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revision 1318 by ksteube, Wed Sep 26 04:39:14 2007 UTC revision 2417 by gross, Wed May 13 08:18:47 2009 UTC
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2    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3  %  %
4  % $Id$  % Copyright (c) 2003-2008 by University of Queensland
5  %  % Earth Systems Science Computational Center (ESSCC)
6  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  % http://www.uq.edu.au/esscc
 %  
 %           Copyright 2003-2007 by ACceSS MNRF  
 %       Copyright 2007 by University of Queensland  
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 %        Primary Business: Queensland, Australia  
 %  Licensed under the Open Software License version 3.0  
 %     http://www.opensource.org/licenses/osl-3.0.php  
7  %  %
8  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  % Primary Business: Queensland, Australia
9    % Licensed under the Open Software License version 3.0
10    % http://www.opensource.org/licenses/osl-3.0.php
11  %  %
12    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
13    
14    
15  \chapter{ The Module \finley}  \chapter{ The Module \finley}
16   \label{CHAPTER ON FINLEY}   \label{CHAPTER ON FINLEY}
17    
18  \begin{figure}  \begin{figure}
19  \centerline{\includegraphics[width=\figwidth]{figures/FinleyMesh.eps}}  \centerline{\includegraphics[width=\figwidth]{figures/FinleyMesh}}
20  \caption{Subdivision of an Ellipse into triangles order 1 (\finleyelement{Tri3})}  \caption{Subdivision of an Ellipse into triangles order 1 (\finleyelement{Tri3})}
21  \label{FINLEY FIG 0}  \label{FINLEY FIG 0}
22  \end{figure}  \end{figure}
23    
24  \begin{figure}  \begin{figure}
25  \centerline{\includegraphics[width=\figwidth]{figures/FinleyContact.eps}}  \centerline{\includegraphics[width=\figwidth]{figures/FinleyContact}}
26  \caption{Mesh around a contact region (\finleyelement{Rec4})}  \caption{Mesh around a contact region (\finleyelement{Rec4})}
27  \label{FINLEY FIG 01}  \label{FINLEY FIG 01}
28  \end{figure}  \end{figure}
# Line 63  subdivision of an ellipse into so called Line 61  subdivision of an ellipse into so called
61  In this case, triangles have been used but other forms of subdivisions  In this case, triangles have been used but other forms of subdivisions
62  can be constructed, e.g. into quadrilaterals or, in the three dimensional case, into tetrahedrons  can be constructed, e.g. into quadrilaterals or, in the three dimensional case, into tetrahedrons
63  and hexahedrons. The idea of the finite element method is to approximate the solution by a function  and hexahedrons. The idea of the finite element method is to approximate the solution by a function
64  which is a polynomial of a certain order and is continuous across it boundary to neighbour elements.  which is a polynomial of a certain order and is continuous across it boundary to neighbor elements.
65  In the example of \fig{FINLEY FIG 0} a linear polynomial is used on each triangle. As one can see, the triangulation  In the example of \fig{FINLEY FIG 0} a linear polynomial is used on each triangle. As one can see, the triangulation
66  is quite a poor approximation of the ellipse. It can be improved by introducing a midpoint on each element edge then  is quite a poor approximation of the ellipse. It can be improved by introducing a midpoint on each element edge then
67  positioning those nodes located on an edge expected to describe the boundary, onto the boundary.  positioning those nodes located on an edge expected to describe the boundary, onto the boundary.
# Line 252  $7$, $10$, $15$ and $20$, respectively. Line 250  $7$, $10$, $15$ and $20$, respectively.
250  20 16 0 1.0  1.0  20 16 0 1.0  1.0
251  \end{verbatim}  \end{verbatim}
252    
253    \clearpage
254  \include{finleyelements}  \input{finleyelements}
255    \clearpage
256    
257  \subsection{Linear Solvers in \LinearPDE}  \subsection{Linear Solvers in \LinearPDE}
258  Currently \finley supports the linear solvers \PCG, \GMRES, \PRESTWENTY and \BiCGStab.  Currently \finley supports the linear solvers \PCG, \GMRES, \PRESTWENTY and \BiCGStab.
# Line 272  in storage allowed in the Line 271  in storage allowed in the
271  incomplete elimination process (default is 1.20).  incomplete elimination process (default is 1.20).
272    
273  \subsection{Functions}  \subsection{Functions}
274  \begin{funcdesc}{Mesh}{fileName,integrationOrder=-1}  \begin{funcdesc}{ReadMesh}{fileName,integrationOrder=-1}
275  creates a \Domain object form the FEM mesh defined in  creates a \Domain object form the FEM mesh defined in
276  file \var{fileName}. The file must be given the \finley file format.  file \var{fileName}. The file must be given the \finley file format.
277  If \var{integrationOrder} is positive, a numerical integration scheme  If \var{integrationOrder} is positive, a numerical integration scheme
# Line 281  degree \var{integrationOrder} \index{int Line 280  degree \var{integrationOrder} \index{int
280  an appropriate integration order is chosen independently.  an appropriate integration order is chosen independently.
281  \end{funcdesc}  \end{funcdesc}
282    
283  \begin{funcdesc}{Interval}{n0,order=1,l0=1.,integrationOrder=-1, \\  \begin{funcdesc}{load}{fileName}
284    periodic0=\False,useElementsOnFace=\False}  recovers a \Domain object from a dump file created by the \
285  Generates a \Domain object representing a interval $[0,l0]$. The interval is filled with  eateseates a \Domain object form the FEM mesh defined in
286  \var{n0} elements.  file \var{fileName}. The file must be given the \finley file format.
 For \var{order}=1 and \var{order}=2  
 \finleyelement{Line2} and    
 \finleyelement{Line3} are used, respectively.  
 In the case of \var{useElementsOnFace}=\False,  
 \finleyelement{Point1} are used to describe the boundary points.  
 In the case of \var{useElementsOnFace}=\True (this option should be used if gradients  
 are calculated on domain faces),  
 \finleyelement{Line2} and    
 \finleyelement{Line3} are used on both ends of the interval.    
287  If \var{integrationOrder} is positive, a numerical integration scheme  If \var{integrationOrder} is positive, a numerical integration scheme
288  chosen which is accurate on each element up to a polynomial of  chosen which is accurate on each element up to a polynomial of
289  degree \var{integrationOrder} \index{integration order}. Otherwise  degree \var{integrationOrder} \index{integration order}. Otherwise
290  an appropriate integration order is chosen independently. If  an appropriate integration order is chosen independently.
 \var{periodic0}=\True, periodic boundary conditions \index{periodic boundary conditions}  
 along the $x_0$-directions are enforced. That means when for any solution of a PDE solved by \finley  
 the value at $x_0=0$ will be identical to the values at $x_0=\var{l0}$.  
291  \end{funcdesc}  \end{funcdesc}
292    
293  \begin{funcdesc}{Rectangle}{n0,n1,order=1,l0=1.,l1=1., integrationOrder=-1, \\  \begin{funcdesc}{Rectangle}{n0,n1,order=1,l0=1.,l1=1., integrationOrder=-1, \\
294    periodic0=\False,periodic1=\False,useElementsOnFace=\False}    periodic0=\False,periodic1=\False,useElementsOnFace=\False,optimize=\False}
295  Generates a \Domain object representing a two dimensional rectangle between  Generates a \Domain object representing a two dimensional rectangle between
296  $(0,0)$ and $(l0,l1)$ with orthogonal edges. The rectangle is filled with  $(0,0)$ and $(l0,l1)$ with orthogonal edges. The rectangle is filled with
297  \var{n0} elements along the $x_0$-axis and  \var{n0} elements along the $x_0$-axis and
# Line 329  the value on the line $x_0=0$ will be id Line 316  the value on the line $x_0=0$ will be id
316  Correspondingly,  Correspondingly,
317  \var{periodic1}=\False sets periodic boundary conditions  \var{periodic1}=\False sets periodic boundary conditions
318  in $x_1$-direction.  in $x_1$-direction.
319    If \var{optimize}=\True mesh node relabeling will be attempted to reduce the computation and also ParMETIS will be used to improve the mesh partition if running on multiple CPUs with MPI.
320  \end{funcdesc}  \end{funcdesc}
321    
322  \begin{funcdesc}{Brick}{n0,n1,n2,order=1,l0=1.,l1=1.,l2=1., integrationOrder=-1, \\  \begin{funcdesc}{Brick}{n0,n1,n2,order=1,l0=1.,l1=1.,l2=1., integrationOrder=-1, \\
323    periodic0=\False,periodic1=\False,periodic2=\False,useElementsOnFace=\False}    periodic0=\False,periodic1=\False,periodic2=\False,useElementsOnFace=\False,optimize=\False}
324  Generates a \Domain object representing a three dimensional brick between  Generates a \Domain object representing a three dimensional brick between
325  $(0,0,0)$ and $(l0,l1,l2)$ with orthogonal faces. The brick is filled with  $(0,0,0)$ and $(l0,l1,l2)$ with orthogonal faces. The brick is filled with
326  \var{n0} elements along the $x_0$-axis,  \var{n0} elements along the $x_0$-axis,
# Line 357  along the $x_0$-directions are enforced. Line 345  along the $x_0$-directions are enforced.
345  the value on the plane $x_0=0$ will be identical to the values on $x_0=\var{l0}$. Correspondingly,  the value on the plane $x_0=0$ will be identical to the values on $x_0=\var{l0}$. Correspondingly,
346  \var{periodic1}=\False and \var{periodic2}=\False sets periodic boundary conditions  \var{periodic1}=\False and \var{periodic2}=\False sets periodic boundary conditions
347  in $x_1$-direction and $x_2$-direction, respectively.  in $x_1$-direction and $x_2$-direction, respectively.
348    If \var{optimize}=\True mesh node relabeling will be attempted to reduce the computation and also ParMETIS will be used to improve the mesh partition if running on multiple CPUs with MPI.
349  \end{funcdesc}  \end{funcdesc}
350    
351  \begin{funcdesc}{GlueFaces}{meshList,safetyFactor=0.2,tolerance=1.e-13}  \begin{funcdesc}{GlueFaces}{meshList,safetyFactor=0.2,tolerance=1.e-13}

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