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trunk/esys2/doc/user/finley.tex revision 104 by jgs, Fri Dec 17 07:43:12 2004 UTC trunk/doc/user/finley.tex revision 2558 by gross, Mon Jul 27 05:03:32 2009 UTC
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1    
2    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3    %
4    % Copyright (c) 2003-2009 by University of Queensland
5    % Earth Systems Science Computational Center (ESSCC)
6    % http://www.uq.edu.au/esscc
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  \chapter{ The module \finley}  
15    \chapter{ The Module \finley}
16   \label{CHAPTER ON FINLEY}   \label{CHAPTER ON FINLEY}
17    
18  \begin{figure}  \begin{figure}
19  \centerline{\includegraphics[width=\figwidth]{FinleyMesh}}  \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]{FinleyContact}}  \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 26  It supports unstructured, 1D, 2D and 3D Line 37  It supports unstructured, 1D, 2D and 3D
37  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}
38  is parallelized using the OpenMP \index{OpenMP} paradigm.  is parallelized using the OpenMP \index{OpenMP} paradigm.
39    
40  \subsection{Meshes}  \section{Formulation}
41    
42    For a single PDE with a solution with a single component the linear PDE is defined in the
43    following form:
44    \begin{equation}\label{FINLEY.SINGLE.1}
45    \begin{array}{cl} &
46    \displaystyle{
47    \int\hackscore{\Omega}
48    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 }  \\
49    + & \displaystyle{\int\hackscore{\Gamma} d \cdot vu \; d{\Gamma} }
50    +  \displaystyle{\int\hackscore{\Gamma^{contact}} d^{contact} \cdot [v][u] \; d{\Gamma} } \\
51    = & \displaystyle{\int\hackscore{\Omega}  X\hackscore{j} \cdot v\hackscore{,j}+ Y \cdot v \; d\Omega }\\
52    + & \displaystyle{\int\hackscore{\Gamma} y \cdot v \; d{\Gamma}}  +
53    \displaystyle{\int\hackscore{\Gamma^{contact}} y^{contact}\cdot [v] \; d{\Gamma}} \\
54    \end{array}
55    \end{equation}
56    
57    \section{Meshes}
58  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
59  \index{FEM!mesh} are defined. \fig{FINLEY FIG 0} shoes an example of the  \index{FEM!mesh} are defined. \fig{FINLEY FIG 0} shows an example of the
60  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}.
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 seen, 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 a quite poor approximation of the ellipse. It can be improved by introducing a midpoint on each element edge and  is quite a poor approximation of the ellipse. It can be improved by introducing a midpoint on each element edge then
67  position those nodes, which are located on an edge expecting to describing the boundary, onto the boundary.  positioning those nodes located on an edge expected to describe the boundary, onto the boundary.
68  In this case the triangle gets a curved edge which requires a parametrization of the triangle using a  In this case the triangle gets a curved edge which requires a parametrization of the triangle using a
69  quadratic polynomial. For this case, the solution is also approximated by a piecewise quadratic polynomial  quadratic polynomial. For this case, the solution is also approximated by a piecewise quadratic polynomial
70  (which explains the name isoparametrical elements), see \Ref{Zienc,NumHand} for more details.    (which explains the name isoparametrical elements), see \Ref{Zienc,NumHand} for more details.  
71    
72  The union of all elements defines the domain of the PDE.  The union of all elements defines the domain of the PDE.
73  Each element is defined by the nodes used to describe is shape. In \fig{FINLEY FIG 0} the element,  Each element is defined by the nodes used to describe its shape. In \fig{FINLEY FIG 0} the element,
74  which have type \finleyelement{Tri3},  which has type \finleyelement{Tri3},
75  with the element reference number $19$ \index{element!reference number} is defined by the nodes  with element reference number $19$ \index{element!reference number} is defined by the nodes
76  with the reference numbers $9$, $11$ and $0$ \index{node!reference number}. Notice that the order is counterclockwise.  with reference numbers $9$, $11$ and $0$ \index{node!reference number}. Notice that the order is counterclockwise.
77  The coefficients of the PDE are evaluated at integration nodes with each individual element.  The coefficients of the PDE are evaluated at integration nodes with each individual element.
78  For quadrilateral elements a Gauss quadrature scheme is used. In the case of triangular elements a  For quadrilateral elements a Gauss quadrature scheme is used. In the case of triangular elements a
79  modified from is applied. The boundary of the domain is also subdivided into elements \index{element!face}. In \fig{FINLEY FIG 0}  modified form is applied. The boundary of the domain is also subdivided into elements. \index{element!face} In \fig{FINLEY FIG 0}
80  line elements with two nodes are used. The elements are also defined by their describing nodes, e.g.  line elements with two nodes are used. The elements are also defined by their describing nodes, e.g.
81  the face element reference number $20$ which has type \finleyelement{Line2} is defined by the nodes  the face element reference number $20$ which has type \finleyelement{Line2} is defined by the nodes
82  with the reference numbers $11$ and $0$. Again the order is crucial, if moving from the first  with the reference numbers $11$ and $0$. Again the order is crucial, if moving from the first
83  to second node the domain has to lay on the left hand side (in case of a two dimension surface element  to second node the domain has to lie on the left hand side (in the case of a two dimension surface element
84  the domain has to lay on left hand side when moving counterclockwise). If the gradient on the  the domain has to lie on the left hand side when moving counterclockwise). If the gradient on the
85  surface of the domain wants to be calculated rich face elements face to be used. Rich elements on a face  surface of the domain is to be calculated rich face elements face to be used. Rich elements on a face
86  is identical to interior elements but with a modified order of nodes such that the 'first' face of the element aligns  are identical to interior elements but with a modified order of nodes such that the 'first' face of the element aligns
87  with the surface of the domian. In \fig{FINLEY FIG 0}  with the surface of the domain. In \fig{FINLEY FIG 0}
88  elements of the type \finleyelement{Tri3Face} are used.  elements of the type \finleyelement{Tri3Face} are used.
89  The face element reference number $20$ as a rich face element is defined by the nodes  The face element reference number $20$ as a rich face element is defined by the nodes
90  with the reference numbers $11$, $0$ and $9$. Notice that the face element $20$ is identical to the  with reference numbers $11$, $0$ and $9$. Notice that the face element $20$ is identical to the
91  interior element $19$ however, in this case, the order of the node is different to align the first  interior element $19$ except that, in this case, the order of the node is different to align the first
92  edge of the triangle (which is the edge starting with the first node) with the boundary of the domain.  edge of the triangle (which is the edge starting with the first node) with the boundary of the domain.
93    
94  Be aware that face elements and elements in the interior of the domain must match, i.e. a face element must be the face  Be aware that face elements and elements in the interior of the domain must match, i.e. a face element must be the face
95  of an interior element or, in case of a rich face element, must be identical to an interior element.  of an interior element or, in case of a rich face element, it must be identical to an interior element.
96  If no face elements are specified  If no face elements are specified
97  \finley implicitly assumes homogeneous natural boundary conditions \index{natural boundary conditions!homogeneous},  \finley implicitly assumes homogeneous natural boundary conditions \index{natural boundary conditions!homogeneous},
98  i.e. \var{d}=$0$ and \var{y}=$0$, on the entire boundary of the domain. For    i.e. \var{d}=$0$ and \var{y}=$0$, on the entire boundary of the domain. For  
# Line 77  even if $d^{contact}$ and $y^{contact}$ Line 105  even if $d^{contact}$ and $y^{contact}$
105  of rectangular elements around a contact region $\Gamma^{contact}$ \index{element!contact}.  of rectangular elements around a contact region $\Gamma^{contact}$ \index{element!contact}.
106  The contact region is described by the  The contact region is described by the
107  elements $4$, $3$ and $6$. Their element type is \finleyelement{Line2_Contact}.  elements $4$, $3$ and $6$. Their element type is \finleyelement{Line2_Contact}.
108  The nodes $9$, $12$, $6$, $5$ are defining contact element $4$, where the coordinates of nodes $12$ and $5$ and  The nodes $9$, $12$, $6$, $5$ define contact element $4$, where the coordinates of nodes $12$ and $5$ and
109  nodes $4$ and $6$ are identical with the idea that nodes $12$ and $9$ are located above and  nodes $4$ and $6$ are identical with the idea that nodes $12$ and $9$ are located above and
110  nodes $5$ and $6$ are below the contact region.    nodes $5$ and $6$ below the contact region.  
111  Again, the order of the nodes within an element is crucial. There is also the option of using rich elements  Again, the order of the nodes within an element is crucial. There is also the option of using rich elements
112  if the gradient wants to be calculated on the contact region. Similar to the rich face elements  if the gradient is to be calculated on the contact region. Similarly to the rich face elements
113  they are constructed from two interior elements with reordering the nodes such that  these are constructed from two interior elements by reordering the nodes such that
114  the 'first' face of the element above and the 'first' face of the element below the  the 'first' face of the element above and the 'first' face of the element below the
115  contact regions are lining up.  The rich version of element  contact regions line up.  The rich version of element
116  $4$ is of type \finleyelement{Rec4Face_Contact} and is defined by the nodes $9$, $12$, $16$, $18$, $6$, $5$, $0$ and  $4$ is of type \finleyelement{Rec4Face_Contact} and is defined by the nodes $9$, $12$, $16$, $18$, $6$, $5$, $0$ and
117  $2$.  $2$.
118    
119  \tab{FINLEY TAB 1} shows the interior element types and the corresponding element types to be used  \tab{FINLEY TAB 1} shows the interior element types and the corresponding element types to be used
120  on face and contacts. \fig{FINLEY.FIG:1}, \fig{FINLEY.FIG:2} and \fig{FINLEY.FIG:4} show the ordering of  on the face and contacts. \fig{FINLEY.FIG:1}, \fig{FINLEY.FIG:2} and \fig{FINLEY.FIG:4} show the ordering of
121  the nodes within an element.  the nodes within an element.
122    
123  \begin{table}  \begin{table}
# Line 107  the nodes within an element. Line 135  the nodes within an element.
135  \linev{\finleyelement{Hex20}}{\finleyelement{Rec8}}{\finleyelement{Hex20Face}}{\finleyelement{Rec8_Contact}}{\finleyelement{Hex20Face_Contact}}  \linev{\finleyelement{Hex20}}{\finleyelement{Rec8}}{\finleyelement{Hex20Face}}{\finleyelement{Rec8_Contact}}{\finleyelement{Hex20Face_Contact}}
136  \end{tablev}  \end{tablev}
137  \caption{Finley elements and corresponding elements to be used on domain faces and contacts.  \caption{Finley elements and corresponding elements to be used on domain faces and contacts.
138  The rich types have to be used if the gradient of function wants to calculated on faces and contacts, resepctively.}  The rich types have to be used if the gradient of function is to be calculated on faces and contacts, respectively.}
139  \label{FINLEY TAB 1}  \label{FINLEY TAB 1}
140  \end{table}  \end{table}
141    
142  The native \finley file format is defined as follows.  The native \finley file format is defined as follows.
143  Each node \var{i} has \var{dim} spatial coordinates \var{Node[i]}, a reference number  Each node \var{i} has \var{dim} spatial coordinates \var{Node[i]}, a reference number
144  \var{Node_ref[i]}, a degree of freedom \var{Node_DOF[i]} and tag \var{Node_tag[i]}.  \var{Node_ref[i]}, a degree of freedom \var{Node_DOF[i]} and tag \var{Node_tag[i]}.
145  In most cases \var{Node_DOF[i]}=\var{Node_ref[i]} however for periodic boundary conditions  In most cases \var{Node_DOF[i]}=\var{Node_ref[i]} however, for periodic boundary conditions,
146  \var{Node_DOF[i]} is chosen differently, see example below. The tag can be used to mark nodes sharing  \var{Node_DOF[i]} is chosen differently, see example below. The tag can be used to mark nodes sharing
147  the same properties. Element \var{i} is defined by the \var{Element_numNodes} nodes \var{Element_Nodes[i]}  the same properties. Element \var{i} is defined by the \var{Element_numNodes} nodes \var{Element_Nodes[i]}
148  which is a list of node reference numbers. The order is crucial.  which is a list of node reference numbers. The order is crucial.
149  It has a reference number \var{Element_ref[i]} and a tag \var{Element_tag[i]}. The tag  It has a reference number \var{Element_ref[i]} and a tag \var{Element_tag[i]}. The tag
150  can be used to mark elements  sharing the same properties. For instance elements above  can be used to mark elements  sharing the same properties. For instance elements above
151  a contact region are marked with $2$ and element below a contact region are marked with $1$.  a contact region are marked with $2$ and elements below a contact region are marked with $1$.
152  \var{Element_Type} and \var{Element_Num} give the element type and the number of elements in the mesh.  \var{Element_Type} and \var{Element_Num} give the element type and the number of elements in the mesh.
153  Analogue notations are used for face and contact elements. The following Python script  Analogue notations are used for face and contact elements. The following Python script
154  prints the mesh definition in the \finley file format:  prints the mesh definition in the \finley file format:
# Line 151  for i in range(ContactElement_Num): Line 179  for i in range(ContactElement_Num):
179     for j in range(ContactElement_numNodes): print " %d"%ContactElement_Nodes[i][j]     for j in range(ContactElement_numNodes): print " %d"%ContactElement_Nodes[i][j]
180     print "\n"     print "\n"
181  # point sources (not supported yet)  # point sources (not supported yet)
182  write("Point1 0",face_element_typ,numFaceElements)  write("Point1 0",face_element_type,numFaceElements)
183  \end{python}  \end{python}
184    
185  The following example of a mesh file defines the mesh shown in \fig{FINLEY FIG 01}:  The following example of a mesh file defines the mesh shown in \fig{FINLEY FIG 01}:
# Line 189  Line2_Contact 3 Line 217  Line2_Contact 3
217  Point1 0  Point1 0
218  \end{verbatim}  \end{verbatim}
219  Notice that the order in which the nodes and elements are given is arbitrary.  Notice that the order in which the nodes and elements are given is arbitrary.
220  In that case rich contact element are used the contact element section get the form  In the case that rich contact elements are used the contact element section gets
221     the form
222  \begin{verbatim}  \begin{verbatim}
223  Rec4Face_Contact 3  Rec4Face_Contact 3
224   4 0  9 12 16 18  6  5  0  2   4 0  9 12 16 18  6  5  0  2
# Line 197  Rec4Face_Contact 3 Line 226  Rec4Face_Contact 3
226   6 0 15 13 19 20 10  8  3  7   6 0 15 13 19 20 10  8  3  7
227  \end{verbatim}  \end{verbatim}
228  Periodic boundary condition \index{boundary conditions!periodic} can be introduced by altering \var{Node_DOF}.  Periodic boundary condition \index{boundary conditions!periodic} can be introduced by altering \var{Node_DOF}.
229  It allows to identify nodes even if they have different physical locations. For instance, to  It allows identification of nodes even if they have different physical locations. For instance, to
230  enforce periodic boundary conditions at the face $x_0=0$ and $x_0=1$ one identifies  enforce periodic boundary conditions at the face $x_0=0$ and $x_0=1$ one identifies
231  the degrees of freedom for nodes $0$, $5$, $12$ and $16$ with the degrees of freedom for  the degrees of freedom for nodes $0$, $5$, $12$ and $16$ with the degrees of freedom for
232  $7$, $10$, $15$ and $20$, respectively. The node section of the \finley mesh gets now the form:    $7$, $10$, $15$ and $20$, respectively. The node section of the \finley mesh gets now the form:  
# Line 221  $7$, $10$, $15$ 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    \input{finleyelements}
255    \clearpage
256    
257    
258    \begin{table}
259    {\small
260    \begin{tabular}{l||c|c|c|c|c|c|c|c}
261    \member{setSolverMethod} & \member{DIRECT}& \member{PCG} & \member{GMRES} & \member{TFQMR} & \member{MINRES} & \member{PRES20} & \member{BICGSTAB} & \member{LUMPING} \\
262    \hline
263     \hline
264     \member{setReordering} & $\checkmark$ & & & & & &\\
265     \hline  \member{setRestart} &  & & $\checkmark$ & & & $20$ & \\
266     \hline\member{setTruncation} &  & & $\checkmark$ & & & $5$ & \\
267       \hline\member{setIterMax} &  & $\checkmark$& $\checkmark$ & $\checkmark$& $\checkmark$& $\checkmark$ & $\checkmark$ \\
268     \hline\member{setTolerance} &  & $\checkmark$& $\checkmark$ & $\checkmark$& $\checkmark$& $\checkmark$ & $\checkmark$ \\
269     \hline\member{setAbsoluteTolerance} &  & $\checkmark$& $\checkmark$ & $\checkmark$& $\checkmark$& $\checkmark$ & $\checkmark$ \\
270    \end{tabular}
271    }
272    \caption{Solvers available for \finley and the \PASO package and the relevant options in \class{SolverOptions}
273     \label{TAB FINLEY SOLVER OPTIONS 1}}
274    \end{table}
275    
276  \include{finleyelements}  \begin{table}
277    {\scriptsize
278    \begin{tabular}{l||c|c|c|c|c|c|c|c}
279    \member{setPreconditioner} &
280    \member{NO_PRECONDITIONER} &
281    \member{AMG} &
282    \member{JACOBI} &
283    \member{GAUSS_SEIDEL}&
284    \member{REC_ILU}&
285    \member{RILU} &
286    \member{ILU0} &
287    \member{DIRECT} \\
288     \hline
289     status: &
290    later &
291    later &
292    $\checkmark$ &
293    $\checkmark$&
294    $\checkmark$ &
295    later &
296    $\checkmark$ &
297    later \\
298    \hline
299    \hline
300    \member{setCoarsening}&
301     &
302    $\checkmark$ &
303    &
304    &
305    &
306     &
307     &
308     \\
309    
310    
311    \hline\member{setLevelMax}&
312     &
313    $\checkmark$ &
314     &
315    &
316    &
317     &
318     &
319     \\
320    
321    \hline\member{setCoarseningThreshold}&
322    &
323    $\checkmark$ &
324     &
325    &
326    &
327     &
328     &
329     \\
330    
331    \hline\member{setMinCoarseMatrixSize} &
332     &
333    $\checkmark$ &
334     &
335    &
336    &
337     &
338     &
339     \\
340    
341    \hline\member{setNumSweeps} &
342     &
343     &
344    $\checkmark$ &
345    $\checkmark$ &
346    &
347     &
348     &
349     \\
350    
351    \hline\member{setNumPreSweeps}&
352     &
353    $\checkmark$ &
354      &
355     &
356     &
357      &
358      &
359      \\
360    
361    \hline\member{setNumPostSweeps} &
362     &
363    $\checkmark$ &
364     &
365    &
366    &
367     &
368    &
369     \\
370    
371    \hline\member{setInnerTolerance}&
372     &
373     &
374     &
375    &
376    &
377     &
378    &
379     \\
380    
381    \hline\member{setDropTolerance}&
382     &
383     &
384     &
385    &
386    &
387     &
388    &
389     \\
390    
391    \hline\member{setDropStorage}&
392     &
393     &
394     &
395    &
396    &
397     &
398    &
399     \\
400    
401    \hline\member{setRelaxationFactor}&
402     &
403     &
404     &
405    &
406    &
407    $\checkmark$  &
408     &
409     \\
410    
411    \hline\member{adaptInnerTolerance}&
412     &
413     &
414     &
415    &
416    &
417     &
418    &
419     \\
420    
421    \hline\member{setInnerIterMax}&
422     &
423     &
424     &
425    &
426    &
427     &
428    &
429     \\
430    \end{tabular}
431    }
432    \caption{Preconditioners available for \finley and the \PASO package and the relevant options in \class{SolverOptions}. \label{TAB FINLEY SOLVER OPTIONS 2}}
433    \end{table}
434    
435  \subsection{Linear Solvers in \LinearPDE}  \subsection{Linear Solvers in \SolverOptions}
436  Currently \finley support the linear solvers \PCG, \GMRES, \PRESTWENTY and \BiCGStab.  Table~\ref{TAB FINLEY SOLVER OPTIONS 1} and
437  For \GMRES the options \var{trancation} and \var{restart} of the \method{getSolution} can be  Table~\ref{TAB FINLEY SOLVER OPTIONS 2} show the solvers and preconditioners supported by
438  used to control the trunction and restart during iteration. Default values are  \finley through the \PASO library. Currently direct solvers are not supported under MPI.
439  \var{truncation}=5 and \var{restart}=20.  By default, \finley is using the iterative solvers \PCG for symmetric and \BiCGStab for non-symmetric problems.
440  The default solver is \BiCGStab but if the symmetry flag is set \PCG is the default solver.  If the direct solver is selected which can be useful when solving very ill-posedequations
441  \finley supports the solver options \var{iter_max} which specifies the maximum number of iterations steps,  \finley uses the \MKL solver package. If \MKL is not available \UMFPACK is used. If \UMFPACK is not available
442  \var{verbose}=\True or \False and \var{preconditioner}=\constant{JACOBI} or \constant {ILU0}.  a suitable iterative solver from the \PASO is used.
 In some installation \finley supports \Direct solver and the  
 solver options \var{reordering}=\constant{util.NO_REORDERING},  
 \constant{util.MINIMUM_FILL_IN} or \constant{util.NESTED_DISSECTION} (default is \constant{util.NO_REORDERING}),  
 \var{drop_tolerance} specifying the threshold for values to be dropped in the  
 incomplete elimation process (default is 0.01) and \var{drop_storage} specifying the maximum increase  
 in storage allowed in the  
 incomplete elimation process (default is 1.20).  
443    
444  \subsection{Functions}  \subsection{Functions}
445  \begin{funcdesc}{Mesh}{fileName,integrationOrder=-1}  \begin{funcdesc}{ReadMesh}{fileName,integrationOrder=-1}
446  creates a \Domain object form the FEM mesh defined in  creates a \Domain object form the FEM mesh defined in
447  file \var{fileName}. The file must be given the \finley file format.  file \var{fileName}. The file must be given the \finley file format.
448  If \var{integrationOrder} is positive, a numerical integration scheme  If \var{integrationOrder} is positive, a numerical integration scheme
# Line 250  degree \var{integrationOrder} \index{int Line 451  degree \var{integrationOrder} \index{int
451  an appropriate integration order is chosen independently.  an appropriate integration order is chosen independently.
452  \end{funcdesc}  \end{funcdesc}
453    
454  \begin{funcdesc}{Interval}{n0,order=1,l0=1.,integrationOrder=-1, \\  \begin{funcdesc}{load}{fileName}
455    periodic0=\False,useElementsOnFace=\False}  recovers a \Domain object from a dump file created by the \
456  Generates a \Domain object representing a interval $[0,l0]$. The interval is filled with  eateseates a \Domain object form the FEM mesh defined in
457  \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.    
458  If \var{integrationOrder} is positive, a numerical integration scheme  If \var{integrationOrder} is positive, a numerical integration scheme
459  chosen which is accurate on each element up to a polynomial of  chosen which is accurate on each element up to a polynomial of
460  degree \var{integrationOrder} \index{integration order}. Otherwise  degree \var{integrationOrder} \index{integration order}. Otherwise
461  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 $x_0=\var{l0}$.  
462  \end{funcdesc}  \end{funcdesc}
463    
464  \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, \\
465    periodic0=\False,periodic1=\False,useElementsOnFace=\False}    periodic0=\False,periodic1=\False,useElementsOnFace=\False,optimize=\False}
466  Generates a \Domain object representing a two dimensional rectangle between  Generates a \Domain object representing a two dimensional rectangle between
467  $(0,0)$ and $(l0,l1)$ with orthogonal edges. The rectangle is filled with  $(0,0)$ and $(l0,l1)$ with orthogonal edges. The rectangle is filled with
468  \var{n0} elements along the $x_0$-axis and  \var{n0} elements along the $x_0$-axis and
# Line 298  the value on the line $x_0=0$ will be id Line 487  the value on the line $x_0=0$ will be id
487  Correspondingly,  Correspondingly,
488  \var{periodic1}=\False sets periodic boundary conditions  \var{periodic1}=\False sets periodic boundary conditions
489  in $x_1$-direction.  in $x_1$-direction.
490    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.
491  \end{funcdesc}  \end{funcdesc}
492    
493  \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, \\
494    periodic0=\False,periodic1=\False,periodic2=\False,useElementsOnFace=\False}    periodic0=\False,periodic1=\False,periodic2=\False,useElementsOnFace=\False,optimize=\False}
495  Generates a \Domain object representing a three dimensional brick between  Generates a \Domain object representing a three dimensional brick between
496  $(0,0,0)$ 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
497  \var{n0} elements along the $x_0$-axis,  \var{n0} elements along the $x_0$-axis,
# Line 326  along the $x_0$-directions are enforced. Line 516  along the $x_0$-directions are enforced.
516  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,
517  \var{periodic1}=\False and \var{periodic2}=\False sets periodic boundary conditions  \var{periodic1}=\False and \var{periodic2}=\False sets periodic boundary conditions
518  in $x_1$-direction and $x_2$-direction, respectively.  in $x_1$-direction and $x_2$-direction, respectively.
519    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.
520  \end{funcdesc}  \end{funcdesc}
521    
522  \begin{funcdesc}{GlueFaces}{meshList,safetyFactor=0.2,tolerance=1.e-13}  \begin{funcdesc}{GlueFaces}{meshList,safetyFactor=0.2,tolerance=1.e-13}
523  Generates a new \Domain object from the list \var{mehList} of \finley meshes.  Generates a new \Domain object from the list \var{meshList} of \finley meshes.
524  Nodes in face elements whose difference of coordinates is less then \var{tolerance} times the  Nodes in face elements whose difference of coordinates is less then \var{tolerance} times the
525  diameter of the domain are merged. The corresponding face elements are removed from the mesh.    diameter of the domain are merged. The corresponding face elements are removed from the mesh.  
526    
# Line 337  TODO: explain \var{safetyFactor} and sho Line 528  TODO: explain \var{safetyFactor} and sho
528  \end{funcdesc}  \end{funcdesc}
529    
530  \begin{funcdesc}{JoinFaces}{meshList,safetyFactor=0.2,tolerance=1.e-13}  \begin{funcdesc}{JoinFaces}{meshList,safetyFactor=0.2,tolerance=1.e-13}
531  Generates a new \Domain object from the list \var{mehList} of \finley meshes.  Generates a new \Domain object from the list \var{meshList} of \finley meshes.
532  Face elements whose nodes coordinates have difference is less then \var{tolerance} times the  Face elements whose nodes coordinates have difference is less then \var{tolerance} times the
533  diameter of the domain are combined to form a contact element \index{element!contact}  diameter of the domain are combined to form a contact element \index{element!contact}
534  The corresponding face elements are removed from the mesh.    The corresponding face elements are removed from the mesh.  

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