/[escript]/trunk/escript/py_src/linearPDEs.py
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Revision 114 - (hide annotations)
Fri Mar 4 07:12:37 2005 UTC (14 years, 9 months ago) by jgs
Original Path: trunk/esys2/escript/py_src/linearPDEs.py
File MIME type: text/x-python
File size: 47740 byte(s)
Merge of development branch back to main trunk on 2005-03-04

1 jgs 102 # $Id$
2    
3     ## @file linearPDEs.py
4    
5     """
6     @brief Functions and classes for linear PDEs
7     """
8    
9     import escript
10     import util
11     import numarray
12    
13    
14     def _CompTuple2(t1,t2):
15     """
16     @brief
17    
18     @param t1
19     @param t2
20     """
21     dif=t1[0]+t1[1]-(t2[0]+t2[1])
22     if dif<0: return 1
23     elif dif>0: return -1
24     else: return 0
25    
26 jgs 108 class PDECoefficient:
27 jgs 102 """
28     @brief
29     """
30 jgs 108 # identifier for location of Data objects defining COEFFICIENTS
31 jgs 102 INTERIOR=0
32     BOUNDARY=1
33     CONTACT=2
34     CONTINUOUS=3
35 jgs 108 # identifier in the pattern of COEFFICIENTS:
36 jgs 102 # the pattern is a tuple of EQUATION,SOLUTION,DIM where DIM represents the spatial dimension, EQUATION the number of equations and SOLUTION the
37     # number of unknowns.
38     EQUATION=3
39     SOLUTION=4
40     DIM=5
41     # indicator for what is altered if the coefficient is altered:
42     OPERATOR=5
43     RIGHTHANDSIDE=6
44     BOTH=7
45     def __init__(self,where,pattern,altering):
46     """
47     @brief Initialise a PDE Coefficient type
48     """
49     self.what=where
50     self.pattern=pattern
51     self.altering=altering
52 jgs 108 self.resetValue()
53 jgs 102
54 jgs 108 def resetValue(self):
55     """
56     @brief resets coefficient value to default
57     """
58     self.value=escript.Data()
59    
60 jgs 102 def getFunctionSpace(self,domain):
61     """
62     @brief defines the FunctionSpace of the coefficient on the domain
63    
64     @param domain
65     """
66     if self.what==self.INTERIOR: return escript.Function(domain)
67     elif self.what==self.BOUNDARY: return escript.FunctionOnBoundary(domain)
68     elif self.what==self.CONTACT: return escript.FunctionOnContactZero(domain)
69     elif self.what==self.CONTINUOUS: return escript.ContinuousFunction(domain)
70    
71 jgs 108 def getValue(self):
72     """
73     @brief returns the value of the coefficient:
74     """
75     return self.value
76    
77     def setValue(self,newValue):
78     """
79     @brief set the value of the coefficient to new value
80     """
81     self.value=newValue
82    
83 jgs 102 def isAlteringOperator(self):
84     """
85     @brief return true if the operator of the PDE is changed when the coefficient is changed
86     """
87     if self.altering==self.OPERATOR or self.altering==self.BOTH:
88     return not None
89     else:
90     return None
91    
92     def isAlteringRightHandSide(self):
93     """
94     @brief return true if the right hand side of the PDE is changed when the coefficient is changed
95     """
96     if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:
97     return not None
98     else:
99     return None
100    
101     def estimateNumEquationsAndNumSolutions(self,shape=(),dim=3):
102     """
103     @brief tries to estimate the number of equations in a given tensor shape for a given spatial dimension dim
104    
105     @param shape
106     @param dim
107     """
108     if len(shape)>0:
109     num=max(shape)+1
110     else:
111     num=1
112     search=[]
113     for u in range(num):
114     for e in range(num):
115     search.append((e,u))
116     search.sort(_CompTuple2)
117     for item in search:
118     s=self.buildShape(item[0],item[1],dim)
119     if len(s)==0 and len(shape)==0:
120     return (1,1)
121     else:
122     if s==shape: return item
123     return None
124    
125     def buildShape(self,e=1,u=1,dim=3):
126     """
127     @brief builds the required shape for a given number of equations e, number of unknowns u and spatial dimension dim
128    
129     @param e
130     @param u
131     @param dim
132     """
133     s=()
134     for i in self.pattern:
135     if i==self.EQUATION:
136     if e>1: s=s+(e,)
137     elif i==self.SOLUTION:
138     if u>1: s=s+(u,)
139     else:
140     s=s+(dim,)
141     return s
142    
143     class LinearPDE:
144     """
145 jgs 108 @brief Class to handel a linear PDE
146 jgs 102
147     class to define a linear PDE of the form
148    
149     -(A_{ijkl}u_{k,l})_{,j} -(B_{ijk}u_k)_{,j} + C_{ikl}u_{k,l} +D_{ik}u_k = - (X_{ij})_{,j} + Y_i
150    
151     with boundary conditons:
152    
153     n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i
154    
155     and contact conditions
156    
157     n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_contact_{ik}[u_k] = - n_j*X_{ij} + y_contact_i
158    
159     and constraints:
160    
161     u_i=r_i where q_i>0
162    
163     """
164 jgs 108 TOL=1.e-13
165 jgs 102 DEFAULT_METHOD=util.DEFAULT_METHOD
166     DIRECT=util.DIRECT
167     CHOLEVSKY=util.CHOLEVSKY
168     PCG=util.PCG
169     CR=util.CR
170     CGS=util.CGS
171     BICGSTAB=util.BICGSTAB
172     SSOR=util.SSOR
173     GMRES=util.GMRES
174     PRES20=util.PRES20
175 jgs 114 ILU0=util.ILU0
176     JACOBI=util.JACOBI
177 jgs 102
178 jgs 104 def __init__(self,domain,numEquations=0,numSolutions=0):
179 jgs 102 """
180     @brief initializes a new linear PDE.
181    
182     @param args
183     """
184 jgs 108 # COEFFICIENTS can be overwritten by subclasses:
185     self.COEFFICIENTS={
186     "A" : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM,PDECoefficient.SOLUTION,PDECoefficient.DIM),PDECoefficient.OPERATOR),
187     "B" : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),
188     "C" : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION,PDECoefficient.DIM),PDECoefficient.OPERATOR),
189     "D" : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),
190     "X" : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM),PDECoefficient.RIGHTHANDSIDE),
191     "Y" : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),
192     "d" : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),
193     "y" : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),
194     "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),
195     "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),
196     "r" : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),
197     "q" : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.SOLUTION,),PDECoefficient.BOTH)}
198 jgs 102
199     # initialize attributes
200     self.__debug=None
201 jgs 104 self.__domain=domain
202     self.__numEquations=numEquations
203     self.__numSolutions=numSolutions
204 jgs 102 self.cleanCoefficients()
205    
206     self.__operator=escript.Operator()
207     self.__operator_isValid=False
208     self.__righthandside=escript.Data()
209     self.__righthandside_isValid=False
210     self.__solution=escript.Data()
211     self.__solution_isValid=False
212    
213     # set some default values:
214     self.__homogeneous_constraint=True
215     self.__row_function_space=escript.Solution(self.__domain)
216     self.__column_function_space=escript.Solution(self.__domain)
217     self.__tolerance=1.e-8
218     self.__solver_method=util.DEFAULT_METHOD
219     self.__matrix_type=self.__domain.getSystemMatrixTypeId(util.DEFAULT_METHOD,False)
220     self.__sym=False
221     self.__lumping=False
222    
223 jgs 108 def createCoefficient(self, name):
224     """
225     @brief create a data object corresponding to coefficient name
226     @param name
227     """
228     return escript.Data(shape = getShapeOfCoefficient(name), \
229 jgs 110 what = getFunctionSpaceForCoefficient(name))
230 jgs 108
231     def __del__(self):
232     pass
233    
234 jgs 102 def getCoefficient(self,name):
235     """
236 jgs 108 @brief return the value of the parameter name
237 jgs 102
238     @param name
239     """
240 jgs 108 return self.COEFFICIENTS[name].getValue()
241 jgs 102
242 jgs 108 def getCoefficientOfPDE(self,name):
243     """
244     @brief return the value of the coefficient name of the general PDE. This method is called by the assembling routine
245     it can be overwritten to map coefficients of a particualr PDE to the general PDE.
246     @param name
247     """
248     return self.getCoefficient(name)
249    
250     def hasCoefficient(self,name):
251 jgs 102 """
252 jgs 108 @brief return true if name is the name of a coefficient
253 jgs 102
254 jgs 108 @param name
255 jgs 102 """
256 jgs 108 return self.COEFFICIENTS.has_key(name)
257 jgs 102
258 jgs 108 def getFunctionSpaceForEquation(self):
259     """
260     @brief return true if the test functions should use reduced order
261     """
262     return self.__row_function_space
263    
264     def getFunctionSpaceForSolution(self):
265     """
266     @brief return true if the interpolation of the solution should use reduced order
267     """
268     return self.__column_function_space
269    
270     def setValue(self,**coefficients):
271 jgs 102 """
272     @brief sets new values to coefficients
273    
274     @param coefficients
275     """
276 jgs 108 self._setValue(**coefficients)
277 jgs 102
278    
279     def cleanCoefficients(self):
280     """
281     @brief resets all coefficients to default values.
282     """
283 jgs 108 for i in self.COEFFICIENTS.iterkeys():
284     self.COEFFICIENTS[i].resetValue()
285 jgs 102
286 jgs 108 def createNewCoefficient(self,name):
287     """
288     @brief returns a new coefficient appropriate for coefficient name:
289     """
290     return escript.Data(0,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))
291    
292    
293 jgs 102 def getShapeOfCoefficient(self,name):
294     """
295     @brief return the shape of the coefficient name
296    
297     @param name
298     """
299     if self.hasCoefficient(name):
300 jgs 108 return self.COEFFICIENTS[name].buildShape(self.getNumEquations(),self.getNumSolutions(),self.getDomain().getDim())
301 jgs 102 else:
302     raise ValueError,"Solution coefficient %s requested"%name
303    
304 jgs 108 def getFunctionSpaceForCoefficient(self,name):
305 jgs 102 """
306     @brief return the atoms of the coefficient name
307    
308     @param name
309     """
310     if self.hasCoefficient(name):
311 jgs 108 return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())
312 jgs 102 else:
313     raise ValueError,"Solution coefficient %s requested"%name
314    
315     def alteredCoefficient(self,name):
316     """
317     @brief annonced that coefficient name has been changed
318    
319     @param name
320     """
321     if self.hasCoefficient(name):
322 jgs 108 if self.COEFFICIENTS[name].isAlteringOperator(): self.__rebuildOperator()
323     if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__rebuildRightHandSide()
324 jgs 102 else:
325 jgs 108 raise ValueError,"unknown coefficient %s requested"%name
326 jgs 102
327     # ===== debug ==============================================================
328     def setDebugOn(self):
329     """
330     @brief
331     """
332     self.__debug=not None
333    
334     def setDebugOff(self):
335     """
336     @brief
337     """
338     self.__debug=None
339    
340     def debug(self):
341     """
342     @brief returns true if the PDE is in the debug mode
343     """
344     return self.__debug
345    
346     #===== Lumping ===========================
347     def setLumpingOn(self):
348     """
349     @brief indicates to use matrix lumping
350     """
351     if not self.isUsingLumping():
352     if self.debug() : print "PDE Debug: lumping is set on"
353     self.__rebuildOperator()
354     self.__lumping=True
355    
356     def setLumpingOff(self):
357     """
358     @brief switches off matrix lumping
359     """
360     if self.isUsingLumping():
361     if self.debug() : print "PDE Debug: lumping is set off"
362     self.__rebuildOperator()
363     self.__lumping=False
364    
365     def setLumping(self,flag=False):
366     """
367     @brief set the matrix lumping flag to flag
368     """
369     if flag:
370     self.setLumpingOn()
371     else:
372     self.setLumpingOff()
373    
374     def isUsingLumping(self):
375     """
376     @brief
377     """
378     return self.__lumping
379    
380     #============ method business =========================================================
381     def setSolverMethod(self,solver=util.DEFAULT_METHOD):
382     """
383     @brief sets a new solver
384     """
385     if not solver==self.getSolverMethod():
386     self.__solver_method=solver
387     if self.debug() : print "PDE Debug: New solver is %s"%solver
388     self.__checkMatrixType()
389    
390     def getSolverMethod(self):
391     """
392     @brief returns the solver method
393     """
394     return self.__solver_method
395    
396     #============ tolerance business =========================================================
397     def setTolerance(self,tol=1.e-8):
398     """
399     @brief resets the tolerance to tol.
400     """
401     if not tol>0:
402     raise ValueException,"Tolerance as to be positive"
403     if tol<self.getTolerance(): self.__rebuildSolution()
404     if self.debug() : print "PDE Debug: New tolerance %e",tol
405     self.__tolerance=tol
406     return
407     def getTolerance(self):
408     """
409     @brief returns the tolerance set for the solution
410     """
411     return self.__tolerance
412    
413     #===== symmetry flag ==========================
414     def isSymmetric(self):
415     """
416     @brief returns true is the operator is considered to be symmetric
417     """
418     return self.__sym
419    
420     def setSymmetryOn(self):
421     """
422     @brief sets the symmetry flag to true
423     """
424     if not self.isSymmetric():
425     if self.debug() : print "PDE Debug: Operator is set to be symmetric"
426     self.__sym=True
427     self.__checkMatrixType()
428    
429     def setSymmetryOff(self):
430     """
431     @brief sets the symmetry flag to false
432     """
433     if self.isSymmetric():
434     if self.debug() : print "PDE Debug: Operator is set to be unsymmetric"
435     self.__sym=False
436     self.__checkMatrixType()
437    
438     def setSymmetryTo(self,flag=False):
439     """
440     @brief sets the symmetry flag to flag
441    
442     @param flag
443     """
444     if flag:
445     self.setSymmetryOn()
446     else:
447     self.setSymmetryOff()
448    
449     #===== order reduction ==========================
450     def setReducedOrderOn(self):
451     """
452     @brief switches to on reduced order
453     """
454     self.setReducedOrderForSolutionOn()
455     self.setReducedOrderForEquationOn()
456    
457     def setReducedOrderOff(self):
458     """
459     @brief switches to full order
460     """
461     self.setReducedOrderForSolutionOff()
462     self.setReducedOrderForEquationOff()
463    
464     def setReducedOrderTo(self,flag=False):
465     """
466     @brief sets order according to flag
467    
468     @param flag
469     """
470     self.setReducedOrderForSolutionTo(flag)
471     self.setReducedOrderForEquationTo(flag)
472    
473    
474     #===== order reduction solution ==========================
475     def setReducedOrderForSolutionOn(self):
476     """
477     @brief switches to reduced order to interpolate solution
478     """
479     new_fs=escript.ReducedSolution(self.getDomain())
480     if self.getFunctionSpaceForSolution()!=new_fs:
481     if self.debug() : print "PDE Debug: Reduced order is used to interpolate solution."
482     self.__column_function_space=new_fs
483     self.__rebuildSystem(deep=True)
484    
485     def setReducedOrderForSolutionOff(self):
486     """
487     @brief switches to full order to interpolate solution
488     """
489     new_fs=escript.Solution(self.getDomain())
490     if self.getFunctionSpaceForSolution()!=new_fs:
491     if self.debug() : print "PDE Debug: Full order is used to interpolate solution."
492     self.__column_function_space=new_fs
493     self.__rebuildSystem(deep=True)
494    
495     def setReducedOrderForSolutionTo(self,flag=False):
496     """
497     @brief sets order for test functions according to flag
498    
499     @param flag
500     """
501     if flag:
502     self.setReducedOrderForSolutionOn()
503     else:
504     self.setReducedOrderForSolutionOff()
505    
506     #===== order reduction equation ==========================
507     def setReducedOrderForEquationOn(self):
508     """
509     @brief switches to reduced order for test functions
510     """
511     new_fs=escript.ReducedSolution(self.getDomain())
512     if self.getFunctionSpaceForEquation()!=new_fs:
513     if self.debug() : print "PDE Debug: Reduced order is used for test functions."
514     self.__row_function_space=new_fs
515     self.__rebuildSystem(deep=True)
516    
517     def setReducedOrderForEquationOff(self):
518     """
519     @brief switches to full order for test functions
520     """
521     new_fs=escript.Solution(self.getDomain())
522     if self.getFunctionSpaceForEquation()!=new_fs:
523     if self.debug() : print "PDE Debug: Full order is used for test functions."
524     self.__row_function_space=new_fs
525     self.__rebuildSystem(deep=True)
526    
527     def setReducedOrderForEquationTo(self,flag=False):
528     """
529     @brief sets order for test functions according to flag
530    
531     @param flag
532     """
533     if flag:
534     self.setReducedOrderForEquationOn()
535     else:
536     self.setReducedOrderForEquationOff()
537    
538     # ==== initialization =====================================================================
539     def __makeNewOperator(self):
540     """
541     @brief
542     """
543     return self.getDomain().newOperator( \
544     self.getNumEquations(), \
545     self.getFunctionSpaceForEquation(), \
546     self.getNumSolutions(), \
547     self.getFunctionSpaceForSolution(), \
548     self.__matrix_type)
549    
550     def __makeNewRightHandSide(self):
551     """
552     @brief
553     """
554     return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)
555    
556     def __makeNewSolution(self):
557     """
558     @brief
559     """
560     return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)
561    
562     def __getFreshOperator(self):
563     """
564     @brief
565     """
566     if self.__operator.isEmpty():
567     self.__operator=self.__makeNewOperator()
568     if self.debug() : print "PDE Debug: New operator allocated"
569     else:
570     self.__operator.setValue(0.)
571 jgs 108 self.__operator.resetSolver()
572 jgs 102 if self.debug() : print "PDE Debug: Operator reset to zero"
573     return self.__operator
574    
575     def __getFreshRightHandSide(self):
576     """
577     @brief
578     """
579     if self.__righthandside.isEmpty():
580     self.__righthandside=self.__makeNewRightHandSide()
581     if self.debug() : print "PDE Debug: New right hand side allocated"
582     else:
583     print "fix self.__righthandside*=0"
584     self.__righthandside*=0.
585     if self.debug() : print "PDE Debug: Right hand side reset to zero"
586     return self.__righthandside
587    
588 jgs 108 #============ some serivice functions =====================================================
589     def getDomain(self):
590     """
591     @brief returns the domain of the PDE
592     """
593     return self.__domain
594    
595     def getDim(self):
596     """
597     @brief returns the spatial dimension of the PDE
598     """
599     return self.getDomain().getDim()
600    
601     def getNumEquations(self):
602     """
603     @brief returns the number of equations
604     """
605     if self.__numEquations>0:
606     return self.__numEquations
607     else:
608     raise ValueError,"Number of equations is undefined. Please specify argument numEquations."
609    
610     def getNumSolutions(self):
611     """
612     @brief returns the number of unknowns
613     """
614     if self.__numSolutions>0:
615     return self.__numSolutions
616     else:
617     raise ValueError,"Number of solution is undefined. Please specify argument numSolutions."
618    
619    
620     def checkSymmetry(self,verbose=True):
621     """
622     @brief returns if the Operator is symmetric. This is a very expensive operation!!! The symmetry flag is not altered.
623     """
624     verbose=verbose or self.debug()
625     out=True
626     if self.getNumSolutions()!=self.getNumEquations():
627     if verbose: print "non-symmetric PDE because of different number of equations and solutions"
628     out=False
629     else:
630     A=self.getCoefficientOfPDE("A")
631     if not A.isEmpty():
632     tol=util.Lsup(A)*self.TOL
633     if self.getNumSolutions()>1:
634     for i in range(self.getNumEquations()):
635     for j in range(self.getDim()):
636     for k in range(self.getNumSolutions()):
637     for l in range(self.getDim()):
638     if util.Lsup(A[i,j,k,l]-A[k,l,i,j])>tol:
639     if verbose: print "non-symmetric PDE because A[%d,%d,%d,%d]!=A[%d,%d,%d,%d]"%(i,j,k,l,k,l,i,j)
640     out=False
641     else:
642     for j in range(self.getDim()):
643     for l in range(self.getDim()):
644     if util.Lsup(A[j,l]-A[l,j])>tol:
645     if verbose: print "non-symmetric PDE because A[%d,%d]!=A[%d,%d]"%(j,l,l,j)
646     out=False
647     B=self.getCoefficientOfPDE("B")
648     C=self.getCoefficientOfPDE("C")
649     if B.isEmpty() and not C.isEmpty():
650     if verbose: print "non-symmetric PDE because B is not present but C is"
651     out=False
652     elif not B.isEmpty() and C.isEmpty():
653     if verbose: print "non-symmetric PDE because C is not present but B is"
654     out=False
655     elif not B.isEmpty() and not C.isEmpty():
656     tol=(util.Lsup(B)+util.Lsup(C))*self.TOL/2.
657     if self.getNumSolutions()>1:
658     for i in range(self.getNumEquations()):
659     for j in range(self.getDim()):
660     for k in range(self.getNumSolutions()):
661 jgs 110 if util.Lsup(B[i,j,k]-C[k,i,j])>tol:
662     if verbose: print "non-symmetric PDE because B[%d,%d,%d]!=C[%d,%d,%d]"%(i,j,k,k,i,j)
663 jgs 108 out=False
664     else:
665     for j in range(self.getDim()):
666     if util.Lsup(B[j]-C[j])>tol:
667     if verbose: print "non-symmetric PDE because B[%d]!=C[%d]"%(j,j)
668     out=False
669     if self.getNumSolutions()>1:
670     D=self.getCoefficientOfPDE("D")
671     if not D.isEmpty():
672     tol=util.Lsup(D)*self.TOL
673     for i in range(self.getNumEquations()):
674     for k in range(self.getNumSolutions()):
675     if util.Lsup(D[i,k]-D[k,i])>tol:
676     if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)
677     out=False
678    
679     return out
680    
681     def getFlux(self,u):
682     """
683     @brief returns the flux J_ij for a given u
684    
685     J_ij=A_{ijkl}u_{k,l}+B_{ijk}u_k-X_{ij}
686    
687     @param u argument of the operator
688    
689     """
690     raise SystemError,"getFlux is not implemented yet"
691     return None
692    
693     def applyOperator(self,u):
694     """
695     @brief applies the operator of the PDE to a given solution u in weak from
696    
697     @param u argument of the operator
698    
699     """
700     return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
701    
702     def getResidual(self,u):
703     """
704     @brief return the residual of u in the weak from
705    
706     @param u
707     """
708     return self.applyOperator(u)-self.getRightHandSide()
709    
710     def _setValue(self,**coefficients):
711     """
712     @brief sets new values to coefficient
713    
714     @param coefficients
715     """
716     # check if the coefficients are legal:
717     for i in coefficients.iterkeys():
718     if not self.hasCoefficient(i):
719     raise ValueError,"Attempt to set unknown coefficient %s"%i
720     # if the number of unknowns or equations is still unknown we try to estimate them:
721     if self.__numEquations<1 or self.__numSolutions<1:
722     for i,d in coefficients.iteritems():
723     if hasattr(d,"shape"):
724     s=d.shape
725     elif hasattr(d,"getShape"):
726     s=d.getShape()
727     else:
728     s=numarray.array(d).shape
729     if s!=None:
730     # get number of equations and number of unknowns:
731     res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(s,self.getDim())
732     if res==None:
733     raise ValueError,"Illegal shape %s of coefficient %s"%(s,i)
734     else:
735     if self.__numEquations<1: self.__numEquations=res[0]
736     if self.__numSolutions<1: self.__numSolutions=res[1]
737     if self.__numEquations<1: raise ValueError,"unidententified number of equations"
738     if self.__numSolutions<1: raise ValueError,"unidententified number of solutions"
739     # now we check the shape of the coefficient if numEquations and numSolutions are set:
740     for i,d in coefficients.iteritems():
741     if d==None:
742     d2=escript.Data()
743     elif isinstance(d,escript.Data):
744     if d.isEmpty():
745     d2=d
746     else:
747     d2=escript.Data(d,self.getFunctionSpaceForCoefficient(i))
748     else:
749     d2=escript.Data(d,self.getFunctionSpaceForCoefficient(i))
750     if not d2.isEmpty():
751     if not self.getShapeOfCoefficient(i)==d2.getShape():
752     raise ValueError,"Expected shape for coefficient %s is %s but actual shape is %s."%(i,self.getShapeOfCoefficient(i),d2.getShape())
753     # overwrite new values:
754     if self.debug(): print "PDE Debug: Coefficient %s has been altered."%i
755     self.COEFFICIENTS[i].setValue(d2)
756     self.alteredCoefficient(i)
757    
758     # reset the HomogeneousConstraintFlag:
759     self.__setHomogeneousConstraintFlag()
760     if len(coefficients)>0 and not self.isUsingLumping() and not self.__homogeneous_constraint: self.__rebuildSystem()
761    
762     def __setHomogeneousConstraintFlag(self):
763     """
764     @brief checks if the constraints are homogeneous and sets self.__homogeneous_constraint accordingly.
765     """
766     self.__homogeneous_constraint=True
767     q=self.getCoefficientOfPDE("q")
768     r=self.getCoefficientOfPDE("r")
769     if not q.isEmpty() and not r.isEmpty():
770     if (q*r).Lsup()>=1.e-13*r.Lsup(): self.__homogeneous_constraint=False
771     if self.debug():
772     if self.__homogeneous_constraint:
773     print "PDE Debug: Constraints are homogeneous."
774     else:
775     print "PDE Debug: Constraints are inhomogeneous."
776    
777    
778 jgs 102 # ==== rebuild switches =====================================================================
779     def __rebuildSolution(self,deep=False):
780     """
781     @brief indicates the PDE has to be reolved if the solution is requested
782     """
783     if self.__solution_isValid and self.debug() : print "PDE Debug: PDE has to be resolved."
784     self.__solution_isValid=False
785 jgs 108 if deep: self.__solution=escript.Data()
786 jgs 102
787    
788     def __rebuildOperator(self,deep=False):
789     """
790     @brief indicates the operator has to be rebuilt next time it is used
791     """
792     if self.__operator_isValid and self.debug() : print "PDE Debug: Operator has to be rebuilt."
793     self.__rebuildSolution(deep)
794     self.__operator_isValid=False
795     if deep: self.__operator=escript.Operator()
796    
797     def __rebuildRightHandSide(self,deep=False):
798     """
799     @brief indicates the right hand side has to be rebuild next time it is used
800     """
801     if self.__righthandside_isValid and self.debug() : print "PDE Debug: Right hand side has to be rebuilt."
802     self.__rebuildSolution(deep)
803     self.__righthandside_isValid=False
804     if deep: self.__righthandside=escript.Data()
805    
806     def __rebuildSystem(self,deep=False):
807     """
808     @brief annonced that all coefficient name has been changed
809     """
810     self.__rebuildSolution(deep)
811     self.__rebuildOperator(deep)
812     self.__rebuildRightHandSide(deep)
813    
814     def __checkMatrixType(self):
815     """
816     @brief reassess the matrix type and, if needed, initiates an operator rebuild
817     """
818     new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod(),self.isSymmetric())
819     if not new_matrix_type==self.__matrix_type:
820     if self.debug() : print "PDE Debug: Matrix type is now %d."%new_matrix_type
821     self.__matrix_type=new_matrix_type
822     self.__rebuildOperator(deep=True)
823    
824     #============ assembling =======================================================
825 jgs 108 def __copyConstraint(self):
826 jgs 102 """
827     @brief copies the constrint condition into u
828     """
829 jgs 108 if not self.__righthandside.isEmpty():
830     q=self.getCoefficientOfPDE("q")
831     r=self.getCoefficientOfPDE("r")
832     if not q.isEmpty():
833     if r.isEmpty():
834     r2=escript.Data(0,self.__righthandside.getShape(),self.__righthandside.getFunctionSpace())
835     else:
836     r2=escript.Data(r,self.__righthandside.getFunctionSpace())
837     self.__righthandside.copyWithMask(r2,escript.Data(q,self.__righthandside.getFunctionSpace()))
838 jgs 102
839 jgs 108 def __applyConstraint(self):
840 jgs 102 """
841 jgs 108 @brief applies the constraints defined by q and r to the system
842 jgs 102 """
843 jgs 108 q=self.getCoefficientOfPDE("q")
844     r=self.getCoefficientOfPDE("r")
845 jgs 102 if not q.isEmpty() and not self.__operator.isEmpty():
846     # q is the row and column mask to indicate where constraints are set:
847     row_q=escript.Data(q,self.getFunctionSpaceForEquation())
848     col_q=escript.Data(q,self.getFunctionSpaceForSolution())
849     u=self.__makeNewSolution()
850     if r.isEmpty():
851     r_s=self.__makeNewSolution()
852     else:
853     r_s=escript.Data(r,self.getFunctionSpaceForSolution())
854     u.copyWithMask(r_s,col_q)
855 jgs 108 if self.isUsingLumping():
856     self.__operator.copyWithMask(escript.Data(1,q.getShape(),self.getFunctionSpaceForEquation()),row_q)
857     else:
858     if not self.__righthandside.isEmpty(): self.__righthandside-=self.__operator*u
859     self.__operator.nullifyRowsAndCols(row_q,col_q,1.)
860 jgs 102
861 jgs 108 def getSystem(self):
862     """
863     @brief return the operator and right hand side of the PDE
864     """
865     if not self.__operator_isValid or not self.__righthandside_isValid:
866     if self.isUsingLumping():
867     if not self.__operator_isValid:
868     if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():
869     raise TypeError,"Lumped matrix requires same order for equations and unknowns"
870     if not self.getCoefficientOfPDE("A").isEmpty():
871     raise Warning,"Lumped matrix does not allow coefficient A"
872     if not self.getCoefficientOfPDE("B").isEmpty():
873     raise Warning,"Lumped matrix does not allow coefficient B"
874     if not self.getCoefficientOfPDE("C").isEmpty():
875     raise Warning,"Lumped matrix does not allow coefficient C"
876     if self.debug() : print "PDE Debug: New lumped operator is built."
877     mat=self.__makeNewOperator()
878     self.getDomain().addPDEToSystem(mat,escript.Data(), \
879     self.getCoefficientOfPDE("A"), \
880     self.getCoefficientOfPDE("B"), \
881     self.getCoefficientOfPDE("C"), \
882     self.getCoefficientOfPDE("D"), \
883     escript.Data(), \
884     escript.Data(), \
885     self.getCoefficientOfPDE("d"), \
886     escript.Data(),\
887     self.getCoefficientOfPDE("d_contact"), \
888     escript.Data())
889     self.__operator=mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)
890     self.__applyConstraint()
891     self.__operator_isValid=True
892     if not self.__righthandside_isValid:
893     if self.debug() : print "PDE Debug: New right hand side is built."
894     self.getDomain().addPDEToRHS(self.__getFreshRightHandSide(), \
895     self.getCoefficientOfPDE("X"), \
896     self.getCoefficientOfPDE("Y"),\
897     self.getCoefficientOfPDE("y"),\
898     self.getCoefficientOfPDE("y_contact"))
899     self.__copyConstraint()
900     self.__righthandside_isValid=True
901     else:
902     if not self.__operator_isValid and not self.__righthandside_isValid:
903     if self.debug() : print "PDE Debug: New system is built."
904     self.getDomain().addPDEToSystem(self.__getFreshOperator(),self.__getFreshRightHandSide(), \
905     self.getCoefficientOfPDE("A"), \
906     self.getCoefficientOfPDE("B"), \
907     self.getCoefficientOfPDE("C"), \
908     self.getCoefficientOfPDE("D"), \
909     self.getCoefficientOfPDE("X"), \
910     self.getCoefficientOfPDE("Y"), \
911     self.getCoefficientOfPDE("d"), \
912     self.getCoefficientOfPDE("y"), \
913     self.getCoefficientOfPDE("d_contact"), \
914     self.getCoefficientOfPDE("y_contact"))
915     self.__applyConstraint()
916     self.__copyConstraint()
917     self.__operator_isValid=True
918     self.__righthandside_isValid=True
919     elif not self.__righthandside_isValid:
920     if self.debug() : print "PDE Debug: New right hand side is built."
921     self.getDomain().addPDEToRHS(self.__getFreshRightHandSide(), \
922     self.getCoefficientOfPDE("X"), \
923     self.getCoefficientOfPDE("Y"),\
924     self.getCoefficientOfPDE("y"),\
925     self.getCoefficientOfPDE("y_contact"))
926     self.__copyConstraint()
927     self.__righthandside_isValid=True
928     elif not self.__operator_isValid:
929     if self.debug() : print "PDE Debug: New operator is built."
930     self.getDomain().addPDEToSystem(self.__getFreshOperator(),escript.Data(), \
931     self.getCoefficientOfPDE("A"), \
932     self.getCoefficientOfPDE("B"), \
933     self.getCoefficientOfPDE("C"), \
934     self.getCoefficientOfPDE("D"), \
935     escript.Data(), \
936     escript.Data(), \
937     self.getCoefficientOfPDE("d"), \
938     escript.Data(),\
939     self.getCoefficientOfPDE("d_contact"), \
940     escript.Data())
941     self.__applyConstraint()
942     self.__operator_isValid=True
943     return (self.__operator,self.__righthandside)
944 jgs 102 def getOperator(self):
945     """
946     @brief returns the operator of the PDE
947     """
948 jgs 108 return self.getSystem()[0]
949 jgs 102
950 jgs 108 def getRightHandSide(self):
951 jgs 102 """
952     @brief returns the right hand side of the PDE
953     """
954 jgs 108 return self.getSystem()[1]
955 jgs 102
956     def solve(self,**options):
957     """
958     @brief solve the PDE
959    
960     @param options
961     """
962     mat,f=self.getSystem()
963     if self.isUsingLumping():
964     out=f/mat
965     else:
966     options[util.TOLERANCE_KEY]=self.getTolerance()
967     options[util.METHOD_KEY]=self.getSolverMethod()
968     options[util.SYMMETRY_KEY]=self.isSymmetric()
969     if self.debug() : print "PDE Debug: solver options: ",options
970     out=mat.solve(f,options)
971     return out
972    
973     def getSolution(self,**options):
974     """
975     @brief returns the solution of the PDE
976    
977     @param options
978     """
979     if not self.__solution_isValid:
980     if self.debug() : print "PDE Debug: PDE is resolved."
981     self.__solution=self.solve(**options)
982     self.__solution_isValid=True
983     return self.__solution
984    
985 jgs 110
986    
987     def ELMAN_RAMAGE(P): return (P-1.).wherePositive()*0.5*(1.-1./(P+1.e-15))
988     def SIMPLIFIED_BROOK_HUGHES(P):
989     c=(P-3.).whereNegative()
990     return P/6.*c+1./2.*(1.-c)
991     def HALF(P): return escript.Scalar(0.5,P.getFunctionSpace())
992    
993    
994 jgs 108 class AdvectivePDE(LinearPDE):
995     """
996     @brief Class to handel a linear PDE domineated by advective terms:
997    
998     class to define a linear PDE of the form
999 jgs 104
1000 jgs 108 -(A_{ijkl}u_{k,l})_{,j} -(B_{ijk}u_k)_{,j} + C_{ikl}u_{k,l} +D_{ik}u_k = - (X_{ij})_{,j} + Y_i
1001 jgs 102
1002 jgs 108 with boundary conditons:
1003 jgs 102
1004 jgs 108 n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i
1005 jgs 102
1006 jgs 108 and contact conditions
1007 jgs 102
1008 jgs 108 n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_contact_{ik}[u_k] = - n_j*X_{ij} + y_contact_i
1009 jgs 102
1010 jgs 108 and constraints:
1011 jgs 102
1012 jgs 108 u_i=r_i where q_i>0
1013 jgs 102
1014 jgs 110 """
1015     def __init__(self,domain,numEquations=0,numSolutions=0,xi=ELMAN_RAMAGE):
1016     LinearPDE.__init__(self,domain,numEquations,numSolutions)
1017     self.__xi=xi
1018     self.__Xi=escript.Data()
1019 jgs 102
1020 jgs 110 def __calculateXi(self,peclet_factor,Z,h):
1021     Z_max=util.Lsup(Z)
1022     if Z_max>0.:
1023     return h*self.__xi(Z*peclet_factor)/(Z+Z_max*self.TOL)
1024     else:
1025     return 0.
1026 jgs 102
1027 jgs 110 def setValue(self,**args):
1028     if "A" in args.keys() or "B" in args.keys() or "C" in args.keys(): self.__Xi=escript.Data()
1029     self._setValue(**args)
1030    
1031     def getXi(self):
1032     if self.__Xi.isEmpty():
1033     B=self.getCoefficient("B")
1034     C=self.getCoefficient("C")
1035     A=self.getCoefficient("A")
1036     h=self.getDomain().getSize()
1037     self.__Xi=escript.Scalar(0.,self.getFunctionSpaceForCoefficient("A"))
1038     if not C.isEmpty() or not B.isEmpty():
1039     if not C.isEmpty() and not B.isEmpty():
1040     Z2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))
1041     if self.getNumEquations()>1:
1042     if self.getNumSolutions()>1:
1043     for i in range(self.getNumEquations()):
1044     for k in range(self.getNumSolutions()):
1045     for l in range(self.getDim()): Z2+=(C[i,k,l]-B[i,l,k])**2
1046     else:
1047     for i in range(self.getNumEquations()):
1048     for l in range(self.getDim()): Z2+=(C[i,l]-B[i,l])**2
1049     else:
1050     if self.getNumSolutions()>1:
1051     for k in range(self.getNumSolutions()):
1052     for l in range(self.getDim()): Z2+=(C[k,l]-B[l,k])**2
1053     else:
1054     for l in range(self.getDim()): Z2+=(C[l]-B[l])**2
1055     length_of_Z=util.sqrt(Z2)
1056     elif C.isEmpty():
1057     length_of_Z=util.length(B)
1058     else:
1059     length_of_Z=util.length(C)
1060 jgs 102
1061 jgs 110 Z_max=util.Lsup(length_of_Z)
1062     if Z_max>0.:
1063     length_of_A=util.length(A)
1064     A_max=util.Lsup(length_of_A)
1065     if A_max>0:
1066     inv_A=1./(length_of_A+A_max*self.TOL)
1067     else:
1068     inv_A=1./self.TOL
1069     peclet_number=length_of_Z*h/2*inv_A
1070     xi=self.__xi(peclet_number)
1071     self.__Xi=h*xi/(length_of_Z+Z_max*self.TOL)
1072     print "@ preclet number = %e"%util.Lsup(peclet_number),util.Lsup(xi),util.Lsup(length_of_Z)
1073     return self.__Xi
1074    
1075 jgs 102
1076 jgs 108 def getCoefficientOfPDE(self,name):
1077     """
1078     @brief return the value of the coefficient name of the general PDE
1079     @param name
1080     """
1081 jgs 110 if not self.getNumEquations() == self.getNumSolutions():
1082     raise ValueError,"AdvectivePDE expects the number of solution componets and the number of equations to be equal."
1083    
1084 jgs 108 if name == "A" :
1085     A=self.getCoefficient("A")
1086     B=self.getCoefficient("B")
1087     C=self.getCoefficient("C")
1088 jgs 110 if B.isEmpty() and C.isEmpty():
1089     Aout=A
1090     else:
1091     if A.isEmpty():
1092     Aout=self.createNewCoefficient("A")
1093     else:
1094     Aout=A[:]
1095     Xi=self.getXi()
1096     if self.getNumEquations()>1:
1097     for i in range(self.getNumEquations()):
1098     for j in range(self.getDim()):
1099 jgs 108 for k in range(self.getNumSolutions()):
1100 jgs 110 for l in range(self.getDim()):
1101     if not C.isEmpty() and not B.isEmpty():
1102     for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*(C[p,i,j]-B[p,j,i])*(C[p,k,l]-B[p,l,k])
1103     elif C.isEmpty():
1104     for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*B[p,j,i]*B[p,l,k]
1105     else:
1106     for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*C[p,i,j]*C[p,k,l]
1107     else:
1108     for j in range(self.getDim()):
1109     for l in range(self.getDim()):
1110     if not C.isEmpty() and not B.isEmpty():
1111     Aout[j,l]+=Xi*(C[j]-B[j])*(C[l]-B[l])
1112     elif C.isEmpty():
1113     Aout[j,l]+=Xi*B[j]*B[l]
1114     else:
1115     Aout[j,l]+=Xi*C[j]*C[l]
1116     return Aout
1117 jgs 108 elif name == "B" :
1118 jgs 110 B=self.getCoefficient("B")
1119     C=self.getCoefficient("C")
1120     D=self.getCoefficient("D")
1121     if C.isEmpty() or D.isEmpty():
1122     Bout=B
1123     else:
1124     Xi=self.getXi()
1125     if B.isEmpty():
1126     Bout=self.createNewCoefficient("B")
1127     else:
1128     Bout=B[:]
1129     if self.getNumEquations()>1:
1130     for k in range(self.getNumSolutions()):
1131     for p in range(self.getNumEquations()):
1132     tmp=Xi*D[p,k]
1133     for i in range(self.getNumEquations()):
1134     for j in range(self.getDim()):
1135     Bout[i,j,k]+=tmp*C[p,i,j]
1136     else:
1137     tmp=Xi*D
1138     for j in range(self.getDim()): Bout[j]+=tmp*C[j]
1139     return Bout
1140 jgs 108 elif name == "C" :
1141 jgs 110 B=self.getCoefficient("B")
1142     C=self.getCoefficient("C")
1143     D=self.getCoefficient("D")
1144     if B.isEmpty() or D.isEmpty():
1145     Cout=C
1146     else:
1147     Xi=self.getXi()
1148     if C.isEmpty():
1149     Cout=self.createNewCoefficient("C")
1150     else:
1151     Cout=C[:]
1152     if self.getNumEquations()>1:
1153     for k in range(self.getNumSolutions()):
1154     for p in range(self.getNumEquations()):
1155     tmp=Xi*D[p,k]
1156     for i in range(self.getNumEquations()):
1157     for l in range(self.getDim()):
1158     Cout[i,k,l]+=tmp*B[p,l,i]
1159     else:
1160     tmp=Xi*D
1161     for j in range(self.getDim()): Cout[j]+=tmp*B[j]
1162     return Cout
1163 jgs 108 elif name == "D" :
1164     return self.getCoefficient("D")
1165     elif name == "X" :
1166 jgs 110 X=self.getCoefficient("X")
1167     Y=self.getCoefficient("Y")
1168     B=self.getCoefficient("B")
1169     C=self.getCoefficient("C")
1170     if Y.isEmpty() or (B.isEmpty() and C.isEmpty()):
1171     Xout=X
1172     else:
1173     if X.isEmpty():
1174     Xout=self.createNewCoefficient("X")
1175     else:
1176     Xout=X[:]
1177     Xi=self.getXi()
1178     if self.getNumEquations()>1:
1179     for p in range(self.getNumEquations()):
1180     tmp=Xi*Y[p]
1181     for i in range(self.getNumEquations()):
1182     for j in range(self.getDim()):
1183     if not C.isEmpty() and not B.isEmpty():
1184     Xout[i,j]+=tmp*(C[p,i,j]-B[p,j,i])
1185     elif C.isEmpty():
1186     Xout[i,j]-=tmp*B[p,j,i]
1187     else:
1188     Xout[i,j]+=tmp*C[p,i,j]
1189     else:
1190     tmp=Xi*Y
1191     for j in range(self.getDim()):
1192     if not C.isEmpty() and not B.isEmpty():
1193     Xout[j]+=tmp*(C[j]-B[j])
1194     elif C.isEmpty():
1195     Xout[j]-=tmp*B[j]
1196     else:
1197     Xout[j]+=tmp*C[j]
1198     return Xout
1199 jgs 108 elif name == "Y" :
1200     return self.getCoefficient("Y")
1201     elif name == "d" :
1202     return self.getCoefficient("d")
1203     elif name == "y" :
1204     return self.getCoefficient("y")
1205     elif name == "d_contact" :
1206     return self.getCoefficient("d_contact")
1207     elif name == "y_contact" :
1208     return self.getCoefficient("y_contact")
1209     elif name == "r" :
1210     return self.getCoefficient("r")
1211     elif name == "q" :
1212     return self.getCoefficient("q")
1213     else:
1214     raise SystemError,"unknown PDE coefficient %s",name
1215    
1216    
1217 jgs 102 class Poisson(LinearPDE):
1218     """
1219     @brief Class to define a Poisson equstion problem:
1220    
1221     class to define a linear PDE of the form
1222    
1223     -u_{,jj} = f
1224    
1225     with boundary conditons:
1226    
1227     n_j*u_{,j} = 0
1228    
1229     and constraints:
1230    
1231     u=0 where q>0
1232    
1233     """
1234    
1235 jgs 108 def __init__(self,domain,f=escript.Data(),q=escript.Data()):
1236     LinearPDE.__init__(self,domain,1,1)
1237     self.COEFFICIENTS={
1238     "f" : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1239     "q" : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.BOTH)}
1240 jgs 102 self.setSymmetryOn()
1241     self.setValue(f,q)
1242    
1243     def setValue(self,f=escript.Data(),q=escript.Data()):
1244 jgs 108 self._setValue(f=f,q=q)
1245    
1246     def getCoefficientOfPDE(self,name):
1247     """
1248     @brief return the value of the coefficient name of the general PDE
1249     @param name
1250     """
1251     if name == "A" :
1252     return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))
1253     elif name == "B" :
1254     return escript.Data()
1255     elif name == "C" :
1256     return escript.Data()
1257     elif name == "D" :
1258     return escript.Data()
1259     elif name == "X" :
1260     return escript.Data()
1261     elif name == "Y" :
1262     return self.getCoefficient("f")
1263     elif name == "d" :
1264     return escript.Data()
1265     elif name == "y" :
1266     return escript.Data()
1267     elif name == "d_contact" :
1268     return escript.Data()
1269     elif name == "y_contact" :
1270     return escript.Data()
1271     elif name == "r" :
1272     return escript.Data()
1273     elif name == "q" :
1274     return self.getCoefficient("q")
1275     else:
1276     raise SystemError,"unknown PDE coefficient %s",name

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