publisher={American Institute of Aeronautics and Astronautics},
}
@article{WiFaVi14,
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year={2014},
volume={185},
issue={11},
pages={3028–3040},
doi={10.1016/j.cpc.2014.07.011}
}
%%% Software
@article{VosSK2010,
...
...
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year="2012"
}
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@article{CantwellYKPS14,
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\noindent{\textbf{LibUtilities:}} This part of the library contains all the basic mathematical and computer science building blocks of the Nektar++ code.
\noindent{\textbf{StdRegions:}} This part of the library contains the objects that express ``standard region'' data and operations. In one dimension, this is the StdSegment. In two
dimensions, this is the StdTri (Triangle) and StdQuad (Quadrilateral). In three dimensions, this is the StdTet (Tetrahedra), StdHex (Hexahedra), StdPrism (Prism) and StdPyr (Pyramid). These represent
the seven different standarized regions over which we support differentiation and integration.
\noindent{\textbf{SpatialDomains:}}
\noindent{\textbf{LocalRegions:}}
\begin{figure}[htb]
\centering
\includegraphics[width=4in]{img/structure1.png}
...
...
@@ -9,6 +178,16 @@
\label{intro:fig1}
\end{figure}
\begin{figure}[htb]
\centering
\includegraphics[width=4in]{img/stdtolocal.pdf}
\caption{Figure stdtolocal}
\label{intro:stdtolocal}
\end{figure}
\begin{figure}[htb]
\centering
\includegraphics[width=4in]{img/structure2.png}
...
...
@@ -17,7 +196,27 @@
\end{figure}
\section{Software Implementations and Frameworks}
\section{Assumed Proficiencies}
The developer guide is designed for the experienced \shp{}
spectral element \cite{DevilleFM02,KaSh05}
discontinuous Galerkin \cite{HesthavenW08}
CanutoHQZ87
Hughes87
SzBa91
TrefethenB97
Demmel97
\section{Other Software Implementations and Frameworks}
In the last ten years a collection of software frameworks has been put forward to try to bridge the gap between the
mathematics of high-order methods and their implementation. A major challenge many practitioners have with
...
...
@@ -46,3 +245,7 @@ and discontinuous Galerkin
strategies for solving a particular problem of interest, but in a way on which others could adopt and build. The discontinuous Galerkin
of Hesthaven and Warburton \cite{HesthavenW08} and a software framework for the discontinuous Petrov-Galerkin method \cite{roberts_camellia:_2014}
provide a similar flexibility to the user-community trying to jump-start their high-order software experience.