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\chapter{ The Module \finley} 
\chapter{ The Module \finley} 
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\label{CHAPTER ON FINLEY} 
\label{CHAPTER ON FINLEY} 
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\begin{figure} 
\begin{figure} 
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\centerline{\includegraphics[width=\figwidth]{figures/FinleyMesh.eps}} 
\centerline{\includegraphics[width=\figwidth]{figures/FinleyMesh}} 
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\caption{Subdivision of an Ellipse into triangles order 1 (\finleyelement{Tri3})} 
\caption{Subdivision of an Ellipse into triangles order 1 (\finleyelement{Tri3})} 
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\label{FINLEY FIG 0} 
\label{FINLEY FIG 0} 
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\end{figure} 
\end{figure} 
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\begin{figure} 
\begin{figure} 
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\centerline{\includegraphics[width=\figwidth]{figures/FinleyContact.eps}} 
\centerline{\includegraphics[width=\figwidth]{figures/FinleyContact}} 
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\caption{Mesh around a contact region (\finleyelement{Rec4})} 
\caption{Mesh around a contact region (\finleyelement{Rec4})} 
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\label{FINLEY FIG 01} 
\label{FINLEY FIG 01} 
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\end{figure} 
\end{figure} 
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In this case, triangles have been used but other forms of subdivisions 
In this case, triangles have been used but other forms of subdivisions 
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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 
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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 
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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. 
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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 
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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 
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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. 
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20 16 0 1.0 1.0 
20 16 0 1.0 1.0 
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\end{verbatim} 
\end{verbatim} 
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\clearpage 
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\include{finleyelements} 
\input{finleyelements} 
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\clearpage 
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\subsection{Linear Solvers in \LinearPDE} 
\subsection{Linear Solvers in \LinearPDE} 
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Currently \finley supports the linear solvers \PCG, \GMRES, \PRESTWENTY and \BiCGStab. 
Currently \finley supports the linear solvers \PCG, \GMRES, \PRESTWENTY and \BiCGStab. 
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incomplete elimination process (default is 1.20). 
incomplete elimination process (default is 1.20). 
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\subsection{Functions} 
\subsection{Functions} 
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\begin{funcdesc}{Mesh}{fileName,integrationOrder=1} 
\begin{funcdesc}{ReadMesh}{fileName,integrationOrder=1} 
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creates a \Domain object form the FEM mesh defined in 
creates a \Domain object form the FEM mesh defined in 
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file \var{fileName}. The file must be given the \finley file format. 
file \var{fileName}. The file must be given the \finley file format. 
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If \var{integrationOrder} is positive, a numerical integration scheme 
If \var{integrationOrder} is positive, a numerical integration scheme 
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chosen which is accurate on each element up to a polynomial of 
chosen which is accurate on each element up to a polynomial of 
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degree \var{integrationOrder} \index{integration order}. Otherwise 
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an appropriate integration order is chosen independently. 
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\end{funcdesc} 
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\begin{funcdesc}{load}{fileName} 
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recovers a \Domain object from a dump file created by the \ 
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eateseates a \Domain object form the FEM mesh defined in 
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file \var{fileName}. The file must be given the \finley file format. 
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If \var{integrationOrder} is positive, a numerical integration scheme 
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chosen which is accurate on each element up to a polynomial of 
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degree \var{integrationOrder} \index{integration order}. Otherwise 
degree \var{integrationOrder} \index{integration order}. Otherwise 
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an appropriate integration order is chosen independently. 
an appropriate integration order is chosen independently. 
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\end{funcdesc} 
\end{funcdesc} 