/[escript]/trunk/doc/user/finley.tex
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revision 625 by gross, Thu Mar 23 00:41:25 2006 UTC revision 993 by gross, Fri Feb 23 06:39:38 2007 UTC
# Line 1  Line 1 
1  % $Id$  % $Id$
2  %  %
3  %           Copyright © 2006 by ACcESS MNRF  %           Copyright © 2006, 2007 by ACcESS MNRF
4  %               \url{http://www.access.edu.au  %               \url{http://www.access.edu.au
5  %         Primary Business: Queensland, Australia.  %         Primary Business: Queensland, Australia.
6  %   Licensed under the Open Software License version 3.0  %   Licensed under the Open Software License version 3.0
# Line 34  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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