{align*} - -\subsubsection{2nd order Diagonally Implicit Runge Kutta (DIRK)} -\begin{align*} - \left[\begin{array}{c|c} - A & U \\ - \hline - B & V - \end{array}\right] = - \left[\begin{array}{cc|c} - \lambda & 0 & 1 \\ - \left(1-\lambda\right) & \lambda & 1 \\ - \hline - \left(1-\lambda\right) & \lambda & 1 - \end{array}\right]\quad \mathrm{with}\quad \lambda=\frac{2-\sqrt{2}}{2},\qquad - \boldsymbol{y}^{[n]}= - \left[\begin{array}{c} - \boldsymbol{y}^{[n]}_0 - \end{array}\right]= - \left[\begin{array}{c} - \boldsymbol{m}\left(t^n,\boldsymbol{y}^{n}\right) - \end{array}\right] -\end{align*} - -\subsubsection{3rd order Diagonally Implicit Runge Kutta (DIRK)} -\begin{align*} - \left[\begin{array}{c|c} - A & U \\ - \hline - B & V - \end{array}\right] = - \left[\begin{array}{ccc|c} - \lambda & 0 & 0 & 1 \\ - \frac{1}{2}\left(1-\lambda\right) & \lambda & 0 & 1 \\ - \frac{1}{4}\left(-6\lambda^2+16\lambda-1\right) & \frac{1}{4}\left(6\lambda^2-20\lambda+5\right) & \lambda & 1 \\ - \hline - \frac{1}{4}\left(-6\lambda^2+16\lambda-1\right) & \frac{1}{4}\left(6\lambda^2-20\lambda+5\right) & \lambda & 1 - \end{array}\right] -\end{align*} -with -\begin{align*} - \lambda=0.4358665215,\qquad - \boldsymbol{y}^{[n]}= - \left[\begin{array}{c} - \boldsymbol{y}^{[n]}_0 - \end{array}\right]= - \left[\begin{array}{c} - \boldsymbol{m}\left(t^n,\boldsymbol{y}^{n}\right) - \end{array}\right] -\end{align*} - -\subsubsection{3rd order L-stable, three stage IMEX DIRK(3,4,3)} -\tiny -\begin{align*} - &\left[\begin{array}{cc|c} - A^{\mathrm{IM}} & A^{\mathrm{EM}} & U \\ - \hline - B^{\mathrm{IM}} & B^{\mathrm{EM}} & V - \end{array}\right] =\\ - &\left[\begin{array}{cc|c} - \left[\begin{array}{cccc} - 0 & 0 & 0 & 0 \\ - 0 & \lambda & 0 & 0 \\ - 0 & \frac{1}{2}\left(1-\lambda\right) & \lambda & 0 \\ - 0 & \frac{1}{4}\left(-6\lambda^2+16\lambda-1\right) & \frac{1}{4}\left(6\lambda^2-20\lambda+5\right) & \lambda - \end{array}\right] & - \left[\begin{array}{cccc} - 0 & 0 & 0 & 0 \\ - \lambda & 0 & 0 & 0 \\ - 0.3212788860 & 0.3966543747 & 0 & 0 \\ - -0.105858296 & 0.5529291479 & 0.5529291479 & 0 - \end{array}\right] & - \left[\begin{array}{c} - 1\\ - 1\\ - 1\\ - 1 - \end{array}\right] \\ - \hline - \left[\begin{array}{cccc} - 0 & \frac{1}{4}\left(-6\lambda^2+16\lambda-1\right) & \frac{1}{4}\left(6\lambda^2-20\lambda+5\right) & \lambda - \end{array}\right] & - \left[\begin{array}{cccc} - 0 & \frac{1}{4}\left(-6\lambda^2+16\lambda-1\right) & \frac{1}{4}\left(6\lambda^2-20\lambda+5\right) & \lambda - \end{array}\right] & - \left[\begin{array}{c} - 1 - \end{array}\right] - \end{array}\right] -\end{align*} -\normalsize -with -\begin{align*} - \lambda=0.4358665215,\qquad - \boldsymbol{y}^{[n]}= - \left[\begin{array}{c} - \boldsymbol{y}^{[n]}_0 - \end{array}\right]= - \left[\begin{array}{c} - \boldsymbol{m}\left(t^n,\boldsymbol{y}^{n}\right) - \end{array}\right] -\end{align*} - diff --git a/docs/developer-guide/developer-guide.tex b/docs/developer-guide/developer-guide.tex deleted file mode 100644 index 3122068c73d9fb79b5903a3655f9c5c7efc5974c..0000000000000000000000000000000000000000 --- a/docs/developer-guide/developer-guide.tex +++ /dev/null @@ -1,467 +0,0 @@ -%%% DOCUMENTCLASS -%%%------------------------------------------------------------------------------- - -\documentclass[ -a4paper, % Stock and paper size. -11pt, % Type size. -% article, -% oneside, -onecolumn, % Only one column of text on a page. -% openright, % Each chapter will start on a recto page. -% openleft, % Each chapter will start on a verso page. -openany, % A chapter may start on either a recto or verso page. -]{memoir} - 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\hspace*{0.05\textwidth}% - \parbox[b]{0.85\textwidth}{% - \vbox{% - {\includegraphics[width=0.2\textwidth]{icon-blue.png}\par} - \vskip1.00\baselineskip - {\Huge\bfseries\raggedright\@title\par} - \vskip2.37\baselineskip - {\huge\bfseries Version \nekver\par} - \vskip4\baselineskip - {\huge\bfseries \textcolor{darkblue}{Developer Guide}\par} - \vskip1.0\baselineskip - {\large\bfseries\@date\par} - \vspace{0.3\textheight} - {\small\noindent\@author}\\[\baselineskip] - }% end of vbox - }% end of parbox - }% end of hbox - \vfill - \null -\endgroup} -\makeatother - -%%% THE DOCUMENT -%%% Where all the important stuff is included! -%%%------------------------------------------------------------------------------- - -\author{Department of Aeronautics, Imperial College London, UK\newline -Scientific Computing and Imaging Institute, University of Utah, USA} -\title{Nektar++: Spectral/hp Element Framework} -\date{\today} - -\begin{document} - -\frontmatter - -% Render pretty title page if not building HTML -\ifdefined\HCode -\begin{center} - \includegraphics[width=0.1\textwidth]{img/icon-blue.png} -\end{center} -\maketitle -\begin{center} - \huge{Developers Guide - Version \nekver} -\end{center} -\else -\titlepage -\fi - -\clearpage - -\ifx\HCode\undefined -\tableofcontents* -\fi - -\clearpage - -\chapter{Introduction} -Nektar++ \cite{CaMoCoBoRo15} is a tensor product based finite element package -designed to allow one to construct efficient classical low polynomial order -$h$-type solvers (where $h$ is the size of the finite element) as well as higher -$p$-order piecewise polynomial order solvers. The framework currently has the -following capabilities: - -\begin{itemize} -\item Representation of one, two and three-dimensional fields as a collection of - piecewise continuous or discontinuous polynomial domains. -\item Segment, plane and volume domains are permissible, as well as domains - representing curves and surfaces (dimensionally-embedded domains). -\item Hybrid shaped elements, i.e triangles and quadrilaterals or tetrahedra, -prisms and hexahedra. -\item Both hierarchical and nodal expansion bases. -\item Continuous or discontinuous Galerkin operators. -\item Cross platform support for Linux, Mac OS X and Windows. -\end{itemize} - -The framework comes with a number of solvers and also allows one to construct a -variety of new solvers. - -Our current goals are to develop: -\begin{itemize} -\item Automatic auto-tuning of optimal operator implementations based upon not -only $h$ and $p$ but also hardware considerations and mesh connectivity. -\item Temporal and spatial adaption. -\item Features enabling evaluation of high-order meshing techniques. -\end{itemize} - -This document provides implementation details for the design of the libraries, -Nektar++-specific data structures and algorithms and other development -information. - -\begin{warningbox} -This document is still under development and may be incomplete in parts. -\end{warningbox} - -For further information and to download the software, visit the Nektar++ website -at \url{http://www.nektar.info}. - -\mainmatter - -\import{core-concepts/}{core-concepts.tex} - -\import{library-design/}{library-design.tex} - -\import{data-structures-algorithms/}{data-structures-algorithms.tex} - -\import{coding-standard/}{coding-standard.tex} - -%\appendix - - -\backmatter - -%%% BIBLIOGRAPHY -%%% ------------------------------------------------------------- - -\bibliographystyle{plain} -\bibliography{../refs} - -\printindex - -\end{document} diff --git a/docs/developer-guide/img/icon-blue.png 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469.305 299.941 469.062 299.047 - 468.941 298.523 c 468.727 297.77 468.547 296.988 468.363 296.207 c 467 -291.02 l 466.879 290.586 465.574 288.559 463.57 288.559 c 462.027 288.559 - 461.691 289.832 461.691 290.906 c 461.691 292.238 462.207 294.004 463.238 - 296.555 c 463.723 297.742 463.844 298.059 463.844 298.641 c 463.844 299.941 - 462.875 301.016 461.359 301.016 c 458.508 301.016 457.387 296.812 457.387 - 296.555 c 457.387 296.266 457.688 296.266 457.75 296.266 c 458.055 296.266 - 458.082 296.32 458.234 296.785 c 459.055 299.508 460.238 300.379 461.266 - 300.379 c 461.512 300.379 462.027 300.379 462.027 299.449 c 462.027 298.727 - 461.723 297.973 461.512 297.422 c 460.297 294.352 459.781 292.73 459.781 - 291.367 c 459.781 288.789 461.66 287.922 463.449 287.922 c 464.633 287.922 - 465.664 288.414 466.512 289.223 c 466.121 287.719 465.754 286.328 464.543 - 284.793 c 463.754 283.809 462.602 282.969 461.207 282.969 c 460.781 282.969 - 459.449 283.055 458.934 284.184 c 459.418 284.184 459.812 284.184 460.207 - 284.531 c 460.508 284.793 460.844 285.168 460.844 285.719 c 460.844 286.59 - 460.023 286.703 459.723 286.703 c 459.023 286.703 458.023 286.242 458.023 - 284.852 c 458.023 283.402 459.355 282.328 461.207 282.328 c 464.332 282.328 - 467.453 284.965 468.273 288.211 c h -f -0.941176 0.898039 0.396078 rg -49.18 85.465 m 339.746 85.465 l 355.449 85.465 368.09 72.824 368.09 57.121 - c 368.09 36.031 l 368.09 20.324 355.449 7.684 339.746 7.684 c 49.18 7.684 - l 33.477 7.684 20.832 20.324 20.832 36.031 c 20.832 57.121 l 20.832 72.824 - 33.477 85.465 49.18 85.465 c h -f -0 g -2.216693 w -1 J -q 1 0 0 -1 0 645.5 cm -49.18 560.035 m 339.746 560.035 l 355.449 560.035 368.09 572.676 368.09 - 588.379 c 368.09 609.469 l 368.09 625.176 355.449 637.816 339.746 637.816 - c 49.18 637.816 l 33.477 637.816 20.832 625.176 20.832 609.469 c 20.832 - 588.379 l 20.832 572.676 33.477 560.035 49.18 560.035 c h -S Q -BT -28.8 0 0 28.8 40.564413 54.567187 Tm -/f-0-0 1 Tf -[(LibUtili)3(ties)]TJ -ET -78.277 40.734 m 78.277 40.809 78.352 41.074 78.352 41.074 c 78.352 41.109 - 78.352 41.336 78.051 41.336 c 77.828 41.336 77.789 41.262 77.676 40.848 - c 76.289 35.336 l 72.504 35.184 68.977 32.035 68.977 28.773 c 68.977 26.484 - 70.664 24.609 73.59 24.422 c 73.402 23.711 73.215 22.922 73.027 22.172 -c 72.727 21.047 72.504 20.148 72.504 20.074 c 72.504 19.848 72.691 19.809 - 72.801 19.809 c 72.914 19.809 72.953 19.848 73.027 19.922 c 73.066 19.961 - 73.215 20.523 73.289 20.859 c 74.191 24.422 l 78.051 24.574 81.539 27.797 - 81.539 30.984 c 81.539 32.898 80.266 35.074 76.926 35.336 c h -73.703 24.949 m 72.277 25.023 70.551 25.887 70.551 28.246 c 70.551 31.137 - 72.613 34.473 76.176 34.809 c h -76.777 34.809 m 78.613 34.699 79.965 33.609 79.965 31.512 c 79.965 28.66 - 77.902 25.246 74.34 24.949 c h -f -83.297 19.113 m 83.188 18.625 83.148 18.512 82.512 18.512 c 82.285 18.512 - 82.062 18.512 82.062 18.137 c 82.062 17.949 82.211 17.875 82.285 17.875 - c 82.699 17.875 83.262 17.949 83.711 17.949 c 84.273 17.949 84.91 17.875 - 85.473 17.875 c 85.625 17.875 85.812 17.949 85.812 18.25 c 85.812 18.512 - 85.586 18.512 85.359 18.512 c 84.984 18.512 84.535 18.512 84.535 18.699 - c 84.535 18.773 84.688 19.227 84.723 19.449 c 84.949 20.352 85.172 21.25 - 85.359 21.961 c 85.547 21.625 86.074 20.988 87.086 20.988 c 89.109 20.988 - 91.359 23.238 91.359 25.711 c 91.359 27.664 90.012 28.523 88.887 28.523 - c 87.836 28.523 86.938 27.812 86.484 27.324 c 86.223 28.301 85.285 28.523 - 84.762 28.523 c 84.125 28.523 83.711 28.074 83.449 27.625 c 83.109 27.062 - 82.848 26.051 82.848 25.938 c 82.848 25.75 83.074 25.75 83.148 25.75 c -83.375 25.75 83.375 25.789 83.484 26.238 c 83.75 27.211 84.086 28.039 84.723 - 28.039 c 85.172 28.039 85.285 27.664 85.285 27.211 c 85.285 27.023 85.25 - 26.836 85.211 26.727 c h -86.484 26.5 m 87.461 27.812 88.285 28.039 88.812 28.039 c 89.484 28.039 - 90.047 27.551 90.047 26.426 c 90.047 25.75 89.672 24.023 89.188 23.051 -c 88.734 22.227 87.949 21.438 87.086 21.438 c 85.887 21.438 85.586 22.711 - 85.586 22.898 c 85.586 22.977 85.625 23.086 85.625 23.164 c h -f -101.027 18.984 m 101.027 19.059 101.027 19.098 100.613 19.512 c 97.652 -22.512 96.863 27.047 96.863 30.723 c 96.863 34.887 97.762 39.047 100.727 - 42.012 c 101.027 42.309 101.027 42.348 101.027 42.422 c 101.027 42.609 -100.949 42.684 100.801 42.684 c 100.539 42.684 98.402 41.035 96.977 37.996 - c 95.777 35.371 95.477 32.711 95.477 30.723 c 95.477 28.848 95.738 25.961 - 97.051 23.223 c 98.512 20.297 100.539 18.723 100.801 18.723 c 100.949 18.723 - 101.027 18.797 101.027 18.984 c h -f -110.398 31.961 m 110.547 32.559 111.109 34.773 112.762 34.773 c 112.875 - 34.773 113.473 34.773 113.961 34.473 c 113.285 34.324 112.836 33.762 112.836 - 33.16 c 112.836 32.785 113.098 32.336 113.734 32.336 c 114.262 32.336 115.012 - 32.746 115.012 33.723 c 115.012 34.961 113.625 35.297 112.797 35.297 c -111.41 35.297 110.586 34.023 110.285 33.496 c 109.688 35.074 108.41 35.297 - 107.699 35.297 c 105.223 35.297 103.836 32.223 103.836 31.621 c 103.836 - 31.359 104.098 31.359 104.137 31.359 c 104.324 31.359 104.398 31.434 104.438 - 31.621 c 105.262 34.172 106.836 34.773 107.66 34.773 c 108.109 34.773 108.938 - 34.547 108.938 33.16 c 108.938 32.41 108.523 30.836 107.66 27.461 c 107.285 - 25.996 106.422 24.984 105.375 24.984 c 105.223 24.984 104.699 24.984 104.172 - 25.285 c 104.773 25.434 105.297 25.922 105.297 26.598 c 105.297 27.234 -104.773 27.422 104.438 27.422 c 103.688 27.422 103.125 26.824 103.125 26.035 - c 103.125 24.949 104.285 24.461 105.336 24.461 c 106.949 24.461 107.812 - 26.148 107.848 26.262 c 108.148 25.398 109.012 24.461 110.438 24.461 c -112.91 24.461 114.262 27.535 114.262 28.137 c 114.262 28.398 114.074 28.398 - 114 28.398 c 113.773 28.398 113.734 28.285 113.66 28.137 c 112.875 25.547 - 111.262 24.984 110.512 24.984 c 109.574 24.984 109.199 25.734 109.199 26.559 - c 109.199 27.086 109.312 27.609 109.574 28.66 c h -f -122.977 30.723 m 122.977 32.559 122.715 35.449 121.402 38.184 c 119.977 - 41.109 117.914 42.684 117.688 42.684 c 117.539 42.684 117.426 42.574 117.426 - 42.422 c 117.426 42.348 117.426 42.309 117.875 41.859 c 120.238 39.496 -121.59 35.711 121.59 30.723 c 121.59 26.598 120.727 22.398 117.766 19.398 - c 117.426 19.098 117.426 19.059 117.426 18.984 c 117.426 18.836 117.539 - 18.723 117.688 18.723 c 117.914 18.723 120.09 20.371 121.477 23.41 c 122.715 - 26.035 122.977 28.699 122.977 30.723 c h -f -2.964922 w -0 J -q 0.558965 0 0 -1 0 645.5 cm -708.515 564.629 m 708.515 630.813 l S Q -q 0.558965 0 0 -1 0 645.5 cm -972.606 564.629 m 972.606 630.813 l S Q -3.416663 w -q 0.558965 0 0 -1 0 645.5 cm -708.725 597.723 m 972.396 597.723 l S Q -0 0 1 rg -1.070034 w -q 0.558965 0 0 -1 0 645.5 cm -708.515 597.723 m 708.515 597.723 734.987 564.629 774.702 564.629 c 834.264 - 564.629 893.833 690.379 973.256 597.723 c 973.256 597.723 955.764 630.813 - 940.159 630.813 c 908.963 630.813 905.175 564.629 873.979 564.629 c 842.776 - 564.629 838.988 630.813 807.792 630.813 c 776.589 630.813 772.808 564.629 - 741.605 564.629 c 726.007 564.629 708.515 597.723 708.515 597.723 c h -S Q -0.803922 0 0 rg -1.89573 w -q 0.558965 0 0 -1 0 645.5 cm -708.515 598.047 m 708.515 598.047 719.208 631.137 725.553 631.301 c 741.605 - 631.715 741.92 564.406 758.154 564.465 c 775.254 564.527 774.059 631.348 - 791.167 631.301 c 810.65 631.25 805.095 564.793 824.585 564.871 c 843.601 - 564.949 838.981 630.902 857.591 631.301 c 876.614 631.707 871.994 565.281 - 890.604 564.871 c 909.214 564.465 904.595 631.301 923.617 631.301 c 942.633 - 631.301 938.013 564.93 956.623 564.871 c 965.736 564.844 973.256 598.047 - 973.256 598.047 c S Q -0 g -1.6 w -[ 4.8 4.8] 0 d -q 1 0 0 -1 0 645.5 cm -446.555 218.176 m 432.012 324.848 l S Q -[ 4.8 4.8] 0 d -q 1 0 0 -1 0 645.5 cm -491.004 315.148 m 494.234 213.324 l S Q -[ 4.8 4.8] 0 d -q 1 0 0 -1 0 645.5 cm -448.172 254.539 m 460.293 165.648 l S Q -[ 4.8 4.8] 0 d -q 1 0 0 -1 0 645.5 cm -412.617 495.359 m 394.836 564.859 l S Q -[ 4.8 4.8] 0 d -q 1 0 0 -1 0 645.5 cm -510.398 497.785 m 542.723 563.242 l S Q -0.729412 0.619608 0.964706 rg -48.375 616.094 m 338.941 616.094 l 354.645 616.094 367.285 603.453 367.285 - 587.75 c 367.285 566.656 l 367.285 550.953 354.645 538.312 338.941 538.312 - c 48.375 538.312 l 32.672 538.312 20.027 550.953 20.027 566.656 c 20.027 - 587.75 l 20.027 603.453 32.672 616.094 48.375 616.094 c h -f -0 g -2.216693 w -1 J -[] 0.0 d -q 1 0 0 -1 0 645.5 cm -48.375 29.406 m 338.941 29.406 l 354.645 29.406 367.285 42.047 367.285 -57.75 c 367.285 78.844 l 367.285 94.547 354.645 107.188 338.941 107.188 -c 48.375 107.188 l 32.672 107.188 20.027 94.547 20.027 78.844 c 20.027 57.75 - l 20.027 42.047 32.672 29.406 48.375 29.406 c h -S Q -BT -28.8 0 0 28.8 39.759128 585.195728 Tm -/f-0-0 1 Tf -[(SolverUt)3(ils)]TJ -ET -2.4 w -0 J -[ 7.2 7.2] 0 d -q 1 0 0 -1 0 645.5 cm -19.355 526.582 m 561.332 526.582 l 570.121 526.582 577.199 531.621 577.199 - 537.879 c 577.199 633 l 577.199 639.258 570.121 644.297 561.332 644.297 - c 19.355 644.297 l 10.562 644.297 3.484 639.258 3.484 633 c 3.484 537.879 - l 3.484 531.621 10.562 526.582 19.355 526.582 c h -S Q -[ 7.2 7.2] 0 d -q 1 0 0 -1 0 645.5 cm -17.07 134.012 m 559.047 134.012 l 567.836 134.012 574.914 139.051 574.914 - 145.309 c 574.914 506.715 l 574.914 512.973 567.836 518.012 559.047 518.012 - c 17.07 518.012 l 8.277 518.012 1.199 512.973 1.199 506.715 c 1.199 145.309 - l 1.199 139.051 8.277 134.012 17.07 134.012 c h -S Q -[ 7.2 7.2] 0 d -q 1 0 0 -1 0 645.5 cm -17.07 1.211 m 559.047 1.211 l 567.836 1.211 574.914 6.25 574.914 12.508 - c 574.914 109.914 l 574.914 116.172 567.836 121.211 559.047 121.211 c 17.07 - 121.211 l 8.277 121.211 1.199 116.172 1.199 109.914 c 1.199 12.508 l 1.199 - 6.25 8.277 1.211 17.07 1.211 c h -S Q -BT -19.2 0 0 19.2 8.05715 490.345947 Tm -/f-2-0 1 Tf -[(SPECTRAL ELEMENT METHOD)]TJ -0.0767334 -20.418523 Td -[(AUXILIARY)]TJ --0.119047 27.357143 Td -[(APPLICATION DOMAI)3(N)]TJ -ET 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bc9d5ae1da95e648953d9a6e21b79a2b99527a00..0000000000000000000000000000000000000000 Binary files a/docs/developer-guide/library-design/img/overview.png and /dev/null differ diff --git a/docs/developer-guide/library-design/library-design.tex b/docs/developer-guide/library-design/library-design.tex deleted file mode 100644 index 2c3bd76969a2543241f046de8494db8abd2d1717..0000000000000000000000000000000000000000 --- a/docs/developer-guide/library-design/library-design.tex +++ /dev/null @@ -1,628 +0,0 @@ -\chapter{Library Design} - -A major challenge which arises when one aims to develop a software package that -implements the spectral/hp element method is to implement the mathematical -structure of the method in a digestible and coherent matter. Obviously, there -are many ways to encapsulate the fundamental concepts related to the -spectral/$hp$ element method, depending on e.g. the intended goal of the -developer or the chosen programming language. We will (without going in too much -detail) give a an overview of how we have chosen to abstract and implement -spectral/hp elements in the \nekpp library. However, we want to emphasise that -this is not the only possible choice. - -Five different sublibraries, employing this characteristic pattern, are provided -in the full \nekpp library: - -\begin{itemize} -\item the supporting utilities sublibrary (LibUtilities library) -\item the standard elemental region sublibrary (StdRegions library) -\item the parametric mapping sublibrary (SpatialDomains library) -\item the local elemental region sublibrary (LocalRegions library) -\item the global region sublibrary (MultiRegions library) -\item the solver support sublibrary (SolverUtils library) -\end{itemize} - -This structure can also be related to the formulation of a global spectral/hp -element expansion, i.e. - -\begin{align*} - u(\boldsymbol{x})=\overbrace{\sum_{e\in\mathcal{E}}\underbrace{\sum_{n\in\mathcal{N}}\phi^e_n(\boldsymbol{x})\hat{u}^e_n}_{\mbox{\scriptsize{LocalRegions - library}}}}^{\mbox{\scriptsize{MultiRegions - library}}}=\sum_{e\in\mathcal{E}}\underbrace{\sum_{n\in\mathcal{N}}\phi^{std}_n\overbrace{(\left[\chi^e\right]^{-1}(\boldsymbol{x}))}^{\mbox{\scriptsize{SpatialDomains - library}}}\hat{u}^e_n}_{\mbox{\scriptsize{StdRegions library}}} -\end{align*} - -A more detailed overview of the \nekpp structure is given in -Figure~\ref{f:library:structure}. A diagram showing the most important classes -in the core sub-libraries, is depicted in the Figure~\ref{f:library:overview}. - -\begin{figure} -\centering -\includegraphics[width=0.6\textwidth]{library-design/img/architecture} -\caption{Structural overview of the Nektar++ libraries} -\label{f:library:structure} -\end{figure} - -\begin{figure} -\centering -\includegraphics[width=\textwidth]{img/overview.png} -\caption{Diagram of the important classes in each library.} -\label{f:library:overview} -\end{figure} - -\section{LibUtilities} - -This contains the underlying building blocks for constructing a spectral element -formulation including linear algebra, polynomial routines and memory management -\cite{Ga39,AbSt64,CaHuYoQu88,GhOs70,KaSh05}. This includes: -\begin{itemize} -\setlength{\itemsep}{0em} -\item Basic Constants -\item Basic Utilities ( Nektar++ Arrays) -\item Expression Templates -\item Foundations -\item Interpreter -\item Kernel -\item Linear Algebra -\item Memory Management -\item Nodal Data -\item Polynomial Subroutines -\item Time Integration -\end{itemize} - -\subsection{The Polylib library} -These are routines for orthogonal polynomial calculus and interpolation based on -codes by Einar Ronquist and Ron Henderson. - -\subsubsection{Abbreviations} -\begin{tabular}{ll} -\toprule -Character(s) & Description \\ -\midrule -z & Set of collocation/quadrature points \\ -w & Set of quadrature weights \\ -D & Derivative matrix \\ -h & Lagrange Interpolant \\ -I & Interpolation matrix \\ -g & Gauss \\ -k & Kronrod \\ -gr & Gauss-Radau \\ -gl & Gauss-Lobatto \\ -j & Jacobi \\ -m & point at minus 1 in Radau rules \\ -p & point at plus 1 in Radau rules \\ -\bottomrule -\end{tabular} - - -\subsubsection{Main routines} -\begin{tabular}{ll} -\toprule -\multicolumn{2}{l}{\textbf{Points and Weights}} \\ -Routine & Description \\ -\midrule -zwgj & Compute Gauss-Jacobi points and weights \\ -zwgrjm & Compute Gauss-Radau-Jacobi points and weights (z=-1) \\ -zwgrjp & Compute Gauss-Radau-Jacobi points and weights (z= 1) \\ -zwglj & Compute Gauss-Lobatto-Jacobi points and weights \\ -zwgk & Compute Gauss-Kronrod-Jacobi points and weights \\ -zwrk & Compute Radau-Kronrod points and weights \\ -zwlk & Compute Lobatto-Kronrod points and weights \\ -JacZeros & Compute Gauss-Jacobi points and weights \\ -\bottomrule -\end{tabular} - -\begin{tabular}{ll} -\toprule -\multicolumn{2}{l}{\textbf{Derivative Matrices}} \\ -Routine & Description \\ -\midrule -Dgj & Compute Gauss-Jacobi derivative matrix \\ -Dgrjm & Compute Gauss-Radau-Jacobi derivative matrix (z=-1) \\ -Dgrjp & Compute Gauss-Radau-Jacobi derivative matrix (z= 1) \\ -Dglj & Compute Gauss-Lobatto-Jacobi derivative matrix \\ -\bottomrule -\end{tabular} - -\begin{tabular}{ll} -\toprule -\multicolumn{2}{l}{\textbf{Lagrange Interpolants}} \\ -Routine & Description \\ -\midrule -hgj & Compute Gauss-Jacobi Lagrange interpolants \\ -hgrjm & Compute Gauss-Radau-Jacobi Lagrange interpolants (z=-1) \\ -hgrjp & Compute Gauss-Radau-Jacobi Lagrange interpolants (z= 1) \\ -hglj & Compute Gauss-Lobatto-Jacobi Lagrange interpolants \\ -\bottomrule -\end{tabular} - -\begin{tabular}{ll} -\toprule -\multicolumn{2}{l}{\textbf{Interpolation Operators}} \\ -Routine & Description \\ -\midrule -Imgj & Compute interpolation operator gj->m \\ -Imgrjm & Compute interpolation operator grj->m (z=-1) \\ -Imgrjp & Compute interpolation operator grj->m (z= 1) \\ -Imglj & Compute interpolation operator glj->m \\ -\bottomrule -\end{tabular} - -\begin{tabular}{ll} -\toprule -\multicolumn{2}{l}{\textbf{Polynomial Evaluation}} \\ -Routine & Description \\ -\midrule -jacobfd & Returns value and derivative of Jacobi poly. at point z \\ -jacobd & Returns derivative of Jacobi poly. at point z (valid at z=-1,1) \\ -\bottomrule -\end{tabular} - -\subsubsection{Local routines} -\begin{tabular}{ll} -\toprule -Routine & Description \\ -\midrule -jacobz & Returns Jacobi polynomial zeros \\ -gammaf & Gamma function for integer values and halves \\ -RecCoeff & Calculates the recurrence coefficients for orthogonal poly \\ -TriQL & QL algorithm for symmetrix tridiagonal matrix \\ -JKMatrix & Generates the Jacobi-Kronrod matrix \\ -\bottomrule -\end{tabular} - -\subsubsection{Notes} -\begin{itemize} -\setlength{\itemsep}{0em} -\item Legendre polynomial $\alpha = \beta = 0$ -\item Chebychev polynomial $\alpha = \beta = -0.5$ -\item All routines are double precision. -\item All array subscripts start from zero, i.e. vector $0..N-1$ -\end{itemize} - - - -\section{StdRegions} -The StdRegions library, a summary of which is shown in -Figure~\ref{f:library:stdregions}, bundles all classes that mimic a -spectral/$hp$ element expansion on a standard region. Such an expansion, i.e. -\begin{align*} -u(\boldsymbol{\xi}_i) = - \sum_{n\in\mathcal{N}}\phi_n(\boldsymbol{\xi}_i)\hat{u}_n, -\end{align*} -can be encapsulated in a class that essentially should only contain three data -structures, respectively representing: - -\begin{itemize} -\item the coefficient vector $\hat{\boldsymbol{u}}$, -\item the discrete basis matrix $\boldsymbol{B}$, and -\item the vector $\boldsymbol{u}$ which represents the value of the expansion -at the quadrature points $\boldsymbol{\xi}_i$. -\end{itemize} - -All standard expansions, independent of the dimensionality or shape of the -standard region, can be abstracted in a similar way. Therefore, it is possible -to define these data structures in an \emph{abstract} base class, i.e. the class -!StdExpansion. This base class can also contain the implementation of methods -that are identical across all shapes. Derived from this base class is another -level of abstraction, i.e. the abstract classes StdExpansion1D, StdExpansion2D -and StdExpansion3D. All other shape-specific classes (such as e.g. StdSegExp or -StdQuadExp) are inherited from these abstract base classes. These shape-specific -classes are the classes from which objects will be instantiated. -They also contain the shape-specific implementation for operations such as -integration or differentiation. - -\begin{figure} -\centering -\includegraphics[width=\textwidth]{img/StdRegions.png} -\caption{Main classes in the StdRegions library.} -\label{f:library:stdregions} -\end{figure} - -\section{SpatialDomains} -The most important family of classes in the SpatialDomains library is the -Geometry family, as can also be seen in Figure~\ref{f:library:spatialdomains}. -These classes are the representation of a (geometric) element in \emph{physical -space}. It has been indicated before that every local element can be considered -as an image of the standard element where the corresponding one-to-one mapping -can be represented as an elemental standard spectral/hp expansion. As such, a -proper encapsulation should at least contain data structures that represent such -an expansion in order to completely define the geometry of the element. -Therefore, we have equipped the classes in the Geometry family with the -following data structures: - -\begin{itemize} -\item an object of !StdExpansion class, and -\item a data structure that contains the metric terms (Jacobian, derivative - metrics) of the transformation. -\end{itemize} - -Note that although the latter data structure is not necessary to define the -geometry, it contains information inherent to the iso-parametric representation -of the element that can later be used in e.g. the LocalRegions library. Again, -the StdExpansion object can be defined in the abstract base class Geometry. -However, for every shape-specific geometry class, it needs to be initialised -according to the corresponding StdRegions class (e.g. for the QuadGeom class, -it needs to be initialised as an StdQuadExp object). - -\begin{figure} -\centering -\includegraphics{img/SpatialDomains.png} -\caption{Main classes in the SpatialDomains library.} -\label{f:library:spatialdomains} -\end{figure} - - -\section{LocalRegions} -The LocalRegions library is designed to encompass all classes that encapsulate -the elemental spectral/hp expansions in physical space, see also the figure -below. It can be appreciated that such a local expansion essentially is a -standard expansion that has a (in C++ parlance) additional coordinate -transformation that maps the standard element to the local element. In an -object-oriented context, these is-a and has-a relationships can be applied as -follows: the classes in the !LocalRegions library are derived from the -{!StdExpansion} class tree but they are supplied with an additional data member -representing the geometry of the local element. Depending on the shape-specific -class in the !LocalRegions library, this additional data member is an object of -the corresponding class in the Geometry class structure. This inheritance -between the !LocalRegions and !StdRegions library also allows for a localised -implementation that prevents code duplication. In order to e.g. evaluate the -integral over a local element, the integrand can be multiplied by the Jacobian -of the coordinate transformation, where after the evaluation is redirected to -the !StdRegions implementation. - -This provides extensions of the spectral element formulation into the world. It -provides spatially local forms of the reference space expansions through a -one-to-one linear mapping from a standard straight-sided region to the physical -space, based on the vertices. - -\subsection{Local Mappings} - -\subsubsection{Linear Mappings} -In one dimension this has the form -\begin{align*} -x = \chi(\xi) = \frac{1-\xi}{2}x_{e-1} + \frac{1+\xi}{2}x_e \quad \xi -\Omega^e -\end{align*} - -In two dimensions, for a quadrilateral, each coordinate is given by -\begin{align*} -x_i = \chi(\xi_1,\xi_2) &= x_i^A\frac{1-\xi_1}{2}\frac{1-\xi_2}{2} + -x_i^B\frac{1+\xi_1}{2}\frac{1-\xi_2}{2} \\ &\qquad+ -x_i^D\frac{1-\xi_1}{2}\frac{1+\xi_2}{2} + -x_i^C\frac{1+\xi_1}{2}\frac{1+\xi_2}{2}, \quad i=1,2 -\end{align*} - -\subsubsection{Curvilinear mappings} - -The mapping can be extended to curved-sided regions through the use of an -iso-parametric representation. In contrast to the linear mapping, where only -information about the vertices of the element were required, a curvilinear -mapping requires information about the shape of each side. This is provided by -shape functions, $f^A(\xi_1), f^B(\xi_2), f^C(\xi_1)$ and -$f^D(\xi_2)$, in the local coordinate system. For example, the linear -blending function is given by -\begin{align*} - x_i = \chi_i(\xi_1,\xi_2) &= f^A(\xi_1)\frac{1-\xi_2}{2} + - f^C(\xi_1)\frac{1+\xi_2}{2} + f^B(\xi_2)\frac{1-\xi_1}{2} + - f^D(\xi_2)\frac{1+\xi_1}{2}\\ &\qquad- - \frac{1-\xi_1}{2}\frac{1-\xi_2}{2}f^A(-1) - - \frac{1+\xi_1}{2}\frac{1-\xi_2}{2}f^A(1)\\ &\qquad- - \frac{1-\xi_1}{2}\frac{1+\xi_2}{2}f^C(-1) - - \frac{1+\xi_1}{2}\frac{1+\xi_2}{2}f^C(1) -\end{align*} - -\subsection{Classes} -All local expansions are derived from the top level Expansion base class. Three -classes, Expansion1D, Expansion2D and Expansion3D, are derived from this and -provided base classes for expansions in one-, two- and three- dimensions, -respectively. The various local expansions are derived from these. The class -hierarchy is shown in Figure~\ref{f:library:localregions}. - -One dimension: -\begin{itemize} -\item SegExp - Line expansion, local version of StdRegions::StdSegExp. -\end{itemize} - -Two dimensions: -\begin{itemize} -\item TriExp - Triangular expansion. -\item QuadExp - Quadrilateral expansion. -\end{itemize} - -Three dimensions: -\begin{itemize} -\item TetExp - Tetrehedral expansion. (All triangular faces) -\item HexExp - Hexahedral expansion. (All rectangular faces) -\item PrismExp - Prism expansion. (Two triangular, three rectangular faces) -\item PyrExp - Pyramid expansion. (One rectangular, four triangular faces) -\end{itemize} - -Other classes: -\begin{itemize} -\item PointExp -\item LinSys -\item MatrixKey -\end{itemize} - -\begin{figure} -\centering -\includegraphics[width=\textwidth]{img/LocalRegions.png} -\caption{Main classes in the LocalRegions library.} -\label{f:library:localregions} -\end{figure} - -\section{Collections} -The Collections library contains optimised approaches to performing finite -element operations on multiple elements. Typically, the geometric information is -handled separately to the core reference operator, allowing the reference -operator to be applied to elements stored in contiguous blocks of memory. While -this does not necessarily reduce the operation count, data transfer from -memory to CPU is often substantially reduced and the contiguous storage -structures enable more efficient access, thereby reducing runtime. - -\subsection{Structure} -The top-level container is the \texttt{Collection} class, which manages one or -more LocalRegions objects of the same type (shape and basis). The -\texttt{Operator} class generically describes an operation of these elements. -Derived classes from \texttt{Operator} are created for each specific operation -(e.g. BwdTrans, IProductWRTBase) on each element type. A factory pattern is used -to instantiate the correct class using the key triple (shape, operator, impl). -All classes relating to a particular operator are collated in a single .cpp -file. - -An example template for a specific \texttt{Operator} class is as follows: -\begin{lstlisting}[style=C++Style] -class [[NAME]] : public Operator -{ - public: - OPERATOR_CREATE([[NAME]]) - - virtual ~[[NAME]]() - { - } - - virtual void operator()( - const Array &input, - Array &output, - Array &output1, - Array &output2, - Array &wsp) - { - [[IMPLEMENTATION]] - } - - protected: - [[MEMBERS]] - - private: - [[NAME]]( - vector pCollExp, - CoalescedGeomDataSharedPtr pGeomData) - : Operator(pCollExp, pGeomData) - { - [[INITIALISATION]] - } -}; -\end{lstlisting} -The placeholders in double square brackets should be replaced as follows: -\begin{itemize} - \item \texttt{[[NAME]]}: The name of the class in the form - \begin{lstlisting} - _{_} - \end{lstlisting} - where the shape need only be included if the operator is shape-specific. - \item \texttt{[[MEMBERS]]}: Any member variables necessary to store precomputed - quantities and ensure computational efficiency. - \item \texttt{[[IMPLEMENTATION]]}: The code which actually computes the action - of the operator on the elements in the collection. - \item \texttt{[[INITIALIZATION]]}: Code to initialize member variables and - precomputed quantities. -\end{itemize} - -\subsection{Instantiation} -Operators are instantiated through the OperatorFactory. Therefore the operator -classes must be registered with the factory during start-up. This is achieved -using static initialisation with either the \texttt{m\_type} or -\texttt{m\_typeArr}. The latter is shown in the following example: -\begin{lstlisting}[style=C++Style] -OperatorKey BwdTrans_StdMat::m_typeArr[] = { - GetOperatorFactory().RegisterCreatorFunction( - OperatorKey(eSegment, eBwdTrans, eStdMat,false), - BwdTrans_StdMat::create, "BwdTrans_StdMat_Seg"), - GetOperatorFactory().RegisterCreatorFunction( - OperatorKey(eTriangle, eBwdTrans, eStdMat,false), - BwdTrans_StdMat::create, "BwdTrans_StdMat_Tri"), - ... -}; -\end{lstlisting} -This instructs the factory to use the \texttt{BwdTrans\_StdMat} class for all -shapes when performing a backward transform using the \texttt{StdMat} approach. -In contrast, if the class is shape specific, the non-array member variable would -be initialised, for example: -\begin{lstlisting}[style=C++Style] -OperatorKey BwdTrans_SumFac_Seg::m_type = GetOperatorFactory(). - RegisterCreatorFunction( - OperatorKey(eSegment, eBwdTrans, eSumFac, false), - BwdTrans_SumFac_Seg::create, "BwdTrans_SumFac_Seg"); -\end{lstlisting} - -\section{MultiRegions} -In the MultiRegions library, all classes and routines are related to the -process of assembling a global spectral/hp expansion out of local elemental -contributions are bundled together. The most important entities of this library -are the base class ExpList and its daughter classes. These classes all are the -abstraction of a multi-elemental spectral/hp element expansion. Three different -types of multi-elemental expansions can be distinguished: - -\subsection{A collection of local expansions} -This collection is just a list of local expansions, without any coupling between -the expansions on the different elements, and can be formulated as: -\begin{align*} -u^{\delta}(\boldsymbol{x})=\sum_{e=1}^{{N_{\mathrm{el}}}}\sum_{n=0}^{N^{e}_m-1}\hat{u}_n^e\phi_n^e(\boldsymbol{x}) -\end{align*} -where -\begin{itemize} -\item ${N_{\mathrm{el}}}$ is the number of elements, -\item $N^{e}_m$ is the number of local expansion modes within the -element $e$, -\item $\phi_n^e(\boldsymbol{x})$ is the $n^{th}$ local expansion mode within -the element $e$, -\item $\hat{u}_n^e$ is the $n^{th}$ local expansion coefficient -\item within the element $e$. -\end{itemize} - -These types of expansion are represented by the classes ExpList0D, ExpList1D, -ExpList2D and ExpList3D, depending on the dimension of the problem (ExpList0D is -used just to deal with boundary conditions for 1D expansions). - -\subsection{A multi-elemental discontinuous global expansion} -The expansions are represented by the classes DisContField1D, DisContField2D and -DisContField3D. Objects of these classes should be used when solving partial -differential equations using a discontinuous Galerkin approach. These classes -enforce a coupling between elements and augment the domain with boundary -conditions. - -All local elemental expansions are now connected to form a global spectral/hp -representation. This type of global expansion can be defined as: -\begin{align*} -u^{\delta}(\boldsymbol{x})=\sum_{n=0}^{N_{\mathrm{dof}}-1}\hat{u}_n - \Phi_n(\boldsymbol{x})=\sum_{e=1}^{{N_{\mathrm{el}}}} - \sum_{n=0}^{N^{e}_m-1}\hat{u}_n^e\phi_n^e(\boldsymbol{x}) -\end{align*} -where -\begin{itemize} -\item $N_{\mathrm{dof}}$ refers to the number of global modes, -\item $\Phi_n(\boldsymbol{x})$ is the $n^{th}$ global -expansion mode, -\item $\hat{u}_n$ is the $n^{th}$ global expansion coefficient. -\end{itemize} - -Typically, a mapping array to relate the global degrees of freedom -$\hat{u}_n$ and local degrees of freedom $\hat{u}_n^e$ is -required to assemble the global expansion out of the local contributions. - -In order to solve (second-order) partial differential equations, information - about the boundary conditions should be incorporated in the expansion. In case - of a standard Galerkin implementation, the Dirichlet boundary conditions can be - enforced by lifting a known solution satisfying these conditions, leaving a - homogeneous Dirichlet problem to be solved. If we denote the unknown solution - by $u^{\mathcal{H}}(\boldsymbol{x})$ and the known Dirichlet - boundary conditions by $u^{\mathcal{D}}(\boldsymbol{x})$ then we can - decompose the solution $u^{\delta}(\boldsymbol{x})$ into the form -\begin{align*} - u^{\delta}(\boldsymbol{x}_i)=u^{\mathcal{D}}(\boldsymbol{x}_i)+ - u^{\mathcal{H}}(\boldsymbol{x}_i)=\sum_{n=0}^{N^{\mathcal{D}}-1} - \hat{u}_n^{\mathcal{D}}\Phi_n(\boldsymbol{x}_i)+ - \sum_{n={N^{\mathcal{D}}}}^{N_{\mathrm{dof}}-1} - \hat{u}_n^{\mathcal{H}}\Phi_n(\boldsymbol{x}_i). -\end{align*} -Implementation-wise, the known solution can be lifted by ordering the known -degrees of freedom $\hat{u}_n^{\mathcal{H}}$ first in the global -solution array $\boldsymbol{\hat{u}}$. - - -\subsection{A multi-elemental continuous global expansion} -The discontinuous case is supplimented with a global continuity condition. In -this case a $C^0$ continuity condition is imposed across the element -interfaces and the expansion is therefore globally continuous. - -This type of global continuous expansion which incorporates the boundary - conditions are represented by the classes ContField1D, ContField2D and - ContField3D. Objects of these classes should be used when solving partial - differential equations using a standard Galerkin approach. - - -\subsection{Additional classes} -Furthermore, we have two more sets of classes: -\begin{itemize} -\item The class LocalToGlobalBaseMap and its daughter classes: - LocalToGlobalC0ContMap and LocalToGlobalDGMap. - - These classes are an abstraction of the mapping from local to global degrees - of freedom and contain one or both of the following mapping arrays: - \begin{itemize} - \item map $[e][n]$ - - This array contains the index of the global degree of freedom corresponding - to the $n^{th}$ local expansion mode within the $e^{th}$ element. - \item bmap $[e][n]$ - - This array contains the index of the global degree of freedom corresponding - to the $n^{th}$ local boundary mode within the - $e^{th}$ element. - \end{itemize} - Next to the mapping array, these classes also contain routines to assemble the - global system from the local contributions, and other routines to transform - between local and global level. -\item The classes GlobalLinSys and GlobalLinSysKey. - - The class GlobalLinSys is an abstraction of the global system matrix - resulting from the global assembly procedure. Depending of the choice to - statically condense the global matrix or not, the relevant blocks are stored - as a member of this class. Given a proper right hand side vector, this class - also contains a routine to solve the resulting matrix system. - - The class GlobalLinSysKey represents a key which uniquely defines a global - matrix. This key can be used to construct or retrieve the global matrix - associated to a certain key. -\end{itemize} - -More information about the implementation of connectivity between elements in -Nektar++ can be found [wiki:Connectivity here]. - -\begin{center} -\includegraphics{img/MultiRegions.png} -\end{center} - -\subsection{Quasi-3D approach} - -The Quasi-3D approach is an extension of the 1D and the 2D spectral/hp element -method. This technique permits to study 3D problems combining the spectral/hp -element method with a spectral method. In the Quasi-3D approach with 1 -homogenous direction, the third dimension (z-axis) is expandend with an harmonic -expansion (a Fourier series). In each quadrature point of the Fourier -discretisation we can find a 2D plane discretised with a 2D spectral/hp elements -expasions. In the case with 2 homogeneous directions a plane is discretised with -a 2D Fourier expansion (y-z palne). In each one of the quadrature point of this -harmonic expansion there is a 1D spectral/hp element discretisation. The -homogenous classes derive directly form ExpList, and they are -ExpListHomogeneous1D and ExpListHomogeneous2D. This classes are used to -represent the collections of 2D (or 1D) spectral/hp element problems which are -located in the Fourier expansions quatradure points to create a 3D problem. As -describer above, we can find the find the continuos or discontinuos case, -depending on the spectral/hp element approach. ExpList2DHomogeneous1D and -ExpList1DHomogeneous2D are used to manage boundary conditions. A description of -the Quasi-3D approach usage can be found in Chapter 3 in the User Guide. - -\begin{center} -\includegraphics[width=\textwidth]{img/Quasi3d.png} -\end{center} - - -\section{SolverUtils} - -\subsection{Drivers} -Drivers govern the high-level execution of a solver. - -\subsubsection{Implementing a new Driver} -To take advantage of the Nektar++ architecture and implement an algorithm -which will wrap around an existing solver, new drivers can be created. This can -be done in a few steps by using DriverStandard.cpp (and .h) as a template: -\begin{itemize} -\item Create the new files called DriverMyAlgorithm.cpp (and .h) -\item Implement constructor and destructor -\item Provide implementation for \texttt{v\_InitObject} and \texttt{v\_Execute} -as necessary. -\item Register the new driver with the driver factory. -\begin{lstlisting}[style=C++Style] -string DriverMyAlgorithm::className = - GetDriverFactory().RegisterCreatorFunction("MyAlgorithm", - DriverMyAlgorithm::create); -string DriverMyAlgorithm::driverLookupId = - LibUtilities::SessionReader::RegisterEnumValue("Driver","MyAlgorithm",0); -\end{lstlisting} -\item Add the new driver to the library. In \inlsh{CMakeLists.txt}, -DriverMyAlgorithm.cpp must be added in the \inlsh{SOLVER\_UTILS\_SOURCES} -section and DriverMyAlgorithm.h in the \inlsh{SOLVER\_UTILS\_HEADERS} section. -\end{itemize} diff --git a/docs/developer-guide/memoir.4ht b/docs/developer-guide/memoir.4ht deleted file mode 100644 index ebe2d9aab92a3d53f78a69f4e815edbedfed5758..0000000000000000000000000000000000000000 --- a/docs/developer-guide/memoir.4ht +++ /dev/null @@ -1,68 +0,0 @@ -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% memoir.4ht 2009-05-21-09:32 % -% Copyright (C) 2003--2009 Eitan M. Gurari % -% % -% This work may be distributed and/or modified under the % -% conditions of the LaTeX Project Public License, either % -% version 1.3c of this license or (at your option) any % -% later version. The latest version of this license is % -% in % -% http://www.latex-project.org/lppl.txt % -% and version 1.3c or later is part of all distributions % -% of LaTeX version 2005/12/01 or later. % -% % -% This work has the LPPL maintenance status "maintained".% -% % -% This Current Maintainer of this work % -% is Eitan M. 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\Hnewline}} - - \begin{document} - \DeclareGraphicsExtensions{.pdf,.eps,.png,.jpg,.mp,.mps} - - \Css{ - body { - margin: 0 auto; - max-width: 800px; - background: \#ffffff; - font-family: "Helvetica Neue", Arial, Freesans, clean, sans-serif; - } - h2 {color: \#000000; text-align: right; font-size: 32pt;} - .chapterHead .titlemark { - font-size: 20pt; - } - a { - color: \#000066; - text-decoration: none; - } - a:hover { - color: \#0000ff; - } - img { - max-width: 800px; - } - .figure { - text-align: center; - } - div .caption { - text-align: center; - } - .author { - font-size: 14pt; - } - .lstlisting { - background: \#eeeeee; - margin-left: 20px; - margin-right: 20px; - padding: 5px; - font-family: "Lucida Console", Monaco, monospace; - } - .lstinline { - padding: 2px; - font-family: "Lucida Console", Monaco, monospace; - } - .notebox { - border: 1px solid \#999999; - border-radius: 10px; - background: \#bbbbbb; - padding: 10px; - margin: 10px; - } - .warningbox { - border: 1px solid \#999999; - border-radius: 10px; - background: \#ffbbbb; - padding: 10px; - margin: 10px; - } - .tipbox { - border: 1px solid \#999999; - border-radius: 10px; - background: \#bbffbb; - padding: 10px; - margin: 10px; - } -} - -\EndPreamble diff --git a/docs/user-guide/CMakeLists.txt b/docs/user-guide/CMakeLists.txt index 3ba4e6769b6e1d405f16230f04813d45dd6ec90d..4e73e573f90bd4c0436185ca7aac9110638df04c 100644 --- a/docs/user-guide/CMakeLists.txt +++ b/docs/user-guide/CMakeLists.txt @@ -44,7 +44,9 @@ ADD_CUSTOM_TARGET(user-guide-pdf ${PDFLATEX} --output-directory ${USERGUIDE} ${USERGUIDESRC}/user-guide.tex COMMAND TEXMFOUTPUT=${USERGUIDE} ${BIBTEX} ${USERGUIDE}/user-guide.aux COMMAND TEXMFOUTPUT=${USERGUIDE} ${MAKEINDEX} ${USERGUIDE}/user-guide.idx - COMMAND export TEXINPUTS=${CMAKE_SOURCE_DIR}//: && + COMMAND TEXINPUTS=${CMAKE_SOURCE_DIR}//: + ${PDFLATEX} --output-directory ${USERGUIDE} ${USERGUIDESRC}/user-guide.tex + COMMAND TEXINPUTS=${CMAKE_SOURCE_DIR}//: ${PDFLATEX} --output-directory ${USERGUIDE} ${USERGUIDESRC}/user-guide.tex WORKING_DIRECTORY ${USERGUIDESRC} ) diff --git a/library/MultiRegions/ExpList.h b/library/MultiRegions/ExpList.h index 9821ddde8998f563f1e0d3cc5e75545257b4f228..efbb880287c886e5f74125760afd750f72c6bbbd 100644 --- a/library/MultiRegions/ExpList.h +++ b/library/MultiRegions/ExpList.h @@ -475,11 +475,11 @@ namespace Nektar /** * This operation is evaluated as: * \f{tabbing} - * \hspace{1cm} \= Do \= $e=$ $1, N_{\mathrm{el}}$ \ \ - * \> \> Do \= $i=$ $0,N_m^e-1$ \ \ + * \hspace{1cm} \= Do \= $e=$ $1, N_{\mathrm{el}}$ \\ + * \> \> Do \= $i=$ $0,N_m^e-1$ \\ * \> \> \> $\boldsymbol{\hat{u}}^{e}[i] = \mbox{sign}[e][i] \cdot - * \boldsymbol{\hat{u}}_g[\mbox{map}[e][i]]$ \ \ - * \> \> continue \ \ + * \boldsymbol{\hat{u}}_g[\mbox{map}[e][i]]$ \\ + * \> \> continue \\ * \> continue * \f} * where \a map\f$[e][i]\f$ is the mapping array and \a diff --git a/library/NekMeshUtils/2DGenerator/2DGenerator.cpp b/library/NekMeshUtils/2DGenerator/2DGenerator.cpp index c79f4f237d0b6d7ad217eced7ac64b93c9fa5047..12e1e91677ed232cddd3e5441fb604ec17b03eb3 100644 --- a/library/NekMeshUtils/2DGenerator/2DGenerator.cpp +++ b/library/NekMeshUtils/2DGenerator/2DGenerator.cpp @@ -33,12 +33,15 @@ // //////////////////////////////////////////////////////////////////////////////// #include +#include #include #include #include +#include + using namespace std; namespace Nektar { @@ -55,6 +58,12 @@ Generator2D::Generator2D(MeshSharedPtr m) : ProcessModule(m) ConfigOption(false, "", "Generate parallelograms on these curves"); m_config["blthick"] = ConfigOption(false, "0.0", "Parallelogram layer thickness"); + m_config["periodic"] = + ConfigOption(false, "", "Set of pairs of periodic curves"); + m_config["bltadjust"] = + ConfigOption(false, "2.0", "Boundary layer thickness adjustment"); + m_config["adjustblteverywhere"] = + ConfigOption(true, "0", "Adjust thickness everywhere"); } Generator2D::~Generator2D() @@ -68,12 +77,9 @@ void Generator2D::Process() cout << endl << "2D meshing" << endl; cout << endl << "\tCurve meshing:" << endl << endl; } - m_mesh->m_numNodes = m_mesh->m_cad->GetNumVerts(); - m_thickness_ID = m_thickness.DefineFunction("x y z", m_config["blthick"].as()); - ParseUtils::GenerateSeqVector(m_config["blcurves"].as().c_str(), m_blCurves); @@ -85,10 +91,8 @@ void Generator2D::Process() LibUtilities::PrintProgressbar(i, m_mesh->m_cad->GetNumCurve(), "Curve progress"); } - vector::iterator f = find(m_blCurves.begin(), m_blCurves.end(), i); - if (f == m_blCurves.end()) { m_curvemeshes[i] = @@ -99,17 +103,24 @@ void Generator2D::Process() m_curvemeshes[i] = MemoryManager::AllocateSharedPtr( i, m_mesh, m_config["blthick"].as()); } - m_curvemeshes[i]->Mesh(); } + //////// + // consider periodic curves + + if (m_config["periodic"].beenSet) + { + PeriodicPrep(); + MakePeriodic(); + } + //////////////////////////////////////// if (m_config["blcurves"].beenSet) { // we need to do the boundary layer generation in a face by face basis MakeBLPrep(); - for (int i = 1; i <= m_mesh->m_cad->GetNumSurf(); i++) { MakeBL(i); @@ -120,7 +131,6 @@ void Generator2D::Process() { cout << endl << "\tFace meshing:" << endl << endl; } - // linear mesh all surfaces for (int i = 1; i <= m_mesh->m_cad->GetNumSurf(); i++) { @@ -130,9 +140,8 @@ void Generator2D::Process() "Face progress"); } - m_facemeshes[i] = - MemoryManager::AllocateSharedPtr(i,m_mesh, - m_curvemeshes, 99+i); + m_facemeshes[i] = MemoryManager::AllocateSharedPtr( + i, m_mesh, m_curvemeshes, 99 + i); m_facemeshes[i]->Mesh(); } @@ -144,28 +153,25 @@ void Generator2D::Process() vector ns; ns.push_back((*it)->m_n1); ns.push_back((*it)->m_n2); - // for each iterator create a LibUtilities::eSegement // push segment into m_mesh->m_element[1] // tag for the elements shoudl be the CAD number of the curves - ElmtConfig conf(LibUtilities::eSegment, 1, false, false); - vector tags; tags.push_back((*it)->m_parentCAD->GetId()); - ElementSharedPtr E2 = GetElementFactory().CreateInstance( LibUtilities::eSegment, conf, ns, tags); - m_mesh->m_element[1].push_back(E2); } + // m_mesh->m_expDim = 1; + // m_mesh->m_element[2].clear(); + ProcessVertices(); ProcessEdges(); ProcessFaces(); ProcessElements(); ProcessComposites(); - Report(); } @@ -193,17 +199,13 @@ void Generator2D::MakeBLPrep() void Generator2D::MakeBL(int faceid) { map > edgeNormals; - int eid = 0; - for (vector::iterator it = m_blCurves.begin(); it != m_blCurves.end(); ++it) { CADOrientation::Orientation edgeo = m_mesh->m_cad->GetCurve(*it)->GetOrienationWRT(faceid); - vector es = m_curvemeshes[*it]->GetMeshEdges(); - // on each !!!EDGE!!! calculate a normal // always to the left unless edgeo is 1 // normal must be done in the parametric space (and then projected back) @@ -214,57 +216,70 @@ void Generator2D::MakeBL(int faceid) Array p1, p2; p1 = es[j]->m_n1->GetCADSurfInfo(faceid); p2 = es[j]->m_n2->GetCADSurfInfo(faceid); + Array n(2); + n[0] = p1[1] - p2[1]; + n[1] = p2[0] - p1[0]; if (edgeo == CADOrientation::eBackwards) { - swap(p1, p2); + n[0] *= -1.0; + n[1] *= -1.0; } - Array n(2); - n[0] = p1[1] - p2[1]; - n[1] = p2[0] - p1[0]; NekDouble mag = sqrt(n[0] * n[0] + n[1] * n[1]); n[0] /= mag; n[1] /= mag; - - Array np = es[j]->m_n1->GetCADSurfInfo(faceid); - np[0] += n[0]; - np[1] += n[1]; - + Array np(2); + np[0] = p1[0] + n[0]; + np[1] = p1[1] + n[1]; Array loc = es[j]->m_n1->GetLoc(); Array locp = m_mesh->m_cad->GetSurf(faceid)->P(np); - n[0] = locp[0] - loc[0]; n[1] = locp[1] - loc[1]; mag = sqrt(n[0] * n[0] + n[1] * n[1]); n[0] /= mag; n[1] /= mag; - edgeNormals[es[j]->m_id] = n; } } + bool adjust = m_config["bltadjust"].beenSet; + NekDouble divider = m_config["bltadjust"].as(); + bool adjustEverywhere = m_config["adjustblteverywhere"].beenSet; + + if (divider < 2.0) + { + WARNINGL1(false, "BndLayerAdjustment too low, corrected to 2.0"); + divider = 2.0; + } + map nodeNormals; map >::iterator it; for (it = m_nodesToEdge.begin(); it != m_nodesToEdge.end(); it++) { - Array n(3); + Array n(3, 0.0); ASSERTL0(it->second.size() == 2, "wierdness, most likely bl_surfs are incorrect"); Array n1 = edgeNormals[it->second[0]->m_id]; Array n2 = edgeNormals[it->second[1]->m_id]; - n[0] = (n1[0] + n2[0]) / 2.0; n[1] = (n1[1] + n2[1]) / 2.0; NekDouble mag = sqrt(n[0] * n[0] + n[1] * n[1]); n[0] /= mag; n[1] /= mag; - NekDouble t = m_thickness.Evaluate(m_thickness_ID, it->first->m_x, it->first->m_y, 0.0, 0.0); + // Adjust thickness according to angle between normals + if (adjust) + { + if (adjustEverywhere || it->first->GetNumCadCurve() > 1) + { + NekDouble angle = acos(n1[0] * n2[0] + n1[1] * n2[1]); + angle = (angle > M_PI) ? 2 * M_PI - angle : angle; + t /= cos(angle / divider); + } + } - n[0] = n[0] * t + it->first->m_x; - n[1] = n[1] * t + it->first->m_y; - n[2] = 0.0; - + n[0] = n[0] * t + it->first->m_x; + n[1] = n[1] * t + it->first->m_y; NodeSharedPtr nn = boost::shared_ptr( new Node(m_mesh->m_numNodes++, n[0], n[1], 0.0)); CADSurfSharedPtr s = m_mesh->m_cad->GetSurf(faceid); @@ -278,7 +293,6 @@ void Generator2D::MakeBL(int faceid) { CADOrientation::Orientation edgeo = m_mesh->m_cad->GetCurve(*it)->GetOrienationWRT(faceid); - vector ns = m_curvemeshes[*it]->GetMeshPoints(); vector newNs; for (int i = 0; i < ns.size(); i++) @@ -287,7 +301,6 @@ void Generator2D::MakeBL(int faceid) } m_curvemeshes[*it] = MemoryManager::AllocateSharedPtr(*it, m_mesh, newNs); - if (edgeo == CADOrientation::eBackwards) { reverse(ns.begin(), ns.end()); @@ -295,22 +308,16 @@ void Generator2D::MakeBL(int faceid) for (int i = 0; i < ns.size() - 1; ++i) { vector qns; - qns.push_back(ns[i]); qns.push_back(ns[i + 1]); qns.push_back(nodeNormals[ns[i + 1]]); qns.push_back(nodeNormals[ns[i]]); - ElmtConfig conf(LibUtilities::eQuadrilateral, 1, false, false); - vector tags; tags.push_back(101); - ElementSharedPtr E = GetElementFactory().CreateInstance( LibUtilities::eQuadrilateral, conf, qns, tags); - E->m_parentCAD = m_mesh->m_cad->GetSurf(faceid); - for (int j = 0; j < E->GetEdgeCount(); ++j) { pair testIns; @@ -328,6 +335,60 @@ void Generator2D::MakeBL(int faceid) } } +void Generator2D::PeriodicPrep() +{ + m_periodicPairs.clear(); + set periodic; + + // Build periodic curve pairs + string s = m_config["periodic"].as(); + vector lines; + + boost::split(lines, s, boost::is_any_of(":")); + + for (vector::iterator il = lines.begin(); il != lines.end(); ++il) + { + vector tmp; + boost::split(tmp, *il, boost::is_any_of(",")); + + ASSERTL0(tmp.size() == 2, "periodic pairs ill-defined"); + + vector data(2); + data[0] = boost::lexical_cast(tmp[0]); + data[1] = boost::lexical_cast(tmp[1]); + + ASSERTL0(!periodic.count(data[0]), "curve already periodic"); + ASSERTL0(!periodic.count(data[1]), "curve already periodic"); + + m_periodicPairs[data[0]] = data[1]; + periodic.insert(data[0]); + periodic.insert(data[1]); + } +} + +void Generator2D::MakePeriodic() +{ + // Override slave curves + + for (map::iterator ip = m_periodicPairs.begin(); + ip != m_periodicPairs.end(); ++ip) + { + m_curvemeshes[ip->second]->PeriodicOverwrite(m_curvemeshes[ip->first]); + } + + if (m_mesh->m_verbose) + { + cout << "\t\tPeriodic boundary conditions" << endl; + for (map::iterator it = m_periodicPairs.begin(); + it != m_periodicPairs.end(); ++it) + { + cout << "\t\t\tCurves " << it->first << " => " << it->second + << endl; + } + cout << endl; + } +} + void Generator2D::Report() { if (m_mesh->m_verbose) diff --git a/library/NekMeshUtils/2DGenerator/2DGenerator.h b/library/NekMeshUtils/2DGenerator/2DGenerator.h index 29d64e08ead96a04c6b470d9e541fcf7bbc50f5d..15100475eb84b5023713be4c76398ee9785efec0 100644 --- a/library/NekMeshUtils/2DGenerator/2DGenerator.h +++ b/library/NekMeshUtils/2DGenerator/2DGenerator.h @@ -61,14 +61,18 @@ public: static ModuleKey className; Generator2D(MeshSharedPtr m); + virtual ~Generator2D(); virtual void Process(); private: - void MakeBLPrep(); + void PeriodicPrep(); + + void MakePeriodic(); + void MakeBL(int faceid); void Report(); @@ -76,6 +80,8 @@ private: std::map m_facemeshes; /// map of individual curve meshes of the curves in the domain std::map m_curvemeshes; + /// map of periodic curve pairs + std::map m_periodicPairs; std::vector m_blCurves; LibUtilities::AnalyticExpressionEvaluator m_thickness; diff --git a/library/NekMeshUtils/CADSystem/CADSystem.cpp b/library/NekMeshUtils/CADSystem/CADSystem.cpp index e914ef9142d8e9a3e02c74daf6b2c45edfe63d1e..3b2d1a1751218deb97a44817fbf97be6b7b85c19 100644 --- a/library/NekMeshUtils/CADSystem/CADSystem.cpp +++ b/library/NekMeshUtils/CADSystem/CADSystem.cpp @@ -33,10 +33,10 @@ // //////////////////////////////////////////////////////////////////////////////// -#include -#include #include #include +#include +#include using namespace std; @@ -45,7 +45,7 @@ namespace Nektar namespace NekMeshUtils { -EngineFactory& GetEngineFactory() +EngineFactory &GetEngineFactory() { typedef Loki::SingletonHolder @@ -53,7 +53,7 @@ EngineFactory& GetEngineFactory() return Type::Instance(); } -CADVertFactory& GetCADVertFactory() +CADVertFactory &GetCADVertFactory() { typedef Loki::SingletonHolder @@ -61,7 +61,7 @@ CADVertFactory& GetCADVertFactory() return Type::Instance(); } -CADCurveFactory& GetCADCurveFactory() +CADCurveFactory &GetCADCurveFactory() { typedef Loki::SingletonHolder @@ -69,7 +69,7 @@ CADCurveFactory& GetCADCurveFactory() return Type::Instance(); } -CADSurfFactory& GetCADSurfFactory() +CADSurfFactory &GetCADSurfFactory() { typedef Loki::SingletonHolder @@ -77,5 +77,37 @@ CADSurfFactory& GetCADSurfFactory() return Type::Instance(); } +Array CADSystem::GetPeriodicTranslationVector(int first, + int second) +{ + ASSERTL0(GetNumSurf() == 1, "wont work for multi surfaces yet"); + + CADCurveSharedPtr c1 = GetCurve(first); + CADCurveSharedPtr c2 = GetCurve(second); + + NekDouble tst = c1->GetTotLength() - c2->GetTotLength(); + ASSERTL0(fabs(tst) < 1e-6, "periodic curves not same length"); + + vector v1 = c1->GetVertex(); + Array p1 = v1[0]->GetLoc(); + + Array p2; + vector v2 = c2->GetVertex(); + if (c1->GetOrienationWRT(1) == c2->GetOrienationWRT(1)) + { + p2 = v2[1]->GetLoc(); + } + else + { + p2 = v2[0]->GetLoc(); + } + + Array ret(3); + ret[0] = p2[0] - p1[0]; + ret[1] = p2[1] - p1[1]; + ret[2] = p2[2] - p1[2]; + + return ret; +} } } diff --git a/library/NekMeshUtils/CADSystem/CADSystem.h b/library/NekMeshUtils/CADSystem/CADSystem.h index bed9bda644084d588c5c9d3db7f3631f544ca0f9..b86df6c18a8e0e7ed05b232a44cf0dfe010c61ad 100644 --- a/library/NekMeshUtils/CADSystem/CADSystem.h +++ b/library/NekMeshUtils/CADSystem/CADSystem.h @@ -43,6 +43,8 @@ #include +#include + #include "CADObject.h" namespace Nektar @@ -201,6 +203,9 @@ public: return m_verts.size(); } + NEKMESHUTILS_EXPORT Array GetPeriodicTranslationVector( + int first, int second); + protected: /// Name of cad file std::string m_name; diff --git a/library/NekMeshUtils/CADSystem/OCE/CADSurfOCE.cpp b/library/NekMeshUtils/CADSystem/OCE/CADSurfOCE.cpp index 9a72cdf6d7280451a0f031a27c8ca6b690b0c781..e0d9b838e7359d115b154b05abbe64819336e981 100644 --- a/library/NekMeshUtils/CADSystem/OCE/CADSurfOCE.cpp +++ b/library/NekMeshUtils/CADSystem/OCE/CADSurfOCE.cpp @@ -61,8 +61,8 @@ void CADSurfOCE::Initialise(int i, TopoDS_Shape in) gp_Pnt ori(0.0, 0.0, 0.0); transform.SetScale(ori, 1.0 / 1000.0); TopLoc_Location mv(transform); - in.Move(mv); + m_occSurface = BRepAdaptor_Surface(TopoDS::Face(in)); m_id = i; @@ -85,14 +85,14 @@ Array CADSurfOCE::locuv(Array p) Array uvr(2); - gp_Pnt2d p2 = m_sas->ValueOfUV(loc, 1e-3); + gp_Pnt2d p2 = m_sas->ValueOfUV(loc, Precision::Confusion()); uvr[0] = p2.X(); uvr[1] = p2.Y(); gp_Pnt p3 = m_sas->Value(p2); - if (p3.Distance(loc) > 1.0) + if (p3.Distance(loc) > 1e-6) { - cout << "large locuv distance " << p3.Distance(loc) << " " << m_id + cout << "large locuv distance " << p3.Distance(loc)/1000.0 << " " << m_id << endl; } @@ -173,13 +173,9 @@ NekDouble CADSurfOCE::DistanceTo(Array p) { gp_Pnt loc(p[0] * 1000.0, p[1] * 1000.0, p[2] * 1000.0); - // alternative locuv methods - ShapeAnalysis_Surface sas(m_s); - sas.SetDomain(m_bounds[0], m_bounds[1], m_bounds[2], m_bounds[3]); - - gp_Pnt2d p2 = sas.ValueOfUV(loc, 1e-7); + gp_Pnt2d p2 = m_sas->ValueOfUV(loc, Precision::Confusion()); - gp_Pnt p3 = sas.Value(p2); + gp_Pnt p3 = m_sas->Value(p2); return p3.Distance(loc); } @@ -189,13 +185,9 @@ void CADSurfOCE::ProjectTo(Array &tp, { gp_Pnt loc(tp[0] * 1000.0, tp[1] * 1000.0, tp[2] * 1000.0); - // alternative locuv methods - ShapeAnalysis_Surface sas(m_s); - sas.SetDomain(m_bounds[0], m_bounds[1], m_bounds[2], m_bounds[3]); - - gp_Pnt2d p2 = sas.ValueOfUV(loc, 1e-7); + gp_Pnt2d p2 = m_sas->ValueOfUV(loc, Precision::Confusion()); - gp_Pnt p3 = sas.Value(p2); + gp_Pnt p3 = m_sas->Value(p2); tp[0] = p3.X() / 1000.0; tp[1] = p3.Y() / 1000.0; @@ -226,7 +218,7 @@ Array CADSurfOCE::N(Array uv) Test(uv); #endif - BRepLProp_SLProps slp(m_occSurface, 2, 1e-6); + BRepLProp_SLProps slp(m_occSurface, 2, 1e-8); slp.SetParameters(uv[0], uv[1]); if (!slp.IsNormalDefined()) diff --git a/library/NekMeshUtils/CADSystem/OCE/OpenCascade.h b/library/NekMeshUtils/CADSystem/OCE/OpenCascade.h index 5f8ea570e3d7d38ef8a4970fe7495c37058fc8e1..abbde7f0c8fc48084b6ddb71f96ecb8996407205 100644 --- a/library/NekMeshUtils/CADSystem/OCE/OpenCascade.h +++ b/library/NekMeshUtils/CADSystem/OCE/OpenCascade.h @@ -71,6 +71,7 @@ #include #include #include +#include #include #include diff --git a/library/NekMeshUtils/MeshElements/Quadrilateral.cpp b/library/NekMeshUtils/MeshElements/Quadrilateral.cpp index b7bf0c919bab612a42d24e30d336e792a1ec21c6..d144f75dfa77479d95c27e3c3e002350a21b9cee 100644 --- a/library/NekMeshUtils/MeshElements/Quadrilateral.cpp +++ b/library/NekMeshUtils/MeshElements/Quadrilateral.cpp @@ -105,6 +105,7 @@ Quadrilateral::Quadrilateral(ElmtConfig pConf, if (sum > 0.0) { reverse(m_edge.begin(), m_edge.end()); + swap(m_vertex[1], m_vertex[3]); } } diff --git a/library/NekMeshUtils/SurfaceMeshing/CurveMesh.cpp b/library/NekMeshUtils/SurfaceMeshing/CurveMesh.cpp index 7b43ffd4f9d425f2fb4cf0874b57e8131d7a60b5..33481fd6e6eab09b97f31138bc17bf8543c035be 100644 --- a/library/NekMeshUtils/SurfaceMeshing/CurveMesh.cpp +++ b/library/NekMeshUtils/SurfaceMeshing/CurveMesh.cpp @@ -353,5 +353,71 @@ void CurveMesh::GetSampleFunction() m_dst[i] = dsti; } } + +void CurveMesh::PeriodicOverwrite(CurveMeshSharedPtr from) +{ + //clear current mesh points and remove edges from edgeset + m_meshpoints.clear(); + for (int i = 0; i < m_meshedges.size(); i++) + { + m_mesh->m_edgeSet.erase(m_meshedges[i]); + } + m_meshedges.clear(); + + /////// + + int tid = from->GetId(); + Array T = + m_mesh->m_cad->GetPeriodicTranslationVector(tid, m_id); + + CADCurveSharedPtr c1 = m_mesh->m_cad->GetCurve(tid); + + bool reversed = c1->GetOrienationWRT(1) == m_cadcurve->GetOrienationWRT(1); + + vector nodes = from->GetMeshPoints(); + + vector > surfs = + m_cadcurve->GetAdjSurf(); + + for (int i = 1; i < nodes.size() - 1; i++) + { + Array loc = nodes[i]->GetLoc(); + NodeSharedPtr nn = NodeSharedPtr(new Node( + m_mesh->m_numNodes++, loc[0] + T[0], loc[1] + T[1], 0.0)); + + for (int j = 0; j < surfs.size(); j++) + { + nn->SetCADSurf(surfs[j].first->GetId(), surfs[j].first, + surfs[j].first->locuv(nn->GetLoc())); + } + + nn->SetCADCurve(m_id, m_cadcurve, m_cadcurve->loct(nn->GetLoc())); + + m_meshpoints.push_back(nn); + } + + // Reverse internal nodes of the vector if necessary + if (reversed) + { + reverse(m_meshpoints.begin(), m_meshpoints.end()); + } + + vector verts = m_cadcurve->GetVertex(); + + m_meshpoints.insert(m_meshpoints.begin(), verts[0]->GetNode()); + m_meshpoints.push_back(verts[1]->GetNode()); + //dont need to realign cad for vertices + + // make edges and add them to the edgeset for the face mesher to use + for (int i = 0; i < m_meshpoints.size() - 1; i++) + { + EdgeSharedPtr e = boost::shared_ptr( + new Edge(m_meshpoints[i], m_meshpoints[i + 1])); + e->m_parentCAD = m_cadcurve; + m_mesh->m_edgeSet.insert(e); + m_meshedges.push_back(e); + } +} + } } diff --git a/library/NekMeshUtils/SurfaceMeshing/CurveMesh.h b/library/NekMeshUtils/SurfaceMeshing/CurveMesh.h index accf248c8ef224aba59318ffc7183d01f6da557b..1075a6b311f2a7872ff5f2b119538ae4bb68ee3f 100644 --- a/library/NekMeshUtils/SurfaceMeshing/CurveMesh.h +++ b/library/NekMeshUtils/SurfaceMeshing/CurveMesh.h @@ -54,6 +54,10 @@ namespace Nektar namespace NekMeshUtils { +//forward +class CurveMesh; +typedef boost::shared_ptr CurveMeshSharedPtr; + class CurveMesh { public: @@ -125,6 +129,13 @@ public: return m_curvelength; } + void PeriodicOverwrite(CurveMeshSharedPtr from); + + int GetId() + { + return m_id; + } + private: /** * @brief get node spacing sampling function @@ -179,7 +190,6 @@ private: int m_blID; }; -typedef boost::shared_ptr CurveMeshSharedPtr; } } diff --git a/utilities/NekMesh/InputModules/InputMCF.cpp b/utilities/NekMesh/InputModules/InputMCF.cpp index 79e4a68f76a6ceec23a52483d34409a40b6cb8d7..a768bd6ffbadc69e2e76a918a1b818d9e5256a41 100644 --- a/utilities/NekMesh/InputModules/InputMCF.cpp +++ b/utilities/NekMesh/InputModules/InputMCF.cpp @@ -33,8 +33,12 @@ // //////////////////////////////////////////////////////////////////////////////// +#include #include + +#include + #include #include @@ -151,7 +155,22 @@ void InputMCF::ParseFile(string nm) } } - map::iterator it; + set periodic; + if (pSession->DefinesElement("NEKTAR/MESHING/PERIODIC")) + { + TiXmlElement *per = mcf->FirstChildElement("PERIODIC"); + TiXmlElement *pair = per->FirstChildElement("P"); + + while (pair) + { + string tmp; + pair->QueryStringAttribute("PAIR", &tmp); + periodic.insert(tmp); + pair = pair->NextSiblingElement("P"); + } + } + + map::iterator it; it = information.find("CADFile"); ASSERTL0(it != information.end(), "no cadfile defined"); @@ -161,12 +180,13 @@ void InputMCF::ParseFile(string nm) ASSERTL0(it != information.end(), "no meshtype defined"); m_makeBL = it->second == "3DBndLayer"; m_2D = it->second == "2D"; + m_manifold = it->second == "Manifold"; if (it->second == "2DBndLayer") { m_makeBL = true; m_2D = true; } - if (!m_makeBL && !m_2D) + if (!m_makeBL && !m_2D && !m_manifold) { ASSERTL0(it->second == "3D", "unsure on MeshType") } @@ -205,6 +225,17 @@ void InputMCF::ParseFile(string nm) it = parameters.find("BndLayerProgression"); m_blprog = it != parameters.end() ? it->second : "2.0"; } + + it = parameters.find("BndLayerAdjustment"); + if (it != parameters.end()) + { + m_adjust = true; + m_adjustment = it->second; + } + else + { + m_adjust = false; + } } m_naca = false; @@ -233,12 +264,14 @@ void InputMCF::ParseFile(string nm) } set::iterator sit; - sit = boolparameters.find("SurfaceOptimiser"); - m_surfopti = sit != boolparameters.end(); - sit = boolparameters.find("WriteOctree"); - m_woct = sit != boolparameters.end(); - sit = boolparameters.find("VariationalOptimiser"); - m_varopti = sit != boolparameters.end(); + sit = boolparameters.find("SurfaceOptimiser"); + m_surfopti = sit != boolparameters.end(); + sit = boolparameters.find("WriteOctree"); + m_woct = sit != boolparameters.end(); + sit = boolparameters.find("VariationalOptimiser"); + m_varopti = sit != boolparameters.end(); + sit = boolparameters.find("BndLayerAdjustEverywhere"); + m_adjustall = sit != boolparameters.end(); m_refine = refinement.size() > 0; if (m_refine) @@ -252,6 +285,18 @@ void InputMCF::ParseFile(string nm) m_refinement = ss.str(); m_refinement.erase(m_refinement.end() - 1); } + + if (periodic.size() > 0) + { + stringstream ss; + for (sit = periodic.begin(); sit != periodic.end(); ++sit) + { + ss << *sit; + ss << ":"; + } + m_periodic = ss.str(); + m_periodic.erase(m_periodic.end() - 1); + } } void InputMCF::Process() @@ -302,7 +347,8 @@ void InputMCF::Process() ////**** LINEAR MESHING ****//// if (m_2D) { - m_mesh->m_expDim = 2; + ////**** 2DGenerator ****//// + m_mesh->m_expDim = 2; m_mesh->m_spaceDim = 2; module = GetModuleFactory().CreateInstance( ModuleKey(eProcessModule, "2dgenerator"), m_mesh); @@ -352,36 +398,44 @@ void InputMCF::Process() return; } - ////**** VolumeMesh ****//// - module = GetModuleFactory().CreateInstance( - ModuleKey(eProcessModule, "volumemesh"), m_mesh); - if (m_makeBL) - { - module->RegisterConfig("blsurfs", m_blsurfs); - module->RegisterConfig("blthick", m_blthick); - module->RegisterConfig("bllayers", m_bllayers); - module->RegisterConfig("blprog", m_blprog); - } - - try + if(m_manifold) { - module->SetDefaults(); - module->Process(); + //dont want to volume mesh + m_mesh->m_expDim = 2; } - catch (runtime_error &e) + else { - cout << "Volume meshing has failed with message:" << endl; - cout << e.what() << endl; - cout << "The linear surface mesh be dumped as a manifold mesh" - << endl; - m_mesh->m_expDim = 2; - m_mesh->m_element[3].clear(); - ProcessVertices(); - ProcessEdges(); - ProcessFaces(); - ProcessElements(); - ProcessComposites(); - return; + ////**** VolumeMesh ****//// + module = GetModuleFactory().CreateInstance( + ModuleKey(eProcessModule, "volumemesh"), m_mesh); + if (m_makeBL) + { + module->RegisterConfig("blsurfs", m_blsurfs); + module->RegisterConfig("blthick", m_blthick); + module->RegisterConfig("bllayers", m_bllayers); + module->RegisterConfig("blprog", m_blprog); + } + + try + { + module->SetDefaults(); + module->Process(); + } + catch (runtime_error &e) + { + cout << "Volume meshing has failed with message:" << endl; + cout << e.what() << endl; + cout << "The linear surface mesh be dumped as a manifold mesh" + << endl; + m_mesh->m_expDim = 2; + m_mesh->m_element[3].clear(); + ProcessVertices(); + ProcessEdges(); + ProcessFaces(); + ProcessElements(); + ProcessComposites(); + return; + } } } @@ -463,7 +517,26 @@ void InputMCF::Process() } } + ////**** Peralign ****//// + if (m_2D && m_periodic.size()) + { + vector lines; + boost::split(lines, m_periodic, boost::is_any_of(":")); + + for (vector::iterator il = lines.begin(); il != lines.end(); + ++il) + { + module = GetModuleFactory().CreateInstance( + ModuleKey(eProcessModule, "peralign"), m_mesh); + + vector tmp(2); + boost::split(tmp, *il, boost::is_any_of(",")); + module->RegisterConfig("surf1", tmp[0]); + } + module->SetDefaults(); + module->Process(); + } } } } diff --git a/utilities/NekMesh/InputModules/InputMCF.h b/utilities/NekMesh/InputModules/InputMCF.h index 31b31f2e4874f653c2b0ea662bf7393cf0a34a01..1073e3a9b951f6d901d6948c5f60f0847846ce25 100644 --- a/utilities/NekMesh/InputModules/InputMCF.h +++ b/utilities/NekMesh/InputModules/InputMCF.h @@ -63,9 +63,10 @@ public: private: std::string m_minDelta, m_maxDelta, m_eps, m_cadfile, m_order, m_blsurfs, m_blthick, m_blprog, m_bllayers, m_refinement, - m_nacadomain; + m_nacadomain, m_periodic, m_adjustment; + bool m_makeBL, m_surfopti, m_varopti, m_refine, m_woct, m_2D, m_splitBL, - m_naca; + m_naca, m_adjust, m_adjustall, m_manifold; }; } diff --git a/utilities/NekMesh/ProcessModules/ProcessPerAlign.cpp b/utilities/NekMesh/ProcessModules/ProcessPerAlign.cpp index fea1e4e43da84a4541a5fd42a5f2e52d3ee4de1d..14053d35048dd1e5886f8fa33944c4cdbe8fee31 100644 --- a/utilities/NekMesh/ProcessModules/ProcessPerAlign.cpp +++ b/utilities/NekMesh/ProcessModules/ProcessPerAlign.cpp @@ -44,6 +44,8 @@ #include "ProcessPerAlign.h" +#include + using namespace std; using namespace Nektar::NekMeshUtils; @@ -70,7 +72,8 @@ ProcessPerAlign::ProcessPerAlign(MeshSharedPtr m) : ProcessModule(m) m_config["surf2"] = ConfigOption(false, "-1", "Tag identifying first surface."); m_config["dir"] = ConfigOption( - false, "", "Direction in which to align (either x, y, or z)"); + false, "", "Direction in which to align (either x, y, or z; " + "or vector with components separated by a comma)"); m_config["orient"] = ConfigOption(true, "0", "Attempt to reorient tets and prisms"); } @@ -103,17 +106,49 @@ void ProcessPerAlign::Process() return; } - if (dir != "x" && dir != "y" && dir != "z") - { - cerr << "WARNING: dir must be set to either x, y or z. " - << "Skipping periodic alignment." << endl; - return; - } + vector tmp1; + boost::split(tmp1, dir, boost::is_any_of(",")); NekDouble vec[3]; - vec[0] = dir == "x" ? 1.0 : 0.0; - vec[1] = dir == "y" ? 1.0 : 0.0; - vec[2] = dir == "z" ? 1.0 : 0.0; + + if (tmp1.size() == 1) + { + //if the direction is not specified and its a 2D mesh and there is CAD + //it can figure out the dir on its own + if (!dir.size() && m_mesh->m_spaceDim == 2 && m_mesh->m_cad) + { + Array T = + m_mesh->m_cad->GetPeriodicTranslationVector(surf1, surf2); + NekDouble mag = sqrt(T[0] * T[0] + T[1] * T[1]); + + vec[0] = T[0] / mag; + vec[1] = T[1] / mag; + vec[2] = T[2] / mag; + } + else + { + if (dir != "x" && dir != "y" && dir != "z") + { + cerr << "WARNING: dir must be set to either x, y or z. " + << "Skipping periodic alignment." << endl; + return; + } + + vec[0] = dir == "x" ? 1.0 : 0.0; + vec[1] = dir == "y" ? 1.0 : 0.0; + vec[2] = dir == "z" ? 1.0 : 0.0; + } + } + else if (tmp1.size() == 3) + { + vec[0] = boost::lexical_cast(tmp1[0]); + vec[1] = boost::lexical_cast(tmp1[1]); + vec[2] = boost::lexical_cast(tmp1[2]); + } + else + { + ASSERTL0(false,"expected three components or letter for direction"); + } CompositeMap::iterator it1 = m_mesh->m_composite.find(surf1); CompositeMap::iterator it2 = m_mesh->m_composite.find(surf2); diff --git a/utilities/NekMesh/Tests/MeshGen/2d-naca.mcf b/utilities/NekMesh/Tests/MeshGen/2d-naca.mcf index 6e6ca06f88edb13f0127cf051cb26c8bff6dac79..5ac8b86b05f8f3b3f88e443aa54a4d7fe1421555 100644 --- a/utilities/NekMesh/Tests/MeshGen/2d-naca.mcf +++ b/utilities/NekMesh/Tests/MeshGen/2d-naca.mcf @@ -16,6 +16,8 @@

+

+

@@ -24,6 +26,7 @@ +