mike first load

developers-guide.bib

+@book{KaSh05,
+  title={Spectral/hp element methods for Computational Fluid Dynamics (Second Edition)},
+  author={George Em Karniadakis and Spencer J. Sherwin},
+  year={2005},
+  publisher={Oxford University Press}
+}
+
+@book{Schwab,
+  title={p-- and hp-- Finite Element Methods: Theory and Applications in Solid and Fluid Mechanics},
+  author={Ch. Schwab},
+  year={1999},
+  publisher={Oxford University Press}
+}
+
+@book{KFN-testing,
+title = {Testing Computer Software},
+author = {Cem Kaner and Jack Falk and Hung Quoc Nguyen},
+year = {2010},
+publisher={John Wiley \& Sons}
+}
+
+@book{CanutoHQZ87,
+       author="C. Canuto and M.Y. Hussaini and A. Quarteroni and T.A. Zang",
+       title="{Spectral Methods in Fluid Mechanics}", 
+       publisher="{Springer-Verlag, New York}",
+       year="1987" }
+
+
+@book{Funaro92,
+       author="D. Funaro",
+       title="{Polynomial Approximations of Differential Equations: Lecture Notes in Physics, Volume 8}", 
+       publisher="{Springer-Verlag, New York}",
+       year="1992" }
+
+@book{KarniadakisK03,
+  author = "George Em Karniadakis and Robert M. Kirby",
+  title  = "Parallel Scientific Computing in C++ and MPI",
+  publisher = "Cambridge University Press",
+  address = "New-York, NY, USA",
+  year = 2003
+}
+
+@Book{Hughes87,
+  author =	 "T. J. R. Hughes",
+  title =	 "The Finite Element Method",
+  publisher =	 "Prentice-Hall, Inc.",
+  year =	 "1987",
+  address =	 "Englewood Cliffs, New Jersey"
+}
+
+@book{SzBa91,
+  author = "B.A. Szab\'{o} and I. Babu\v{s}ka",
+  title  = "Finite Element Analysis",
+  publisher = "John Wiley \& Sons",
+  address = "New York",
+  year = 1991
+}
+
+@book{TrefethenB97,
+  author = "Lloyd N. Trefethen and David Bau, III",
+  title  = "Numerical Linear Algebra",
+  publisher = "SIAM",
+  address = "Philadelphia, PA, USA",
+  year = 1997
+}
+
+@book{Demmel97,
+author = "James W. Demmel",
+title = "Applied Numerical Linear Algebra",
+publisher = "SIAM",
+  address = "Philadelphia, PA, USA",
+  year = 1997
+}
+
+@article{Pa84,
+  title={A spectral element method for fluid dynamics: laminar flow in a channel expansion},
+  author={Patera, Anthony T},
+  journal={Journal of computational Physics},
+  volume={54},
+  number={3},
+  pages={468--488},
+  year={1984},
+  publisher={Elsevier}
+}
+
+@article{BaSzKa81,
+  title={The p-version of the finite element method},
+  author={Babuska, Ivo and Szabo, Barna A and Katz, I Norman},
+  journal={SIAM journal on numerical analysis},
+  volume={18},
+  number={3},
+  pages={515--545},
+  year={1981},
+  publisher={SIAM}
+}
+
+@article{BlSh04,
+  title={Formulation of a Galerkin spectral element--Fourier method for three-dimensional incompressible flows in cylindrical geometries},
+  author={Blackburn, Hugh M and Sherwin, SJ},
+  journal={Journal of Computational Physics},
+  volume={197},
+  number={2},
+  pages={759--778},
+  year={2004},
+  publisher={Elsevier}
+}
+
+@article{VeSoZi07,
+  title={Modular $hp$-{FEM} system {HERMES} and its application to {M}axwell’s equations},
+  author={Vejchodsk{\`y}, Tom{\'a}{\v{s}} and {\v{S}}ol{\'\i}n, Pavel and Z{\'\i}tka, Martin},
+  journal={Mathematics and Computers in Simulation},
+  volume={76},
+  number={1},
+  pages={223--228},
+  year={2007},
+  publisher={Elsevier}
+}
+
+@article{DeKlNoOh11,
+  title={A generic interface for parallel and adaptive discretization schemes: abstraction principles and the {DUNE-FEM} module},
+  author={Dedner, Andreas and Kl{\"o}fkorn, Robert and Nolte, Martin and Ohlberger, Mario},
+  journal={Computing},
+  volume={90},
+  number={3-4},
+  pages={165--196},
+  year={2010},
+  publisher={Springer}
+}
+
+@article{BaHaKa07,
+  title={deal.{II}--a general-purpose object-oriented finite element library},
+  author={Bangerth, Wolfgang and Hartmann, Ralf and Kanschat, Guido},
+  journal={ACM Transactions on Mathematical Software (TOMS)},
+  volume={33},
+  number={4},
+  pages={24},
+  year={2007},
+  publisher={ACM}
+}
+
+@book{HeWa07,
+  title={Nodal discontinuous Galerkin methods: algorithms, analysis, and applications},
+  author={Hesthaven, Jan S and Warburton, Tim},
+  volume={54},
+  year={2007},
+  publisher={Springer}
+}
+
+@inproceedings{MeDePeFaWi14,
+  title = 	 {A Guide to the Implementation of Boundary Conditions in Compact High-Order Methods for Compressible Aerodynamics},
+  author =   {Mengaldo, G. and De Grazia, D. and Peiro, J. and Farrington, A. and Witherden, F. and Vincent, P. E. and Sherwin, S. J.},
+  year = 	 {2014},
+  booktitle = {7th AIAA Theoretical Fluid Mechanics Conference},
+  series = 	 {AIAA Aviation},
+  publisher = {American Institute of Aeronautics and Astronautics},
+}
+
+@article{WiFaVi14,
+  title={{PyFR}: An open source framework for solving advection–diffusion type problems on streaming architectures using the flux reconstruction approach},
+  author={Witherden, FR and Farrington, AM and Vincent, PE},
+  journal={Computer Physics Communications},
+  year={2014},
+  volume={185},
+  issue={11},
+  pages={3028–3040},
+  doi={10.1016/j.cpc.2014.07.011}
+}
+
+
 %%% Software
 
 @article{VosSK2010,
@@ -127,3 +296,83 @@ publisher = "Springer Lecture Notes in Computational Science and Engineering, Vo
 year = "2012"
 }
 
+@article{AinsworthAD11,
+author = "Mark Ainsworth and Gaelle Andriamaro and Oleg Davydov",
+title = "Bernstein-B{\'e}zier Finite Elements of Arbitrary Order and Optimal Assembly Procedures",
+journal =  "SIAM Journal of Scientific Computing",
+volume = "33",
+issue = "6",
+pages = "3087-3109",
+year = "2011"
+}
+
+@article{Ainsworth14,
+author = "Mark Ainsworth",
+title = "Pyramid Algorithms for Bernstein-B{\'e}zier Finite Elements of High, Nonuniform Order in Any Dimension",
+journal = "SIAM Journal of Scientific Computing",
+volume = "36",
+issue = "2",
+pages = "A543-A569",
+year = "2014"
+}
+
+@article{WarburtonPH00,
+  author = "T. Warburton and L.F. Pavarino and J.S. Hesthaven",
+  title = "A Pseudo-spectral scheme for the incompressible {N}avier-{S}tokes equations using unstructured nodal elements",
+  journal =      "J. Comp. Phys.",
+  volume = "164",
+  pages = "1-21",
+  year = "2000"
+}
+
+@article{Dubiner91,
+        author  = "M. Dubiner",
+        title   = "Spectral Methods on Triangles and Other Domains",
+        journal = "J. Sci. Comp.",
+        volume  = "6",
+        pages   = "345",
+        year    = "1991"
+}
+
+@Article{Hesthaven98,
+  author = 	 {Hesthaven, J.S. },
+  title = 	 {From electrostatics to almost optimal nodal sets for 
+polynomial interpolation in a simplex},
+  journal = 	 {SIAM J. Numer. Anal.},
+  year = 	 {1998},
+  volume =	 {35},
+  number =	 {2},
+  pages =	 {655-676},
+}
+
+@Article{TaylorWV00,
+  author = 	 {Taylor, M. and Wingate, B.A. and Vincent, R.E.},
+  title = 	 {An Algorithm for computing {F}ekete points in the triangle},
+  journal = 	 {SIAM J. Num. Anal.},
+  year = 	 {2000},
+  volume =	 {38},
+  pages =	 {1707-1720},
+}
+
+@article{Duffy82,
+	author  = "Duffy, M.G.",
+	title   = "Quadrature over a pyramid or cube of integrands
+	with a singularity at a vertex",
+	journal ="SIAM J. Numer. Anal.", 
+	volume  = "19",
+	pages   = "1260",
+	year    = "1982"
+}
+
+@article{CantwellYKPS14,
+ author = "C.D. Cantwell and S. Yakovlev and R.M. Kirby and N.S. Peters and S.J. Sherwin",
+ title = "High-order continuous spectral/hp element discretisation for reaction-diffusion problems on a surface", 
+ journal = "Journal of Computational Physics",
+ volume = "257", 
+ issue = "A",
+ pages = "813-829", 
+ year = "2014"
+ }
+
+
+

developers-guide.tex

 \input{shared/devguide-preamble.tex}
 
+\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf}
+
 \newcommand\nek{\emph{Nektar++}}
 \newcommand\shp{spectral/$hp$}
 \newcommand\Shp{Spectral/$hp$}
@@ -31,11 +33,14 @@
 %
 %\clearpage
 
+%\input{test.tex}
 
 \input{preface/preface.tex}
 %
 \input{introduction/introduction.tex}
 %
+\input{prelims/prelims.tex}
+%
 \input{library/library-master.tex}
 
 \bibliographystyle{plain}

library/Collections/collections-algorithms.tex

+%
+\section{The Fundamental Algorithms within Collections}
\ No newline at end of file

library/Collections/collections-datastructures.tex

+%
+\section{The Fundamental Data Structures within Collections}
\ No newline at end of file

library/Collections/collections-fundamentals.tex

+%
+\section{The Fundamentals Behind Collections}
\ No newline at end of file

library/FieldUtils/fieldutils-algorithms.tex

+%
+\section{The Fundamental Algorithms within FieldUtils}
\ No newline at end of file

library/FieldUtils/fieldutils-datastructures.tex

+%
+\section{The Fundamental Data Structures within FieldUtils}
\ No newline at end of file

library/FieldUtils/fieldutils-fundamentals.tex

+%
+\section{The Fundamentals Behind FieldUtils}
\ No newline at end of file

library/GlobalMapping/globalmapping-algorithms.tex

+%
+\section{The Fundamental Algorithms within GlobalMapping}
\ No newline at end of file

library/GlobalMapping/globalmapping-datastructures.tex

+%
+\section{The Fundamental Data Structures within GlobalMapping}
\ No newline at end of file

library/GlobalMapping/globalmapping-fundamentals.tex

+%
+\section{The Fundamentals Behind GlobalMapping}
\ No newline at end of file

library/LibUtilities/basicconst.tex

+%
+\section{BasicConst}
+
+\lstinputlisting[language=C++, firstline=47, lastline=59]{../nektar/library/LibUtilities/BasicConst/NektarUnivConsts.hpp}
\ No newline at end of file

library/LibUtilities/basicutils.tex

+%
+\section{BasicUtils}
+

library/LibUtilities/communication.tex

+%
+\section{Communication}
+

library/LibUtilities/fft.tex

+%
+\section{FFT}
+

library/LibUtilities/foundations.tex

 %
-\section{Foundations}
\ No newline at end of file
+\section{Foundations}
+The two basic building blocks of all that is done in Nektar++ are the concepts of Points and of a Basis.  The Point objects denote positions
+in space, either on compact domains (normally $[-1,1]^d$ where $d$ is the dimension in a reference domain mapped to world-space) 
+or periodic domains (i.e. in the case of points used in Fourier expansions).   The Basis objects denote functions (e.g. polynomials) evaluated
+at a given set of points.
+
+\subsection{Points}
+
+\begin{itemize}
+\item PointsKey
+\item Points
+\end{itemize}
+
+\subsection{Basis}
+
+\begin{itemize}
+\item BasisKey
+\item Basis
+\end{itemize}
+
+\begin{figure}[htb]
+\centering
+\includegraphics[width=4in]{img/basismemory.pdf}
+\caption{Figure 1}
+\label{foundations:basismemory}
+\end{figure}

library/LibUtilities/interpreter.tex

+%
+\section{Interpreter}
+

library/LibUtilities/kernel.tex

+%
+\section{Kernel}
+

library/LibUtilities/memory.tex

+%
+\section{Memory}

library/LibUtilities/polylib.tex

+%
+\section{Polylib}

library/LibUtilities/timeintegration.tex

+%
+\section{Time Integration}

library/LocalRegions/localreg-algorithms.tex

+%
+\section{The Fundamental Algorithms within LocalRegions}
\ No newline at end of file

library/LocalRegions/localreg-datastructures.tex

+%
+\section{The Fundamental Data Structures within LocalRegions}
+
+
+\begin{figure}[htb]
+\centering
+\includegraphics[width=6in]{img/expansiontree.pdf}
+\caption{Figure local regions tree}
+\label{localregions:localclasstree}
+\end{figure}
\ No newline at end of file

library/LocalRegions/localreg-fundamentals.tex

+%
+\section{The Fundamentals Behind LocalRegions}
\ No newline at end of file

library/MultiRegions/multireg-algorithms.tex

+%
+\section{The Fundamental Algorithms within MultiRegions}
\ No newline at end of file

library/MultiRegions/multireg-datastructures.tex

+%
+\section{The Fundamental Data Structures within MultiRegions}
+
+
+\begin{figure}[htb]
+\centering
+\includegraphics[width=6in]{img/multiregiontree.pdf}
+\caption{Figure 1}
+\label{multiregions:multiregionstree}
+\end{figure}

library/MultiRegions/multireg-fundamentals.tex

+%
+\section{The Fundamentals Behind MultiRegions}
\ No newline at end of file

library/SolverUtils/solverutils-algorithms.tex

+%
+\section{The Fundamental Algorithms within SolverUtils}
\ No newline at end of file

library/SolverUtils/solverutils-datastructures.tex

+%
+\section{The Fundamental Data Structures within SolverUtils}
\ No newline at end of file

library/SolverUtils/solverutils-fundamentals.tex

+%
+\section{The Fundamentals Behind SolverUtils}
\ No newline at end of file

library/SpatialDomains/spdomains-algorithms.tex

+%
+\section{The Fundamental Algorithms within SpatialDomains}
\ No newline at end of file

library/SpatialDomains/spdomains-datastructures.tex

+%
+\section{The Fundamental Data Structures within SpatialDomains}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Reference to World-Space Mapping}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsubsection{Geometry}
+
+\begin{figure}[htb]
+\centering
+\includegraphics[width=6in]{img/geomtree.pdf}
+\caption{Figure geometry tree}
+\label{spatialdomains:geomtree}
+\end{figure}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsubsection{GeomFactors}
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{MeshGraph}
\ No newline at end of file

library/SpatialDomains/spdomains-fundamentals.tex

+%
+\section{The Fundamentals Behind SpatialDomains}
+
+
+
+\subsection{Regular}
+$$
+\vec{x} = (x_j)^T,\, j=1,\ldots,D
+$$
+
+$$
+\vec{\xi} = (\xi_j)^T,\, j=1,\ldots,D
+$$
+
+$$
+\vec{x} = \chi(\vec{xi}) 
+$$
+
+$$
+{\bf J} = \frac{\partial x_i}{\partial \xi_j}
+$$
+
+$$
+{\bf g} = {\bf J}^T{\bf J}
+$$
+
+$$
+g = \det{\bf g}
+$$
+
+
+\cite{CantwellYKPS14}
+
+
+\subsection{Deformed}
+

library/StdRegions/stdreg-algorithms.tex

+%
+\section{The Fundamental Algorithms within StdRegions}
\ No newline at end of file

library/StdRegions/stdreg-datastructures.tex

+%
+\section{The Fundamental Data Structures within StdRegions}
+
+\begin{figure}[htb]
+\centering
+\includegraphics[width=6in]{img/stdexpansiontree.pdf}
+\caption{Figure 1}
+\label{stdregions:stdexpansiontree}
+\end{figure}

library/StdRegions/stdreg-fundamentals.tex

+%
+\section{The Fundamentals Behind StdRegions}
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Reference Element Transformations That Facilitate Separability}
+
+
+
+\begin{figure}[htb]
+\centering
+\includegraphics[width=4in]{img/afg002.pdf}
+\caption{Duffy mapping between a right-sided triangle and a square domain.}
+\label{stdregions:duffy}
+\end{figure}
+
+Duffy \cite{Duffy82}
+
+Dubiner \cite{Dubiner91}
+
+Ainsworth \cite{AinsworthAD11,Ainsworth14}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Reference Elements On Primative Geometric Types}
+
+Hesthaven \cite{Hesthaven98}
+
+Taylor \cite{TaylorWV00}

library/library-master.tex

@@ -4,38 +4,190 @@
 \chapter{Inside the Library: LibUtilities}
 
 In this chapter, we walk the reader through the different components of the LibUtilities Directory.
+We have ordered them in alphabetical order by directory name, not by level of importance or
+relevance to the code.  Since all of these items are considered foundational to Nektar++, they
+should all be considered equally important and relevant.   Along the same lines -- since all of
+these areas of the code represent the deepest members of the code hierarchy, these
+items should rarely be modified. 
 
+%
+\input{library/LibUtilities/basicconst.tex}
+%
+\input{library/LibUtilities/basicutils.tex}
+%
+\input{library/LibUtilities/communication.tex}
+%
+\input{library/LibUtilities/fft.tex}
+%
 \input{library/LibUtilities/foundations.tex}
 %
+\input{library/LibUtilities/interpreter.tex}
+%
+\input{library/LibUtilities/kernel.tex}
+%
 \input{library/LibUtilities/linearalgebra.tex}
-
+%
+\input{library/LibUtilities/memory.tex}
+%
+\input{library/LibUtilities/polylib.tex}
+%
+\input{library/LibUtilities/timeintegration.tex}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \chapter{Inside the Library: StdRegions}
 
 In this chapter, we walk the reader through the different components of the StdRegions Directory.
+We begin with a discussion of the mathematical fundamentals, for which we use the book
+by Karniadakis and Sherwin \cite{KaSh05} as our principle reference.  We then provide
+the reader with an overview of the primary data structures introduced within the
+StdRegions Directory (often done through C++ objects), and then present the major 
+algorithms -- expressed as either object methods or functions -- employed over these data structures.  
+
+\input{library/StdRegions/stdreg-fundamentals.tex}
+%
+\input{library/StdRegions/stdreg-datastructures.tex}
+%
+\input{library/StdRegions/stdreg-algorithms.tex}
 
-\input{library/StdRegions/fundamentals.tex}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \chapter{Inside the Library: SpatialDomains}
 
 In this chapter, we walk the reader through the different components of the SpatialDomains Directory.
-
-\input{library/SpatialDomains/fundamentals.tex}
+We begin with a discussion of the mathematical fundamentals, for which we use the book
+by Karniadakis and Sherwin \cite{KaSh05} as our principle reference.  We then provide
+the reader with an overview of the primary data structures introduced within the
+SpatialDomains Directory (often done through C++ objects), and then present the major 
+algorithms -- expressed as either object methods or functions -- employed over these data structures.  
+
+
+The SpatialDomains Directory and its corresponding class definitions serve two principal purposes:
+\begin{enumerate}
+\item To hold the elemental geometric information (i.e. vertex information, curve information and reference-to-world mapping information); and
+\item To facility reading in and writing out geometry-related information.
+\end{enumerate}
+
+When designing Nektar++, developing a class hierarchy for StdRegions (those fundamental domains over which we define
+integration and differentiation) and LocalRegions (i.e. elements in world-space) was fairly straightforward following \cite{KaSh05}.
+For instance, a triangle in world-space {\em is-a} standard triangle.  The first question that arose was where to store geometric 
+information, as information within the LocalRegions element or as information encapsulated from the element so that multiple Expansions could
+all point to the same geometric information.  The decision we made was to store geometric information -- that is, the vertex information
+in world-space that defines an element and the edge and face curvature information -- in its own data structure that could be shared by
+multiple Expansions (functions) over the same domain (element) in world-space.  Hence SpatialDomains started as the directory
+containing Geometry and GeomFactors class definitions to meet the first item listed above.   A LocalRegion {\em is-a} StdRegion and {\em has-a}
+SpatialDomain (i.e. Geometry and GeomFactors).
+
+We then realized that in order to jump-start the process of constructing elements and combining them together into MultiRegions (collections of 
+elements that represent a (sub)-domain of interest), we needed devise a light-weight data structure into which we could load geometric information
+from our geometry file and from which we could then construct Expansions (with their mappings, etc.).  The light-weight data structure we
+devised was MeshGraph, and it was meant to meet the second item listed above.
+
+
+\input{library/SpatialDomains/spdomains-fundamentals.tex}
+%
+\input{library/SpatialDomains/spdomains-datastructures.tex}
+%
+\input{library/SpatialDomains/spdomains-algorithms.tex}
 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%