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revision 155 by jgs, Wed Nov 9 02:02:19 2005 UTC revision 993 by gross, Fri Feb 23 06:39:38 2007 UTC
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1  % $Id$  % $Id$
2    %
3    %           Copyright © 2006, 2007 by ACcESS MNRF
4    %               \url{http://www.access.edu.au
5    %         Primary Business: Queensland, Australia.
6    %   Licensed under the Open Software License version 3.0
7    %      http://www.opensource.org/licenses/osl-3.0.php
8    %
9    
10    
11    
12  \chapter{ The module \finley}  \chapter{ The module \finley}
13   \label{CHAPTER ON FINLEY}   \label{CHAPTER ON FINLEY}
14    
15  \begin{figure}  \begin{figure}
16  \centerline{\includegraphics[width=\figwidth]{FinleyMesh}}  \centerline{\includegraphics[width=\figwidth]{figures/FinleyMesh.eps}}
17  \caption{Subdivision of an Ellipse into triangles order 1 (\finleyelement{Tri3})}  \caption{Subdivision of an Ellipse into triangles order 1 (\finleyelement{Tri3})}
18  \label{FINLEY FIG 0}  \label{FINLEY FIG 0}
19  \end{figure}  \end{figure}
20    
21  \begin{figure}  \begin{figure}
22  \centerline{\includegraphics[width=\figwidth]{FinleyContact}}  \centerline{\includegraphics[width=\figwidth]{figures/FinleyContact.eps}}
23  \caption{Mesh around a contact region (\finleyelement{Rec4})}  \caption{Mesh around a contact region (\finleyelement{Rec4})}
24  \label{FINLEY FIG 01}  \label{FINLEY FIG 01}
25  \end{figure}  \end{figure}
# Line 26  It supports unstructured, 1D, 2D and 3D Line 34  It supports unstructured, 1D, 2D and 3D
34  library through the \LinearPDE class of \escript supporting its full functionality. {\it finley}  library through the \LinearPDE class of \escript supporting its full functionality. {\it finley}
35  is parallelized using the OpenMP \index{OpenMP} paradigm.  is parallelized using the OpenMP \index{OpenMP} paradigm.
36    
37  \subsection{Meshes}  \section{Formulation}
38    
39    For a single PDE with a solution with a single component the linear PDE is defined in the
40    following form:
41    \begin{equation}\label{FINLEY.SINGLE.1}
42    \begin{array}{cl} &
43    \displaystyle{
44    \int\hackscore{\Omega}
45    A\hackscore{jl} \cdot v\hackscore{,j}u\hackscore{,l}+ B\hackscore{j} \cdot v\hackscore{,j} u+ C\hackscore{l} \cdot v u\hackscore{,l}+D \cdot vu \; d\Omega }  \\
46    + & \displaystyle{\int\hackscore{\Gamma} d \cdot vu \; d{\Gamma} }
47    +  \displaystyle{\int\hackscore{\Gamma^{contact}} d^{contact} \cdot [v][u] \; d{\Gamma} } \\
48    = & \displaystyle{\int\hackscore{\Omega}  X\hackscore{j} \cdot v\hackscore{,j}+ Y \cdot v \; d\Omega }\\
49    + & \displaystyle{\int\hackscore{\Gamma} y \cdot v \; d{\Gamma}}  +
50    \displaystyle{\int\hackscore{\Gamma^{contact}} y^{contact}\cdot [v] \; d{\Gamma}} \\
51    \end{array}
52    \end{equation}
53    
54    \section{Meshes}
55  To understand the usage of \finley one needs to have an understanding of how the finite element meshes  To understand the usage of \finley one needs to have an understanding of how the finite element meshes
56  \index{FEM!mesh} are defined. \fig{FINLEY FIG 0} shows an example of the  \index{FEM!mesh} are defined. \fig{FINLEY FIG 0} shows an example of the
57  subdivision of an ellipse into so called elements \index{FEM!elements} \index{element}.  subdivision of an ellipse into so called elements \index{FEM!elements} \index{element}.

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