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1  % $Id$  
2    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3  %  %
4  %           Copyright © 2006, 2007 by ACcESS MNRF  % Copyright (c) 2003-2009 by University of Queensland
5  %               \url{http://www.access.edu.au  % Earth Systems Science Computational Center (ESSCC)
6  %         Primary Business: Queensland, Australia.  % http://www.uq.edu.au/esscc
 %   Licensed under the Open Software License version 3.0  
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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 58  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.
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    \finley supports macro elements\index{macro elements}. For these elements a piecewise linear approximation is used on an element which is further subdivided (in the case \finley halved). As such these elements do not provide more than a further mesh refinement but should be used in the case of incompressible flows, see \class{StokesProblemCartesian}. For these problems a linear approximation of the pressure across the element is used (use the \ReducedSolutionFS \FunctionSpace) while the refined element is used to approximate velocity. So a macro element provides a continuous pressure approximation together with a velocity approximation on a refined mesh. This approach is necessary to make sure that the  incompressible flow has a unique solution.
72    
73  The union of all elements defines the domain of the PDE.  The union of all elements defines the domain of the PDE.
74  Each element is defined by the nodes used to describe its 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,
# Line 81  to second node the domain has to lie on Line 85  to second node the domain has to lie on
85  the domain has to lie on the 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
86  surface of the domain is 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
87  are 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
88  with the surface of the domian. In \fig{FINLEY FIG 0}  with the surface of the domain. In \fig{FINLEY FIG 0}
89  elements of the type \finleyelement{Tri3Face} are used.  elements of the type \finleyelement{Tri3Face} are used.
90  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
91  with 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
# Line 113  contact regions line up.  The rich versi Line 117  contact regions line up.  The rich versi
117  $4$ 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
118  $2$.  $2$.
119    
120    
121    
122  \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
123  on the 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
124  the nodes within an element.  the nodes within an element.
# Line 130  the nodes within an element. Line 136  the nodes within an element.
136  \linev{\finleyelement{Tet10}}{\finleyelement{Tri9}}{\finleyelement{Tet10Face}}{\finleyelement{Tri9_Contact}}{\finleyelement{Tet10Face_Contact}}  \linev{\finleyelement{Tet10}}{\finleyelement{Tri9}}{\finleyelement{Tet10Face}}{\finleyelement{Tri9_Contact}}{\finleyelement{Tet10Face_Contact}}
137  \linev{\finleyelement{Hex8}}{\finleyelement{Rec4}}{\finleyelement{Hex8Face}}{\finleyelement{Rec4_Contact}}{\finleyelement{Hex8Face_Contact}}  \linev{\finleyelement{Hex8}}{\finleyelement{Rec4}}{\finleyelement{Hex8Face}}{\finleyelement{Rec4_Contact}}{\finleyelement{Hex8Face_Contact}}
138  \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}}
139    \linev{\finleyelement{Hex27}}{\finleyelement{Rec9}}{N\textbackslash A}{N\textbackslash A}{N\textbackslash A}
140    \linev{\finleyelement{Hex27Macro}}{\finleyelement{Rec9Macro}}{N\textbackslash A}{N\textbackslash A}{N\textbackslash A}
141    \linev{\finleyelement{Tet10Macro}}{\finleyelement{Tri6Macro}}{N\textbackslash A}{N\textbackslash A}{N\textbackslash A}
142    \linev{\finleyelement{Rec9Macro}}{\finleyelement{Line3Macro}}{N\textbackslash A}{N\textbackslash A}{N\textbackslash A}
143    \linev{\finleyelement{Tri6Macro}}{\finleyelement{Line3Macro}}{N\textbackslash A}{N\textbackslash A}{N\textbackslash A}
144  \end{tablev}  \end{tablev}
145  \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.
146  The rich types have to be used if the gradient of function is to be 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.}
147  \label{FINLEY TAB 1}  \label{FINLEY TAB 1}
148  \end{table}  \end{table}
149    
# Line 176  for i in range(ContactElement_Num): Line 187  for i in range(ContactElement_Num):
187     for j in range(ContactElement_numNodes): print " %d"%ContactElement_Nodes[i][j]     for j in range(ContactElement_numNodes): print " %d"%ContactElement_Nodes[i][j]
188     print "\n"     print "\n"
189  # point sources (not supported yet)  # point sources (not supported yet)
190  write("Point1 0",face_element_typ,numFaceElements)  write("Point1 0",face_element_type,numFaceElements)
191  \end{python}  \end{python}
192    
193  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 247  $7$, $10$, $15$ and $20$, respectively. Line 258  $7$, $10$, $15$ and $20$, respectively.
258  20 16 0 1.0  1.0  20 16 0 1.0  1.0
259  \end{verbatim}  \end{verbatim}
260    
261    \clearpage
262    \input{finleyelements}
263    \clearpage
264    
265  \include{finleyelements}  \section{Macro Elements}
266    \label{SEC FINLEY MACRO}
267    
268  \subsection{Linear Solvers in \LinearPDE}  
269  Currently \finley supports the linear solvers \PCG, \GMRES, \PRESTWENTY and \BiCGStab.  
270  For \GMRES the options \var{trancation} and \var{restart} of the \method{getSolution} can be  \begin{table}
271  used to control the trunction and restart during iteration. Default values are  {\scriptsize
272  \var{truncation}=5 and \var{restart}=20.  \begin{tabular}{l||c|c|c|c|c|c|c|c}
273  The default solver is \BiCGStab  but if the symmetry flag is set \PCG is the default solver.  \member{setSolverMethod} & \member{DIRECT}& \member{PCG} & \member{GMRES} & \member{TFQMR} & \member{MINRES} & \member{PRES20} & \member{BICGSTAB} & \member{LUMPING} \\
274  \finley supports the solver options \var{iter_max} which specifies the maximum number of iterations steps,  \hline
275  \var{verbose}=\True or \False and \var{preconditioner}=\constant{JACOBI} or \constant {ILU0}.   \hline
276  In some installations \finley supports the \Direct solver and the   \member{setReordering} & $\checkmark$ & & & & & &\\
277  solver options \var{reordering}=\constant{util.NO_REORDERING},   \hline  \member{setRestart} &  & & $\checkmark$ & & & $20$ & \\
278  \constant{util.MINIMUM_FILL_IN} or \constant{util.NESTED_DISSECTION} (default is \constant{util.NO_REORDERING}),   \hline\member{setTruncation} &  & & $\checkmark$ & & & $5$ & \\
279  \var{drop_tolerance} specifying the threshold for values to be dropped in the     \hline\member{setIterMax} &  & $\checkmark$& $\checkmark$ & $\checkmark$& $\checkmark$& $\checkmark$ & $\checkmark$ \\
280  incomplete elimation process (default is 0.01) and \var{drop_storage} specifying the maximum increase   \hline\member{setTolerance} &  & $\checkmark$& $\checkmark$ & $\checkmark$& $\checkmark$& $\checkmark$ & $\checkmark$ \\
281  in storage allowed in the   \hline\member{setAbsoluteTolerance} &  & $\checkmark$& $\checkmark$ & $\checkmark$& $\checkmark$& $\checkmark$ & $\checkmark$ \\
282  incomplete elimation process (default is 1.20).  \hline\member{setReordering} & $\checkmark$ & & & & & & & \\
283    \end{tabular}
284    }
285    \caption{Solvers available for
286    \finley
287    and the \PASO package and the relevant options in \class{SolverOptions}.
288    \MKL supports
289    \MINIMUMFILLIN
290    and
291    \NESTEDDESCTION
292    reordering.
293    Currently the \UMFPACK interface does not support any reordering.
294    \label{TAB FINLEY SOLVER OPTIONS 1} }
295    \end{table}
296    
297    \begin{table}
298    {\scriptsize
299    \begin{tabular}{l||c|c|c|c|c|c|c|c}
300    \member{setPreconditioner} &
301    \member{NO_PRECONDITIONER} &
302    \member{AMG} &
303    \member{JACOBI} &
304    \member{GAUSS_SEIDEL}&
305    \member{REC_ILU}&
306    \member{RILU} &
307    \member{ILU0} &
308    \member{DIRECT} \\
309     \hline
310     status: &
311    later &
312    later &
313    $\checkmark$ &
314    $\checkmark$&
315    $\checkmark$ &
316    later &
317    $\checkmark$ &
318    later \\
319    \hline
320    \hline
321    \member{setCoarsening}&
322     &
323    $\checkmark$ &
324    &
325    &
326    &
327     &
328     &
329     \\
330    
331    
332    \hline\member{setLevelMax}&
333     &
334    $\checkmark$ &
335     &
336    &
337    &
338     &
339     &
340     \\
341    
342    \hline\member{setCoarseningThreshold}&
343    &
344    $\checkmark$ &
345     &
346    &
347    &
348     &
349     &
350     \\
351    
352    \hline\member{setMinCoarseMatrixSize} &
353     &
354    $\checkmark$ &
355     &
356    &
357    &
358     &
359     &
360     \\
361    
362    \hline\member{setNumSweeps} &
363     &
364     &
365    $\checkmark$ &
366    $\checkmark$ &
367    &
368     &
369     &
370     \\
371    
372    \hline\member{setNumPreSweeps}&
373     &
374    $\checkmark$ &
375      &
376     &
377     &
378      &
379      &
380      \\
381    
382    \hline\member{setNumPostSweeps} &
383     &
384    $\checkmark$ &
385     &
386    &
387    &
388     &
389    &
390     \\
391    
392    \hline\member{setInnerTolerance}&
393     &
394     &
395     &
396    &
397    &
398     &
399    &
400     \\
401    
402    \hline\member{setDropTolerance}&
403     &
404     &
405     &
406    &
407    &
408     &
409    &
410     \\
411    
412    \hline\member{setDropStorage}&
413     &
414     &
415     &
416    &
417    &
418     &
419    &
420     \\
421    
422    \hline\member{setRelaxationFactor}&
423     &
424     &
425     &
426    &
427    &
428    $\checkmark$  &
429     &
430     \\
431    
432    \hline\member{adaptInnerTolerance}&
433     &
434     &
435     &
436    &
437    &
438     &
439    &
440     \\
441    
442    \hline\member{setInnerIterMax}&
443     &
444     &
445     &
446    &
447    &
448     &
449    &
450     \\
451    \end{tabular}
452    }
453    \caption{Preconditioners available for \finley and the \PASO package and the relevant options in \class{SolverOptions}. \label{TAB FINLEY SOLVER OPTIONS 2}}
454    \end{table}
455    
456    \subsection{Linear Solvers in \SolverOptions}
457    Table~\ref{TAB FINLEY SOLVER OPTIONS 1} and
458    Table~\ref{TAB FINLEY SOLVER OPTIONS 2} show the solvers and preconditioners supported by
459    \finley through the \PASO library. Currently direct solvers are not supported under MPI.
460    By default, \finley is using the iterative solvers \PCG for symmetric and \BiCGStab for non-symmetric problems.
461    If the direct solver is selected which can be useful when solving very ill-posedequations
462    \finley uses the \MKL \footnote{If the stiffness matrix is non-regular \MKL may return without
463    returning a proper error code. If you observe suspicious solutions when using MKL, this may cause by a non-invertible operator. } solver package. If \MKL is not available \UMFPACK is used. If \UMFPACK is not available
464    a suitable iterative solver from the \PASO is used.
465    
466  \subsection{Functions}  \subsection{Functions}
467  \begin{funcdesc}{Mesh}{fileName,integrationOrder=-1}  \begin{funcdesc}{ReadMesh}{fileName \optional{, \optional{integrationOrder=-1}, optimize=True}}
468  creates a \Domain object form the FEM mesh defined in  creates a \Domain object form the FEM mesh defined in
469  file \var{fileName}. The file must be given the \finley file format.  file \var{fileName}. The file must be given the \finley file format.
470  If \var{integrationOrder} is positive, a numerical integration scheme  If \var{integrationOrder} is positive, a numerical integration scheme
471  chosen which is accurate on each element up to a polynomial of  chosen which is accurate on each element up to a polynomial of
472  degree \var{integrationOrder} \index{integration order}. Otherwise  degree \var{integrationOrder} \index{integration order}. Otherwise
473    an appropriate integration order is chosen independently.
474    By default the labeling of mesh nodes and element distribution is
475    optimized. Set \var{optimize=False} to switch off relabeling and redistribution.
476    \end{funcdesc}
477    
478    \begin{funcdesc}{ReadGmsh}{fileName \optional{, \optional{integrationOrder=-1}, optimize=True\optional{, useMacroElements=False}}}
479    creates a \Domain object form the FEM mesh defined in
480    file \var{fileName}. The file must be given the \gmshextern file format.
481    If \var{integrationOrder} is positive, a numerical integration scheme
482    chosen which is accurate on each element up to a polynomial of
483    degree \var{integrationOrder} \index{integration order}. Otherwise
484  an appropriate integration order is chosen independently.  an appropriate integration order is chosen independently.
485    By default the labeling of mesh nodes and element distribution is
486    optimized. Set \var{optimize=False} to switch off relabeling and redistribution.
487    If \var{useMacroElements} is set, second order elements are interpreated as macro elements~\index{macro elements}.
488    Currently \function{ReadGmsh} does not support MPI.  
489  \end{funcdesc}  \end{funcdesc}
490    
491  \begin{funcdesc}{Interval}{n0,order=1,l0=1.,integrationOrder=-1, \\  \begin{funcdesc}{MakeDomain}{design\optional{, integrationOrder=-1\optional{, optimizeLabeling=True\optional{, useMacroElements=False}}}}
492    periodic0=\False,useElementsOnFace=\False}  Creates a Finley \Domain from a \class{Design} object using \gmshextern.
493  Generates a \Domain object representing a interval $[0,l0]$. The interval is filled with  The \class{Design} \var{design} defines the geometry.
 \var{n0} elements.  
 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.    
494  If \var{integrationOrder} is positive, a numerical integration scheme  If \var{integrationOrder} is positive, a numerical integration scheme
495  chosen which is accurate on each element up to a polynomial of  chosen which is accurate on each element up to a polynomial of
496  degree \var{integrationOrder} \index{integration order}. Otherwise  degree \var{integrationOrder} \index{integration order}. Otherwise
497  an appropriate integration order is chosen independently. If  an appropriate integration order is chosen independently.
498  \var{periodic0}=\True, periodic boundary conditions \index{periodic boundary conditions}  Set \var{optimizeLabeling=False} to switch off relabeling and redistribution (not recommended).
499  along the $x_0$-directions are enforced. That means when for any solution of a PDE solved by \finley  If \var{useMacroElements} is set, macro elements~\index{macro elements} are used.
500  the value at $x_0=0$ will be identical to the values at $x_0=\var{l0}$.  Currently \function{MakeDomain} does not support MPI.  
501  \end{funcdesc}  \end{funcdesc}
502    
503    
504    \begin{funcdesc}{load}{fileName}
505    recovers a \Domain object from a dump file created by the \
506    eateseates a \Domain object form the FEM mesh defined in
507    file \var{fileName}. The file must be given the \finley file format.
508    If \var{integrationOrder} is positive, a numerical integration scheme
509    chosen which is accurate on each element up to a polynomial of
510    degree \var{integrationOrder} \index{integration order}. Otherwise
511    an appropriate integration order is chosen independently.
512    \end{funcdesc}
513    
514    
515  \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, \\
516    periodic0=\False,periodic1=\False,useElementsOnFace=\False}    periodic0=\False, periodic1=\False, useElementsOnFace=\False, useMacroElements=\False, optimize=\False}
517  Generates a \Domain object representing a two dimensional rectangle between  Generates a \Domain object representing a two dimensional rectangle between
518  $(0,0)$ and $(l0,l1)$ with orthogonal edges. The rectangle is filled with  $(0,0)$ and $(l0,l1)$ with orthogonal edges. The rectangle is filled with
519  \var{n0} elements along the $x_0$-axis and  \var{n0} elements along the $x_0$-axis and
# Line 310  For \var{order}=1 and \var{order}=2 Line 524  For \var{order}=1 and \var{order}=2
524  In the case of \var{useElementsOnFace}=\False,  In the case of \var{useElementsOnFace}=\False,
525  \finleyelement{Line2} and    \finleyelement{Line2} and  
526  \finleyelement{Line3} are used to subdivide the edges of the rectangle, respectively.  \finleyelement{Line3} are used to subdivide the edges of the rectangle, respectively.
527    If \var{order}=-1, \finleyelement{Rec8Macro} and \finleyelement{Line3Macro}~\index{macro elements}. This option should be used when solving incompressible fluid flow problem, e.g. \class{StokesProblemCartesian}.
528  In the case of \var{useElementsOnFace}=\True (this option should be used if gradients  In the case of \var{useElementsOnFace}=\True (this option should be used if gradients
529  are calculated on domain faces),  are calculated on domain faces),
530  \finleyelement{Rec4Face} and    \finleyelement{Rec4Face} and  
# Line 324  the value on the line $x_0=0$ will be id Line 539  the value on the line $x_0=0$ will be id
539  Correspondingly,  Correspondingly,
540  \var{periodic1}=\False sets periodic boundary conditions  \var{periodic1}=\False sets periodic boundary conditions
541  in $x_1$-direction.  in $x_1$-direction.
542    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.
543  \end{funcdesc}  \end{funcdesc}
544    
545  \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, \\
546    periodic0=\False,periodic1=\False,periodic2=\False,useElementsOnFace=\False}    periodic0=\False,periodic1=\False,periodic2=\False,useElementsOnFace=\False, useMacroElements=\False, optimize=\False}
547  Generates a \Domain object representing a three dimensional brick between  Generates a \Domain object representing a three dimensional brick between
548  $(0,0,0)$ 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
549  \var{n0} elements along the $x_0$-axis,  \var{n0} elements along the $x_0$-axis,
# Line 343  In the case of \var{useElementsOnFace}=\ Line 559  In the case of \var{useElementsOnFace}=\
559  are calculated on domain faces),  are calculated on domain faces),
560  \finleyelement{Hex8Face} and    \finleyelement{Hex8Face} and  
561  \finleyelement{Hex20Face} are used on the brick faces, respectively.    \finleyelement{Hex20Face} are used on the brick faces, respectively.  
562    If \var{order}=-1, \finleyelement{Hex20Macro} and \finleyelement{Rec8Macro}~\index{macro elements}. This option should be used when solving incompressible fluid flow problem, e.g. \class{StokesProblemCartesian}.
563  If \var{integrationOrder} is positive, a numerical integration scheme  If \var{integrationOrder} is positive, a numerical integration scheme
564  chosen which is accurate on each element up to a polynomial of  chosen which is accurate on each element up to a polynomial of
565  degree \var{integrationOrder} \index{integration order}. Otherwise  degree \var{integrationOrder} \index{integration order}. Otherwise
# Line 352  along the $x_0$-directions are enforced. Line 569  along the $x_0$-directions are enforced.
569  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,
570  \var{periodic1}=\False and \var{periodic2}=\False sets periodic boundary conditions  \var{periodic1}=\False and \var{periodic2}=\False sets periodic boundary conditions
571  in $x_1$-direction and $x_2$-direction, respectively.  in $x_1$-direction and $x_2$-direction, respectively.
572    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.
573  \end{funcdesc}  \end{funcdesc}
574    
575  \begin{funcdesc}{GlueFaces}{meshList,safetyFactor=0.2,tolerance=1.e-13}  \begin{funcdesc}{GlueFaces}{meshList,safetyFactor=0.2,tolerance=1.e-13}
576  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.
577  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
578  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.  
579    
# Line 363  TODO: explain \var{safetyFactor} and sho Line 581  TODO: explain \var{safetyFactor} and sho
581  \end{funcdesc}  \end{funcdesc}
582    
583  \begin{funcdesc}{JoinFaces}{meshList,safetyFactor=0.2,tolerance=1.e-13}  \begin{funcdesc}{JoinFaces}{meshList,safetyFactor=0.2,tolerance=1.e-13}
584  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.
585  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
586  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}
587  The corresponding face elements are removed from the mesh.    The corresponding face elements are removed from the mesh.  

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