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Revision 430 - (show annotations)
Wed Jan 11 06:40:50 2006 UTC (13 years, 8 months ago) by gross
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ILU has been replicated is called RILU (recursive ILU) now. ILU will now be reimplemented.
1 # $Id$
2
3 #
4 # COPYRIGHT ACcESS 2004 - All Rights Reserved
5 #
6 # This software is the property of ACcESS. No part of this code
7 # may be copied in any form or by any means without the expressed written
8 # consent of ACcESS. Copying, use or modification of this software
9 # by any unauthorised person is illegal unless that
10 # person has a software license agreement with ACcESS.
11 #
12 """
13 The module provides an interface to define and solve linear partial
14 differential equations (PDEs) within L{escript}. L{linearPDEs} does not provide any
15 solver capabilities in itself but hands the PDE over to
16 the PDE solver library defined through the L{Domain<escript.Domain>} of the PDE.
17 The general interface is provided through the L{LinearPDE} class. The
18 L{AdvectivePDE} which is derived from the L{LinearPDE} class
19 provides an interface to PDE dominated by its advective terms. The L{Poisson},
20 L{Helmholtz}, L{LameEquation}, L{AdvectionDiffusion}
21 classs which are also derived form the L{LinearPDE} class should be used
22 to define of solve these sepecial PDEs.
23
24 @var __author__: name of author
25 @var __licence__: licence agreement
26 @var __url__: url entry point on documentation
27 @var __version__: version
28 @var __date__: date of the version
29 """
30
31 import escript
32 import util
33 import numarray
34
35 __author__="Lutz Gross, l.gross@uq.edu.au"
36 __licence__="contact: esys@access.uq.edu.au"
37 __url__="http://www.iservo.edu.au/esys/escript"
38 __version__="$Revision$"
39 __date__="$Date$"
40
41
42 class IllegalCoefficient(ValueError):
43 """
44 raised if an illegal coefficient of the general ar particular PDE is requested.
45 """
46
47 class IllegalCoefficientValue(ValueError):
48 """
49 raised if an incorrect value for a coefficient is used.
50 """
51
52 class UndefinedPDEError(ValueError):
53 """
54 raised if a PDE is not fully defined yet.
55 """
56
57 class PDECoefficient(object):
58 """
59 A class for describing a PDE coefficient
60
61 @cvar INTERIOR: indicator that coefficient is defined on the interior of the PDE domain
62 @cvar BOUNDARY: indicator that coefficient is defined on the boundary of the PDE domain
63 @cvar CONTACT: indicator that coefficient is defined on the contact region within the PDE domain
64 @cvar SOLUTION: indicator that coefficient is defined trough a solution of the PDE
65 @cvar REDUCED: indicator that coefficient is defined trough a reduced solution of the PDE
66 @cvar BY_EQUATION: indicator that the dimension of the coefficient shape is defined by the number PDE equations
67 @cvar BY_SOLUTION: indicator that the dimension of the coefficient shape is defined by the number PDE solutions
68 @cvar BY_DIM: indicator that the dimension of the coefficient shape is defined by the spatial dimension
69 @cvar OPERATOR: indicator that the the coefficient alters the operator of the PDE
70 @cvar RIGHTHANDSIDE: indicator that the the coefficient alters the right hand side of the PDE
71 @cvar BOTH: indicator that the the coefficient alters the operator as well as the right hand side of the PDE
72
73 """
74 INTERIOR=0
75 BOUNDARY=1
76 CONTACT=2
77 SOLUTION=3
78 REDUCED=4
79 BY_EQUATION=5
80 BY_SOLUTION=6
81 BY_DIM=7
82 OPERATOR=10
83 RIGHTHANDSIDE=11
84 BOTH=12
85
86 def __init__(self,where,pattern,altering):
87 """
88 Initialise a PDE Coefficient type
89
90 @param where: describes where the coefficient lives
91 @type where: one of L{INTERIOR}, L{BOUNDARY}, L{CONTACT}, L{SOLUTION}, L{REDUCED}
92 @param pattern: describes the shape of the coefficient and how the shape is build for a given
93 spatial dimension and numbers of equation and solution in then PDE. For instance,
94 (L{BY_EQUATION},L{BY_SOLUTION},L{BY_DIM}) descrbes a rank 3 coefficient which
95 is instanciated as shape (3,2,2) in case of a three equations and two solution components
96 on a 2-dimensional domain. In the case of single equation and a single solution component
97 the shape compoments marked by L{BY_EQUATION} or L{BY_SOLUTION} are dropped. In this case
98 the example would be read as (2,).
99 @type pattern: C{tuple} of L{BY_EQUATION}, L{BY_SOLUTION}, L{BY_DIM}
100 @param altering: indicates what part of the PDE is altered if the coefficiennt is altered
101 @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}
102
103 """
104 super(PDECoefficient, self).__init__()
105 self.what=where
106 self.pattern=pattern
107 self.altering=altering
108 self.resetValue()
109
110 def resetValue(self):
111 """
112 resets coefficient value to default
113 """
114 self.value=escript.Data()
115
116 def getFunctionSpace(self,domain,reducedEquationOrder=False,reducedSolutionOrder=False):
117 """
118 defines the L{FunctionSpace<escript.FunctionSpace>} of the coefficient
119
120 @param domain: domain on which the PDE uses the coefficient
121 @type domain: L{Domain<escript.Domain>}
122 @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
123 @type domain: C{bool}
124 @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
125 @type domain: C{bool}
126 @return: L{FunctionSpace<escript.FunctionSpace>} of the coefficient
127 @rtype: L{FunctionSpace<escript.FunctionSpace>}
128 """
129 if self.what==self.INTERIOR:
130 return escript.Function(domain)
131 elif self.what==self.BOUNDARY:
132 return escript.FunctionOnBoundary(domain)
133 elif self.what==self.CONTACT:
134 return escript.FunctionOnContactZero(domain)
135 elif self.what==self.SOLUTION:
136 if reducedEquationOrder and reducedSolutionOrder:
137 return escript.ReducedSolution(domain)
138 else:
139 return escript.Solution(domain)
140 elif self.what==self.REDUCED:
141 return escript.ReducedSolution(domain)
142
143 def getValue(self):
144 """
145 returns the value of the coefficient
146
147 @return: value of the coefficient
148 @rtype: L{Data<escript.Data>}
149 """
150 return self.value
151
152 def setValue(self,domain,numEquations=1,numSolutions=1,reducedEquationOrder=False,reducedSolutionOrder=False,newValue=None):
153 """
154 set the value of the coefficient to a new value
155
156 @param domain: domain on which the PDE uses the coefficient
157 @type domain: L{Domain<escript.Domain>}
158 @param numEquations: number of equations of the PDE
159 @type numEquations: C{int}
160 @param numSolutions: number of components of the PDE solution
161 @type numSolutions: C{int}
162 @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
163 @type domain: C{bool}
164 @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
165 @type domain: C{bool}
166 @param newValue: number of components of the PDE solution
167 @type newValue: any object that can be converted into a L{Data<escript.Data>} object with the appropriate shape and L{FunctionSpace<escript.FunctionSpace>}
168 @raise IllegalCoefficientValue: if the shape of the assigned value does not match the shape of the coefficient
169 """
170 if newValue==None:
171 newValue=escript.Data()
172 elif isinstance(newValue,escript.Data):
173 if not newValue.isEmpty():
174 try:
175 newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
176 except:
177 raise IllegalCoefficientValue,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)
178 else:
179 newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
180 if not newValue.isEmpty():
181 if not self.getShape(domain,numEquations,numSolutions)==newValue.getShape():
182 raise IllegalCoefficientValue,"Expected shape of coefficient is %s but actual shape is %s."%(self.getShape(domain,numEquations,numSolutions),newValue.getShape())
183 self.value=newValue
184
185 def isAlteringOperator(self):
186 """
187 checks if the coefficient alters the operator of the PDE
188
189 @return: True if the operator of the PDE is changed when the coefficient is changed
190 @rtype: C{bool}
191 """
192 if self.altering==self.OPERATOR or self.altering==self.BOTH:
193 return not None
194 else:
195 return None
196
197 def isAlteringRightHandSide(self):
198 """
199 checks if the coefficeint alters the right hand side of the PDE
200
201 @rtype: C{bool}
202 @return: True if the right hand side of the PDE is changed when the coefficient is changed
203 """
204 if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:
205 return not None
206 else:
207 return None
208
209 def estimateNumEquationsAndNumSolutions(self,domain,shape=()):
210 """
211 tries to estimate the number of equations and number of solutions if the coefficient has the given shape
212
213 @param domain: domain on which the PDE uses the coefficient
214 @type domain: L{Domain<escript.Domain>}
215 @param shape: suggested shape of the coefficient
216 @type shape: C{tuple} of C{int} values
217 @return: the number of equations and number of solutions of the PDE is the coefficient has shape s.
218 If no appropriate numbers could be identified, C{None} is returned
219 @rtype: C{tuple} of two C{int} values or C{None}
220 """
221 dim=domain.getDim()
222 if len(shape)>0:
223 num=max(shape)+1
224 else:
225 num=1
226 search=[]
227 if self.definesNumEquation() and self.definesNumSolutions():
228 for u in range(num):
229 for e in range(num):
230 search.append((e,u))
231 search.sort(self.__CompTuple2)
232 for item in search:
233 s=self.getShape(domain,item[0],item[1])
234 if len(s)==0 and len(shape)==0:
235 return (1,1)
236 else:
237 if s==shape: return item
238 elif self.definesNumEquation():
239 for e in range(num,0,-1):
240 s=self.getShape(domain,e,0)
241 if len(s)==0 and len(shape)==0:
242 return (1,None)
243 else:
244 if s==shape: return (e,None)
245
246 elif self.definesNumSolutions():
247 for u in range(num,0,-1):
248 s=self.getShape(domain,0,u)
249 if len(s)==0 and len(shape)==0:
250 return (None,1)
251 else:
252 if s==shape: return (None,u)
253 return None
254 def definesNumSolutions(self):
255 """
256 checks if the coefficient allows to estimate the number of solution components
257
258 @return: True if the coefficient allows an estimate of the number of solution components
259 @rtype: C{bool}
260 """
261 for i in self.pattern:
262 if i==self.BY_SOLUTION: return True
263 return False
264
265 def definesNumEquation(self):
266 """
267 checks if the coefficient allows to estimate the number of equations
268
269 @return: True if the coefficient allows an estimate of the number of equations
270 @rtype: C{bool}
271 """
272 for i in self.pattern:
273 if i==self.BY_EQUATION: return True
274 return False
275
276 def __CompTuple2(self,t1,t2):
277 """
278 Compare two tuples of possible number of equations and number of solutions
279
280 @param t1: The first tuple
281 @param t2: The second tuple
282
283 """
284
285 dif=t1[0]+t1[1]-(t2[0]+t2[1])
286 if dif<0: return 1
287 elif dif>0: return -1
288 else: return 0
289
290 def getShape(self,domain,numEquations=1,numSolutions=1):
291 """
292 builds the required shape of the coefficient
293
294 @param domain: domain on which the PDE uses the coefficient
295 @type domain: L{Domain<escript.Domain>}
296 @param numEquations: number of equations of the PDE
297 @type numEquations: C{int}
298 @param numSolutions: number of components of the PDE solution
299 @type numSolutions: C{int}
300 @return: shape of the coefficient
301 @rtype: C{tuple} of C{int} values
302 """
303 dim=domain.getDim()
304 s=()
305 for i in self.pattern:
306 if i==self.BY_EQUATION:
307 if numEquations>1: s=s+(numEquations,)
308 elif i==self.BY_SOLUTION:
309 if numSolutions>1: s=s+(numSolutions,)
310 else:
311 s=s+(dim,)
312 return s
313
314 class LinearPDE(object):
315 """
316 This class is used to define a general linear, steady, second order PDE
317 for an unknown function M{u} on a given domain defined through a L{Domain<escript.Domain>} object.
318
319 For a single PDE with a solution with a single component the linear PDE is defined in the following form:
320
321 M{-grad(A[j,l]*grad(u)[l]+B[j]u)[j]+C[l]*grad(u)[l]+D*u =-grad(X)[j,j]+Y}
322
323 where M{grad(F)} denotes the spatial derivative of M{F}. Einstein's summation convention,
324 ie. summation over indexes appearing twice in a term of a sum is performed, is used.
325 The coefficients M{A}, M{B}, M{C}, M{D}, M{X} and M{Y} have to be specified through L{Data<escript.Data>} objects in the
326 L{Function<escript.Function>} on the PDE or objects that can be converted into such L{Data<escript.Data>} objects.
327 M{A} is a rank two, M{B}, M{C} and M{X} are rank one and M{D} and M{Y} are scalar.
328
329 The following natural boundary conditions are considered:
330
331 M{n[j]*(A[i,j]*grad(u)[l]+B[j]*u)+d*u=n[j]*X[j]+y}
332
333 where M{n} is the outer normal field calculated by L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
334 Notice that the coefficients M{A}, M{B} and M{X} are defined in the PDE. The coefficients M{d} and M{y} are
335 each a scalar in the L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
336
337
338 Constraints for the solution prescribing the value of the solution at certain locations in the domain. They have the form
339
340 M{u=r} where M{q>0}
341
342 M{r} and M{q} are each scalar where M{q} is the characteristic function defining where the constraint is applied.
343 The constraints override any other condition set by the PDE or the boundary condition.
344
345 The PDE is symmetrical if
346
347 M{A[i,j]=A[j,i]} and M{B[j]=C[j]}
348
349 For a system of PDEs and a solution with several components the PDE has the form
350
351 M{-grad(A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]*u[k])[j]+C[i,k,l]*grad(u[k])[l]+D[i,k]*u[k] =-grad(X[i,j])[j]+Y[i] }
352
353 M{A} is a ramk four, M{B} and M{C} are each a rank three, M{D} and M{X} are each a rank two and M{Y} is a rank one.
354 The natural boundary conditions take the form:
355
356 M{n[j]*(A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]*u[k])+d[i,k]*u[k]=n[j]*X[i,j]+y[i]}
357
358
359 The coefficient M{d} is a rank two and M{y} is a rank one both in the L{FunctionOnBoundary<escript.FunctionOnBoundary>}. Constraints take the form
360
361
362 M{u[i]=r[i]} where M{q[i]>0}
363
364 M{r} and M{q} are each rank one. Notice that at some locations not necessarily all components must have a constraint.
365
366 The system of PDEs is symmetrical if
367
368 - M{A[i,j,k,l]=A[k,l,i,j]}
369 - M{B[i,j,k]=C[k,i,j]}
370 - M{D[i,k]=D[i,k]}
371 - M{d[i,k]=d[k,i]}
372
373 L{LinearPDE} also supports solution discontinuities over a contact region in the domain. To specify the conditions across the
374 discontinuity we are using the generalised flux M{J} which is in the case of a systems of PDEs and several components of the solution
375 defined as
376
377 M{J[i,j]=A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]*u[k]-X[i,j]}
378
379 For the case of single solution component and single PDE M{J} is defined
380
381 M{J_{j}=A[i,j]*grad(u)[j]+B[i]*u-X[i]}
382
383 In the context of discontinuities M{n} denotes the normal on the discontinuity pointing from side 0 towards side 1
384 calculated from L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnContactZero<escript.FunctionOnContactZero>}. For a system of PDEs
385 the contact condition takes the form
386
387 M{n[j]*J0[i,j]=n[j]*J1[i,j]=y_contact[i]- d_contact[i,k]*jump(u)[k]}
388
389 where M{J0} and M{J1} are the fluxes on side 0 and side 1 of the discontinuity, respectively. M{jump(u)}, which is the difference
390 of the solution at side 1 and at side 0, denotes the jump of M{u} across discontinuity along the normal calcualted by
391 L{jump<util.jump>}.
392 The coefficient M{d_contact} is a rank two and M{y_contact} is a rank one both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
393 In case of a single PDE and a single component solution the contact condition takes the form
394
395 M{n[j]*J0_{j}=n[j]*J1_{j}=y_contact-d_contact*jump(u)}
396
397 In this case the the coefficient M{d_contact} and M{y_contact} are eaach scalar
398 both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
399
400 @cvar DEFAULT: The default method used to solve the system of linear equations
401 @cvar DIRECT: The direct solver based on LDU factorization
402 @cvar CHOLEVSKY: The direct solver based on LDLt factorization (can only be applied for symmetric PDEs)
403 @cvar PCG: The preconditioned conjugate gradient method (can only be applied for symmetric PDEs)
404 @cvar CR: The conjugate residual method
405 @cvar CGS: The conjugate gardient square method
406 @cvar BICGSTAB: The stabilized BiConjugate Gradient method.
407 @cvar SSOR: The symmetric overrealaxtion method
408 @cvar ILU0: The incomplete LU factorization preconditioner with no fill in
409 @cvar ILUT: The incomplete LU factorization preconditioner with will in
410 @cvar JACOBI: The Jacobi preconditioner
411 @cvar GMRES: The Gram-Schmidt minimum residual method
412 @cvar PRES20: Special GMRES with restart after 20 steps and truncation after 5 residuals
413 @cvar LUMPING: Matrix lumping.
414 @cvar NO_REORDERING: No matrix reordering allowed
415 @cvar MINIMUM_FILL_IN: Reorder matrix to reduce fill-in during factorization
416 @cvar NESTED_DISSECTION: Reorder matrix to improve load balancing during factorization
417 @cvar PASO: PASO solver package
418 @cvar SCSL: SGI SCSL solver library
419 @cvar MKL: Intel's MKL solver library
420 @cvar UMFPACK: the UMFPACK library
421 @cvar ITERATIVE: The default iterative solver
422 @cvar AMG: algebraic multi grid
423 @cvar RILU: recursive ILU
424
425 """
426 DEFAULT= 0
427 DIRECT= 1
428 CHOLEVSKY= 2
429 PCG= 3
430 CR= 4
431 CGS= 5
432 BICGSTAB= 6
433 SSOR= 7
434 ILU0= 8
435 ILUT= 9
436 JACOBI= 10
437 GMRES= 11
438 PRES20= 12
439 LUMPING= 13
440 NO_REORDERING= 17
441 MINIMUM_FILL_IN= 18
442 NESTED_DISSECTION= 19
443 SCSL= 14
444 MKL= 15
445 UMFPACK= 16
446 ITERATIVE= 20
447 PASO= 21
448 AMG= 22
449 RILU = 23
450
451 __TOL=1.e-13
452 __PACKAGE_KEY="package"
453 __METHOD_KEY="method"
454 __SYMMETRY_KEY="symmetric"
455 __TOLERANCE_KEY="tolerance"
456 __PRECONDITIONER_KEY="preconditioner"
457
458
459 def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):
460 """
461 initializes a new linear PDE
462
463 @param domain: domain of the PDE
464 @type domain: L{Domain<escript.Domain>}
465 @param numEquations: number of equations. If numEquations==None the number of equations
466 is exracted from the PDE coefficients.
467 @param numSolutions: number of solution components. If numSolutions==None the number of solution components
468 is exracted from the PDE coefficients.
469 @param debug: if True debug informations are printed.
470
471 """
472 super(LinearPDE, self).__init__()
473 #
474 # the coefficients of the general PDE:
475 #
476 self.__COEFFICIENTS_OF_GENEARL_PDE={
477 "A" : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
478 "B" : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
479 "C" : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
480 "D" : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
481 "X" : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
482 "Y" : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
483 "d" : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
484 "y" : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
485 "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
486 "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
487 "r" : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
488 "q" : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
489
490 # COEFFICIENTS can be overwritten by subclasses:
491 self.COEFFICIENTS=self.__COEFFICIENTS_OF_GENEARL_PDE
492 self.__altered_coefficients=False
493 # initialize attributes
494 self.__debug=debug
495 self.__domain=domain
496 self.__numEquations=numEquations
497 self.__numSolutions=numSolutions
498 self.__resetSystem()
499
500 # set some default values:
501 self.__reduce_equation_order=False
502 self.__reduce_solution_order=False
503 self.__tolerance=1.e-8
504 self.__solver_method=self.DEFAULT
505 self.__solver_package=self.DEFAULT
506 self.__preconditioner=self.DEFAULT
507 self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT,self.DEFAULT,False)
508 self.__sym=False
509
510 self.resetCoefficients()
511 self.trace("PDE Coeffients are %s"%str(self.COEFFICIENTS.keys()))
512 # =============================================================================
513 # general stuff:
514 # =============================================================================
515 def __str__(self):
516 """
517 returns string representation of the PDE
518
519 @return: a simple representation of the PDE
520 @rtype: C{str}
521 """
522 return "<LinearPDE %d>"%id(self)
523 # =============================================================================
524 # debug :
525 # =============================================================================
526 def setDebugOn(self):
527 """
528 switches on debugging
529 """
530 self.__debug=not None
531
532 def setDebugOff(self):
533 """
534 switches off debugging
535 """
536 self.__debug=None
537
538 def trace(self,text):
539 """
540 print the text message if debugging is swiched on.
541 @param text: message
542 @type text: C{string}
543 """
544 if self.__debug: print "%s: %s"%(str(self),text)
545
546 # =============================================================================
547 # some service functions:
548 # =============================================================================
549 def getDomain(self):
550 """
551 returns the domain of the PDE
552
553 @return: the domain of the PDE
554 @rtype: L{Domain<escript.Domain>}
555 """
556 return self.__domain
557
558 def getDim(self):
559 """
560 returns the spatial dimension of the PDE
561
562 @return: the spatial dimension of the PDE domain
563 @rtype: C{int}
564 """
565 return self.getDomain().getDim()
566
567 def getNumEquations(self):
568 """
569 returns the number of equations
570
571 @return: the number of equations
572 @rtype: C{int}
573 @raise UndefinedPDEError: if the number of equations is not be specified yet.
574 """
575 if self.__numEquations==None:
576 raise UndefinedPDEError,"Number of equations is undefined. Please specify argument numEquations."
577 else:
578 return self.__numEquations
579
580 def getNumSolutions(self):
581 """
582 returns the number of unknowns
583
584 @return: the number of unknowns
585 @rtype: C{int}
586 @raise UndefinedPDEError: if the number of unknowns is not be specified yet.
587 """
588 if self.__numSolutions==None:
589 raise UndefinedPDEError,"Number of solution is undefined. Please specify argument numSolutions."
590 else:
591 return self.__numSolutions
592
593 def reduceEquationOrder(self):
594 """
595 return status for order reduction for equation
596
597 @return: return True is reduced interpolation order is used for the represenation of the equation
598 @rtype: L{bool}
599 """
600 return self.__reduce_equation_order
601
602 def reduceSolutionOrder(self):
603 """
604 return status for order reduction for the solution
605
606 @return: return True is reduced interpolation order is used for the represenation of the solution
607 @rtype: L{bool}
608 """
609 return self.__reduce_solution_order
610
611 def getFunctionSpaceForEquation(self):
612 """
613 returns the L{FunctionSpace<escript.FunctionSpace>} used to discretize the equation
614
615 @return: representation space of equation
616 @rtype: L{FunctionSpace<escript.FunctionSpace>}
617 """
618 if self.reduceEquationOrder():
619 return escript.ReducedSolution(self.getDomain())
620 else:
621 return escript.Solution(self.getDomain())
622
623 def getFunctionSpaceForSolution(self):
624 """
625 returns the L{FunctionSpace<escript.FunctionSpace>} used to represent the solution
626
627 @return: representation space of solution
628 @rtype: L{FunctionSpace<escript.FunctionSpace>}
629 """
630 if self.reduceSolutionOrder():
631 return escript.ReducedSolution(self.getDomain())
632 else:
633 return escript.Solution(self.getDomain())
634
635
636 def getOperator(self):
637 """
638 provides access to the operator of the PDE
639
640 @return: the operator of the PDE
641 @rtype: L{Operator<escript.Operator>}
642 """
643 m=self.getSystem()[0]
644 if self.isUsingLumping():
645 return self.copyConstraint(1./m)
646 else:
647 return m
648
649 def getRightHandSide(self):
650 """
651 provides access to the right hand side of the PDE
652 @return: the right hand side of the PDE
653 @rtype: L{Data<escript.Data>}
654 """
655 r=self.getSystem()[1]
656 if self.isUsingLumping():
657 return self.copyConstraint(r)
658 else:
659 return r
660
661 def applyOperator(self,u=None):
662 """
663 applies the operator of the PDE to a given u or the solution of PDE if u is not present.
664
665 @param u: argument of the operator. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
666 the current solution is used.
667 @type u: L{Data<escript.Data>} or None
668 @return: image of u
669 @rtype: L{Data<escript.Data>}
670 """
671 if u==None:
672 return self.getOperator()*self.getSolution()
673 else:
674 self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
675
676 def getResidual(self,u=None):
677 """
678 return the residual of u or the current solution if u is not present.
679
680 @param u: argument in the residual calculation. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
681 the current solution is used.
682 @type u: L{Data<escript.Data>} or None
683 @return: residual of u
684 @rtype: L{Data<escript.Data>}
685 """
686 return self.applyOperator(u)-self.getRightHandSide()
687
688 def checkSymmetry(self,verbose=True):
689 """
690 test the PDE for symmetry.
691
692 @param verbose: if equal to True or not present a report on coefficients which are breaking the symmetry is printed.
693 @type verbose: C{bool}
694 @return: True if the PDE is symmetric.
695 @rtype: L{Data<escript.Data>}
696 @note: This is a very expensive operation. It should be used for degugging only! The symmetry flag is not altered.
697 """
698 verbose=verbose or self.__debug
699 out=True
700 if self.getNumSolutions()!=self.getNumEquations():
701 if verbose: print "non-symmetric PDE because of different number of equations and solutions"
702 out=False
703 else:
704 A=self.getCoefficientOfGeneralPDE("A")
705 if not A.isEmpty():
706 tol=util.Lsup(A)*self.__TOL
707 if self.getNumSolutions()>1:
708 for i in range(self.getNumEquations()):
709 for j in range(self.getDim()):
710 for k in range(self.getNumSolutions()):
711 for l in range(self.getDim()):
712 if util.Lsup(A[i,j,k,l]-A[k,l,i,j])>tol:
713 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)
714 out=False
715 else:
716 for j in range(self.getDim()):
717 for l in range(self.getDim()):
718 if util.Lsup(A[j,l]-A[l,j])>tol:
719 if verbose: print "non-symmetric PDE because A[%d,%d]!=A[%d,%d]"%(j,l,l,j)
720 out=False
721 B=self.getCoefficientOfGeneralPDE("B")
722 C=self.getCoefficientOfGeneralPDE("C")
723 if B.isEmpty() and not C.isEmpty():
724 if verbose: print "non-symmetric PDE because B is not present but C is"
725 out=False
726 elif not B.isEmpty() and C.isEmpty():
727 if verbose: print "non-symmetric PDE because C is not present but B is"
728 out=False
729 elif not B.isEmpty() and not C.isEmpty():
730 tol=(util.Lsup(B)+util.Lsup(C))*self.__TOL/2.
731 if self.getNumSolutions()>1:
732 for i in range(self.getNumEquations()):
733 for j in range(self.getDim()):
734 for k in range(self.getNumSolutions()):
735 if util.Lsup(B[i,j,k]-C[k,i,j])>tol:
736 if verbose: print "non-symmetric PDE because B[%d,%d,%d]!=C[%d,%d,%d]"%(i,j,k,k,i,j)
737 out=False
738 else:
739 for j in range(self.getDim()):
740 if util.Lsup(B[j]-C[j])>tol:
741 if verbose: print "non-symmetric PDE because B[%d]!=C[%d]"%(j,j)
742 out=False
743 if self.getNumSolutions()>1:
744 D=self.getCoefficientOfGeneralPDE("D")
745 if not D.isEmpty():
746 tol=util.Lsup(D)*self.__TOL
747 for i in range(self.getNumEquations()):
748 for k in range(self.getNumSolutions()):
749 if util.Lsup(D[i,k]-D[k,i])>tol:
750 if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)
751 out=False
752 d=self.getCoefficientOfGeneralPDE("d")
753 if not d.isEmpty():
754 tol=util.Lsup(d)*self.__TOL
755 for i in range(self.getNumEquations()):
756 for k in range(self.getNumSolutions()):
757 if util.Lsup(d[i,k]-d[k,i])>tol:
758 if verbose: print "non-symmetric PDE because d[%d,%d]!=d[%d,%d]"%(i,k,k,i)
759 out=False
760 d_contact=self.getCoefficientOfGeneralPDE("d_contact")
761 if not d_contact.isEmpty():
762 tol=util.Lsup(d_contact)*self.__TOL
763 for i in range(self.getNumEquations()):
764 for k in range(self.getNumSolutions()):
765 if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
766 if verbose: print "non-symmetric PDE because d_contact[%d,%d]!=d_contact[%d,%d]"%(i,k,k,i)
767 out=False
768 return out
769
770 def getSolution(self,**options):
771 """
772 returns the solution of the PDE. If the solution is not valid the PDE is solved.
773
774 @return: the solution
775 @rtype: L{Data<escript.Data>}
776 @param options: solver options
777 @keyword verbose: True to get some information during PDE solution
778 @type verbose: C{bool}
779 @keyword reordering: reordering scheme to be used during elimination. Allowed values are
780 L{NO_REORDERING}, L{MINIMUM_FILL_IN}, L{NESTED_DISSECTION}
781 @keyword iter_max: maximum number of iteration steps allowed.
782 @keyword drop_tolerance: threshold for drupping in L{ILUT}
783 @keyword drop_storage: maximum of allowed memory in L{ILUT}
784 @keyword truncation: maximum number of residuals in L{GMRES}
785 @keyword restart: restart cycle length in L{GMRES}
786 """
787 if not self.__solution_isValid:
788 mat,f=self.getSystem()
789 if self.isUsingLumping():
790 self.__solution=self.copyConstraint(f*mat)
791 else:
792 options[self.__TOLERANCE_KEY]=self.getTolerance()
793 options[self.__METHOD_KEY]=self.getSolverMethod()[0]
794 options[self.__PRECONDITIONER_KEY]=self.getSolverMethod()[1]
795 options[self.__PACKAGE_KEY]=self.getSolverPackage()
796 options[self.__SYMMETRY_KEY]=self.isSymmetric()
797 self.trace("PDE is resolved.")
798 self.trace("solver options: %s"%str(options))
799 self.__solution=mat.solve(f,options)
800 self.__solution_isValid=True
801 return self.__solution
802
803 def getFlux(self,u=None):
804 """
805 returns the flux M{J} for a given M{u}
806
807 M{J[i,j]=A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]u[k]-X[i,j]}
808
809 or
810
811 M{J[j]=A[i,j]*grad(u)[l]+B[j]u-X[j]}
812
813 @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.
814 @type u: L{Data<escript.Data>} or None
815 @return: flux
816 @rtype: L{Data<escript.Data>}
817 """
818 if u==None: u=self.getSolution()
819 return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u))+util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u)-util.self.getCoefficientOfGeneralPDE("X")
820 # =============================================================================
821 # solver settings:
822 # =============================================================================
823 def setSolverMethod(self,solver=None,preconditioner=None):
824 """
825 sets a new solver
826
827 @param solver: sets a new solver method.
828 @type solver: one of L{DEFAULT}, L{ITERATIVE} L{DIRECT}, L{CHOLEVSKY}, L{PCG}, L{CR}, L{CGS}, L{BICGSTAB}, L{SSOR}, L{GMRES}, L{PRES20}, L{LUMPING}.
829 @param preconditioner: sets a new solver method.
830 @type solver: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}
831 """
832 if solver==None: solve=self.DEFAULT
833 if preconditioner==None: preconditioner=self.DEFAULT
834 if not (solver,preconditioner)==self.getSolverMethod():
835 self.__solver_method=solver
836 self.__preconditioner=preconditioner
837 self.__checkMatrixType()
838 self.trace("New solver is %s"%self.getSolverMethodName())
839
840 def getSolverMethodName(self):
841 """
842 returns the name of the solver currently used
843
844 @return: the name of the solver currently used.
845 @rtype: C{string}
846 """
847
848 m=self.getSolverMethod()
849 p=self.getSolverPackage()
850 method=""
851 if m[0]==self.DEFAULT: method="DEFAULT"
852 elif m[0]==self.DIRECT: method= "DIRECT"
853 elif m[0]==self.ITERATIVE: method= "ITERATIVE"
854 elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
855 elif m[0]==self.PCG: method= "PCG"
856 elif m[0]==self.CR: method= "CR"
857 elif m[0]==self.CGS: method= "CGS"
858 elif m[0]==self.BICGSTAB: method= "BICGSTAB"
859 elif m[0]==self.SSOR: method= "SSOR"
860 elif m[0]==self.GMRES: method= "GMRES"
861 elif m[0]==self.PRES20: method= "PRES20"
862 elif m[0]==self.LUMPING: method= "LUMPING"
863 if m[1]==self.DEFAULT: method+="+DEFAULT"
864 elif m[1]==self.JACOBI: method+= "+JACOBI"
865 elif m[1]==self.ILU0: method+= "+ILU0"
866 elif m[1]==self.ILUT: method+= "+ILUT"
867 elif m[1]==self.SSOR: method+= "+SSOR"
868 if p==self.DEFAULT: package="DEFAULT"
869 elif p==self.PASO: package= "PASO"
870 elif p==self.MKL: package= "MKL"
871 elif p==self.SCSL: package= "SCSL"
872 elif p==self.UMFPACK: package= "UMFPACK"
873 else : method="unknown"
874 return "%s solver of %s package"%(method,package)
875
876
877 def getSolverMethod(self):
878 """
879 returns the solver method
880
881 @return: the solver method currently be used.
882 @rtype: C{int}
883 """
884 return self.__solver_method,self.__preconditioner
885
886 def setSolverPackage(self,package=None):
887 """
888 sets a new solver package
889
890 @param solver: sets a new solver method.
891 @type solver: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMLPACK}
892 """
893 if package==None: package=self.DEFAULT
894 if not package==self.getSolverPackage():
895 self.__solver_method=solver
896 self.__checkMatrixType()
897 self.trace("New solver is %s"%self.getSolverMethodName())
898
899 def getSolverPackage(self):
900 """
901 returns the package of the solver
902
903 @return: the solver package currently being used.
904 @rtype: C{int}
905 """
906 return self.__solver_package
907
908 def isUsingLumping(self):
909 """
910 checks if matrix lumping is used a solver method
911
912 @return: True is lumping is currently used a solver method.
913 @rtype: C{bool}
914 """
915 return self.getSolverMethod()[0]==self.LUMPING
916
917 def setTolerance(self,tol=1.e-8):
918 """
919 resets the tolerance for the solver method to tol where for an appropriate norm M{|.|}
920
921 M{|L{getResidual}()|<tol*|L{getRightHandSide}()|}
922
923 defines the stopping criterion.
924
925 @param tol: new tolerance for the solver. If the tol is lower then the current tolerence
926 the system will be resolved.
927 @type tol: positive C{float}
928 @raise ValueException: if tolerance is not positive.
929 """
930 if not tol>0:
931 raise ValueException,"Tolerance as to be positive"
932 if tol<self.getTolerance(): self.__invalidateSolution()
933 self.trace("New tolerance %e"%tol)
934 self.__tolerance=tol
935 return
936
937 def getTolerance(self):
938 """
939 returns the tolerance set for the solution
940
941 @return: tolerance currently used.
942 @rtype: C{float}
943 """
944 return self.__tolerance
945
946 # =============================================================================
947 # symmetry flag:
948 # =============================================================================
949 def isSymmetric(self):
950 """
951 checks if symmetry is indicated.
952
953 @return: True is a symmetric PDE is indicated, otherwise False is returned
954 @rtype: C{bool}
955 """
956 return self.__sym
957
958 def setSymmetryOn(self):
959 """
960 sets the symmetry flag.
961 """
962 if not self.isSymmetric():
963 self.trace("PDE is set to be symmetric")
964 self.__sym=True
965 self.__checkMatrixType()
966
967 def setSymmetryOff(self):
968 """
969 removes the symmetry flag.
970 """
971 if self.isSymmetric():
972 self.trace("PDE is set to be unsymmetric")
973 self.__sym=False
974 self.__checkMatrixType()
975
976 def setSymmetryTo(self,flag=False):
977 """
978 sets the symmetry flag to flag
979
980 @param flag: If flag, the symmetry flag is set otherwise the symmetry flag is released.
981 @type flag: C{bool}
982 """
983 if flag:
984 self.setSymmetryOn()
985 else:
986 self.setSymmetryOff()
987
988 # =============================================================================
989 # function space handling for the equation as well as the solution
990 # =============================================================================
991 def setReducedOrderOn(self):
992 """
993 switches on reduced order for solution and equation representation
994
995 @raise RuntimeError: if order reduction is altered after a coefficient has been set.
996 """
997 self.setReducedOrderForSolutionOn()
998 self.setReducedOrderForEquationOn()
999
1000 def setReducedOrderOff(self):
1001 """
1002 switches off reduced order for solution and equation representation
1003
1004 @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1005 """
1006 self.setReducedOrderForSolutionOff()
1007 self.setReducedOrderForEquationOff()
1008
1009 def setReducedOrderTo(self,flag=False):
1010 """
1011 sets order reduction for both solution and equation representation according to flag.
1012 @param flag: if flag is True, the order reduction is switched on for both solution and equation representation, otherwise or
1013 if flag is not present order reduction is switched off
1014 @type flag: C{bool}
1015 @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1016 """
1017 self.setReducedOrderForSolutionTo(flag)
1018 self.setReducedOrderForEquationTo(flag)
1019
1020
1021 def setReducedOrderForSolutionOn(self):
1022 """
1023 switches on reduced order for solution representation
1024
1025 @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1026 """
1027 if not self.__reduce_solution_order:
1028 if self.__altered_coefficients:
1029 raise RuntimeError,"order cannot be altered after coefficients have been defined."
1030 self.trace("Reduced order is used to solution representation.")
1031 self.__reduce_solution_order=True
1032 self.__resetSystem()
1033
1034 def setReducedOrderForSolutionOff(self):
1035 """
1036 switches off reduced order for solution representation
1037
1038 @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1039 """
1040 if self.__reduce_solution_order:
1041 if self.__altered_coefficients:
1042 raise RuntimeError,"order cannot be altered after coefficients have been defined."
1043 self.trace("Full order is used to interpolate solution.")
1044 self.__reduce_solution_order=False
1045 self.__resetSystem()
1046
1047 def setReducedOrderForSolutionTo(self,flag=False):
1048 """
1049 sets order for test functions according to flag
1050
1051 @param flag: if flag is True, the order reduction is switched on for solution representation, otherwise or
1052 if flag is not present order reduction is switched off
1053 @type flag: C{bool}
1054 @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1055 """
1056 if flag:
1057 self.setReducedOrderForSolutionOn()
1058 else:
1059 self.setReducedOrderForSolutionOff()
1060
1061 def setReducedOrderForEquationOn(self):
1062 """
1063 switches on reduced order for equation representation
1064
1065 @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1066 """
1067 if not self.__reduce_equation_order:
1068 if self.__altered_coefficients:
1069 raise RuntimeError,"order cannot be altered after coefficients have been defined."
1070 self.trace("Reduced order is used for test functions.")
1071 self.__reduce_equation_order=True
1072 self.__resetSystem()
1073
1074 def setReducedOrderForEquationOff(self):
1075 """
1076 switches off reduced order for equation representation
1077
1078 @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1079 """
1080 if self.__reduce_equation_order:
1081 if self.__altered_coefficients:
1082 raise RuntimeError,"order cannot be altered after coefficients have been defined."
1083 self.trace("Full order is used for test functions.")
1084 self.__reduce_equation_order=False
1085 self.__resetSystem()
1086
1087 def setReducedOrderForEquationTo(self,flag=False):
1088 """
1089 sets order for test functions according to flag
1090
1091 @param flag: if flag is True, the order reduction is switched on for equation representation, otherwise or
1092 if flag is not present order reduction is switched off
1093 @type flag: C{bool}
1094 @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1095 """
1096 if flag:
1097 self.setReducedOrderForEquationOn()
1098 else:
1099 self.setReducedOrderForEquationOff()
1100
1101 # =============================================================================
1102 # private method:
1103 # =============================================================================
1104 def __checkMatrixType(self):
1105 """
1106 reassess the matrix type and, if a new matrix is needed, resets the system.
1107 """
1108 new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod()[0],self.getSolverPackage(),self.isSymmetric())
1109 if not new_matrix_type==self.__matrix_type:
1110 self.trace("Matrix type is now %d."%new_matrix_type)
1111 self.__matrix_type=new_matrix_type
1112 self.__resetSystem()
1113 #
1114 # rebuild switches :
1115 #
1116 def __invalidateSolution(self):
1117 """
1118 indicates the PDE has to be resolved if the solution is requested
1119 """
1120 if self.__solution_isValid: self.trace("PDE has to be resolved.")
1121 self.__solution_isValid=False
1122
1123 def __invalidateOperator(self):
1124 """
1125 indicates the operator has to be rebuilt next time it is used
1126 """
1127 if self.__operator_is_Valid: self.trace("Operator has to be rebuilt.")
1128 self.__invalidateSolution()
1129 self.__operator_is_Valid=False
1130
1131 def __invalidateRightHandSide(self):
1132 """
1133 indicates the right hand side has to be rebuild next time it is used
1134 """
1135 if self.__righthandside_isValid: self.trace("Right hand side has to be rebuilt.")
1136 self.__invalidateSolution()
1137 self.__righthandside_isValid=False
1138
1139 def __invalidateSystem(self):
1140 """
1141 annonced that everthing has to be rebuild:
1142 """
1143 if self.__righthandside_isValid: self.trace("System has to be rebuilt.")
1144 self.__invalidateSolution()
1145 self.__invalidateOperator()
1146 self.__invalidateRightHandSide()
1147
1148 def __resetSystem(self):
1149 """
1150 annonced that everthing has to be rebuild:
1151 """
1152 self.trace("New System is built from scratch.")
1153 self.__operator=escript.Operator()
1154 self.__operator_is_Valid=False
1155 self.__righthandside=escript.Data()
1156 self.__righthandside_isValid=False
1157 self.__solution=escript.Data()
1158 self.__solution_isValid=False
1159 #
1160 # system initialization:
1161 #
1162 def __getNewOperator(self):
1163 """
1164 returns an instance of a new operator
1165 """
1166 self.trace("New operator is allocated.")
1167 return self.getDomain().newOperator( \
1168 self.getNumEquations(), \
1169 self.getFunctionSpaceForEquation(), \
1170 self.getNumSolutions(), \
1171 self.getFunctionSpaceForSolution(), \
1172 self.__matrix_type)
1173
1174 def __getNewRightHandSide(self):
1175 """
1176 returns an instance of a new right hand side
1177 """
1178 self.trace("New right hand side is allocated.")
1179 if self.getNumEquations()>1:
1180 return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)
1181 else:
1182 return escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)
1183
1184 def __getNewSolution(self):
1185 """
1186 returns an instance of a new solution
1187 """
1188 self.trace("New solution is allocated.")
1189 if self.getNumSolutions()>1:
1190 return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)
1191 else:
1192 return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)
1193
1194 def __makeFreshSolution(self):
1195 """
1196 makes sure that the solution is instantiated and returns it initialized by zeros
1197 """
1198 if self.__solution.isEmpty():
1199 self.__solution=self.__getNewSolution()
1200 else:
1201 self.__solution*=0
1202 self.trace("Solution is reset to zero.")
1203 return self.__solution
1204
1205 def __makeFreshRightHandSide(self):
1206 """
1207 makes sure that the right hand side is instantiated and returns it initialized by zeros
1208 """
1209 if self.__righthandside.isEmpty():
1210 self.__righthandside=self.__getNewRightHandSide()
1211 else:
1212 self.__righthandside*=0
1213 self.trace("Right hand side is reset to zero.")
1214 return self.__righthandside
1215
1216 def __makeFreshOperator(self):
1217 """
1218 makes sure that the operator is instantiated and returns it initialized by zeros
1219 """
1220 if self.__operator.isEmpty():
1221 self.__operator=self.__getNewOperator()
1222 else:
1223 self.__operator.resetValues()
1224 self.trace("Operator reset to zero")
1225 return self.__operator
1226
1227 def __applyConstraint(self):
1228 """
1229 applies the constraints defined by q and r to the system
1230 """
1231 if not self.isUsingLumping():
1232 q=self.getCoefficientOfGeneralPDE("q")
1233 r=self.getCoefficientOfGeneralPDE("r")
1234 if not q.isEmpty() and not self.__operator.isEmpty():
1235 # q is the row and column mask to indicate where constraints are set:
1236 row_q=escript.Data(q,self.getFunctionSpaceForEquation())
1237 col_q=escript.Data(q,self.getFunctionSpaceForSolution())
1238 u=self.__getNewSolution()
1239 if r.isEmpty():
1240 r_s=self.__getNewSolution()
1241 else:
1242 r_s=escript.Data(r,self.getFunctionSpaceForSolution())
1243 u.copyWithMask(r_s,col_q)
1244 if not self.__righthandside.isEmpty():
1245 self.__righthandside-=self.__operator*u
1246 self.__righthandside=self.copyConstraint(self.__righthandside)
1247 self.__operator.nullifyRowsAndCols(row_q,col_q,1.)
1248 # =============================================================================
1249 # function giving access to coefficients of the general PDE:
1250 # =============================================================================
1251 def getCoefficientOfGeneralPDE(self,name):
1252 """
1253 return the value of the coefficient name of the general PDE.
1254
1255 @note: This method is called by the assembling routine it can be overwritten
1256 to map coefficients of a particular PDE to the general PDE.
1257 @param name: name of the coefficient requested.
1258 @type name: C{string}
1259 @return: the value of the coefficient name
1260 @rtype: L{Data<escript.Data>}
1261 @raise IllegalCoefficient: if name is not one of coefficients
1262 M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.
1263 """
1264 if self.hasCoefficientOfGeneralPDE(name):
1265 return self.getCoefficient(name)
1266 else:
1267 raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1268
1269 def hasCoefficientOfGeneralPDE(self,name):
1270 """
1271 checks if name is a the name of a coefficient of the general PDE.
1272
1273 @param name: name of the coefficient enquired.
1274 @type name: C{string}
1275 @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1276 @rtype: C{bool}
1277
1278 """
1279 return self.__COEFFICIENTS_OF_GENEARL_PDE.has_key(name)
1280
1281 def createCoefficientOfGeneralPDE(self,name):
1282 """
1283 returns a new instance of a coefficient for coefficient name of the general PDE
1284
1285 @param name: name of the coefficient requested.
1286 @type name: C{string}
1287 @return: a coefficient name initialized to 0.
1288 @rtype: L{Data<escript.Data>}
1289 @raise IllegalCoefficient: if name is not one of coefficients
1290 M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.
1291 """
1292 if self.hasCoefficientOfGeneralPDE(name):
1293 return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
1294 else:
1295 raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1296
1297 def getFunctionSpaceForCoefficientOfGeneralPDE(self,name):
1298 """
1299 return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name of the general PDE
1300
1301 @param name: name of the coefficient enquired.
1302 @type name: C{string}
1303 @return: the function space to be used for coefficient name
1304 @rtype: L{FunctionSpace<escript.FunctionSpace>}
1305 @raise IllegalCoefficient: if name is not one of coefficients
1306 M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.
1307 """
1308 if self.hasCoefficientOfGeneralPDE(name):
1309 return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
1310 else:
1311 raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1312
1313 def getShapeOfCoefficientOfGeneralPDE(self,name):
1314 """
1315 return the shape of the coefficient name of the general PDE
1316
1317 @param name: name of the coefficient enquired.
1318 @type name: C{string}
1319 @return: the shape of the coefficient name
1320 @rtype: C{tuple} of C{int}
1321 @raise IllegalCoefficient: if name is not one of coefficients
1322 M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.
1323 """
1324 if self.hasCoefficientOfGeneralPDE(name):
1325 return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1326 else:
1327 raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1328
1329 # =============================================================================
1330 # functions giving access to coefficients of a particular PDE implementation:
1331 # =============================================================================
1332 def getCoefficient(self,name):
1333 """
1334 returns the value of the coefficient name
1335
1336 @param name: name of the coefficient requested.
1337 @type name: C{string}
1338 @return: the value of the coefficient name
1339 @rtype: L{Data<escript.Data>}
1340 @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1341 """
1342 if self.hasCoefficient(name):
1343 return self.COEFFICIENTS[name].getValue()
1344 else:
1345 raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1346
1347 def hasCoefficient(self,name):
1348 """
1349 return True if name is the name of a coefficient
1350
1351 @param name: name of the coefficient enquired.
1352 @type name: C{string}
1353 @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1354 @rtype: C{bool}
1355 """
1356 return self.COEFFICIENTS.has_key(name)
1357
1358 def createCoefficient(self, name):
1359 """
1360 create a L{Data<escript.Data>} object corresponding to coefficient name
1361
1362 @return: a coefficient name initialized to 0.
1363 @rtype: L{Data<escript.Data>}
1364 @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1365 """
1366 if self.hasCoefficient(name):
1367 return escript.Data(0.,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))
1368 else:
1369 raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1370
1371 def getFunctionSpaceForCoefficient(self,name):
1372 """
1373 return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name
1374
1375 @param name: name of the coefficient enquired.
1376 @type name: C{string}
1377 @return: the function space to be used for coefficient name
1378 @rtype: L{FunctionSpace<escript.FunctionSpace>}
1379 @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1380 """
1381 if self.hasCoefficient(name):
1382 return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())
1383 else:
1384 raise ValueError,"unknown coefficient %s requested"%name
1385 def getShapeOfCoefficient(self,name):
1386 """
1387 return the shape of the coefficient name
1388
1389 @param name: name of the coefficient enquired.
1390 @type name: C{string}
1391 @return: the shape of the coefficient name
1392 @rtype: C{tuple} of C{int}
1393 @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1394 """
1395 if self.hasCoefficient(name):
1396 return self.COEFFICIENTS[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1397 else:
1398 raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1399
1400 def resetCoefficients(self):
1401 """
1402 resets all coefficients to there default values.
1403 """
1404 for i in self.COEFFICIENTS.iterkeys():
1405 self.COEFFICIENTS[i].resetValue()
1406
1407 def alteredCoefficient(self,name):
1408 """
1409 announce that coefficient name has been changed
1410
1411 @param name: name of the coefficient enquired.
1412 @type name: C{string}
1413 @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1414 @note: if name is q or r, the method will not trigger a rebuilt of the system as constraints are applied to the solved system.
1415 """
1416 if self.hasCoefficient(name):
1417 self.trace("Coefficient %s has been altered."%name)
1418 if not ((name=="q" or name=="r") and self.isUsingLumping()):
1419 if self.COEFFICIENTS[name].isAlteringOperator(): self.__invalidateOperator()
1420 if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__invalidateRightHandSide()
1421 else:
1422 raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1423
1424 def copyConstraint(self,u):
1425 """
1426 copies the constraint into u and returns u.
1427
1428 @param u: a function of rank 0 is a single PDE is solved and of shape (numSolution,) for a system of PDEs
1429 @type u: L{Data<escript.Data>}
1430 @return: the input u modified by the constraints.
1431 @rtype: L{Data<escript.Data>}
1432 @warning: u is altered if it has the appropriate L{FunctionSpace<escript.FunctionSpace>}
1433 """
1434 q=self.getCoefficientOfGeneralPDE("q")
1435 r=self.getCoefficientOfGeneralPDE("r")
1436 if not q.isEmpty():
1437 if u.isEmpty(): u=escript.Data(0.,q.getShape(),q.getFunctionSpace())
1438 if r.isEmpty():
1439 r=escript.Data(0,u.getShape(),u.getFunctionSpace())
1440 else:
1441 r=escript.Data(r,u.getFunctionSpace())
1442 u.copyWithMask(r,escript.Data(q,u.getFunctionSpace()))
1443 return u
1444
1445 def setValue(self,**coefficients):
1446 """
1447 sets new values to coefficients
1448
1449 @param coefficients: new values assigned to coefficients
1450 @keyword A: value for coefficient A.
1451 @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1452 @keyword B: value for coefficient B
1453 @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1454 @keyword C: value for coefficient C
1455 @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1456 @keyword D: value for coefficient D
1457 @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1458 @keyword X: value for coefficient X
1459 @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1460 @keyword Y: value for coefficient Y
1461 @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1462 @keyword d: value for coefficient d
1463 @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1464 @keyword y: value for coefficient y
1465 @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1466 @keyword d_contact: value for coefficient d_contact
1467 @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1468 or L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1469 @keyword y_contact: value for coefficient y_contact
1470 @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1471 or L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1472 @keyword r: values prescribed to the solution at the locations of constraints
1473 @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1474 depending of reduced order is used for the solution.
1475 @keyword q: mask for location of constraints
1476 @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1477 depending of reduced order is used for the representation of the equation.
1478 @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1479 """
1480 # check if the coefficients are legal:
1481 for i in coefficients.iterkeys():
1482 if not self.hasCoefficient(i):
1483 raise IllegalCoefficient,"Attempt to set unknown coefficient %s"%i
1484 # if the number of unknowns or equations is still unknown we try to estimate them:
1485 if self.__numEquations==None or self.__numSolutions==None:
1486 for i,d in coefficients.iteritems():
1487 if hasattr(d,"shape"):
1488 s=d.shape
1489 elif hasattr(d,"getShape"):
1490 s=d.getShape()
1491 else:
1492 s=numarray.array(d).shape
1493 if s!=None:
1494 # get number of equations and number of unknowns:
1495 res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(self.getDomain(),s)
1496 if res==None:
1497 raise IllegalCoefficientValue,"Illegal shape %s of coefficient %s"%(s,i)
1498 else:
1499 if self.__numEquations==None: self.__numEquations=res[0]
1500 if self.__numSolutions==None: self.__numSolutions=res[1]
1501 if self.__numEquations==None: raise UndefinedPDEError,"unidententified number of equations"
1502 if self.__numSolutions==None: raise UndefinedPDEError,"unidententified number of solutions"
1503 # now we check the shape of the coefficient if numEquations and numSolutions are set:
1504 for i,d in coefficients.iteritems():
1505 try:
1506 self.COEFFICIENTS[i].setValue(self.getDomain(),self.getNumEquations(),self.getNumSolutions(),self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1507 except IllegalCoefficientValue,m:
1508 raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1509 self.alteredCoefficient(i)
1510
1511 self.__altered_coefficients=True
1512 # check if the systrem is inhomogeneous:
1513 if len(coefficients)>0 and not self.isUsingLumping():
1514 q=self.getCoefficientOfGeneralPDE("q")
1515 r=self.getCoefficientOfGeneralPDE("r")
1516 homogeneous_constraint=True
1517 if not q.isEmpty() and not r.isEmpty():
1518 if util.Lsup(q*r)>=1.e-13*util.Lsup(r):
1519 self.trace("Inhomogeneous constraint detected.")
1520 self.__invalidateSystem()
1521
1522 def getSystem(self):
1523 """
1524 return the operator and right hand side of the PDE
1525
1526 @return: the discrete version of the PDE
1527 @rtype: C{tuple} of L{Operator,<escript.Operator>} and L{Data<escript.Data>}.
1528 """
1529 if not self.__operator_is_Valid or not self.__righthandside_isValid:
1530 if self.isUsingLumping():
1531 if not self.__operator_is_Valid:
1532 if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution(): raise TypeError,"Lumped matrix requires same order for equations and unknowns"
1533 if not self.getCoefficientOfGeneralPDE("A").isEmpty(): raise Warning,"Using coefficient A in lumped matrix can produce wrong results"
1534 if not self.getCoefficientOfGeneralPDE("B").isEmpty(): raise Warning,"Using coefficient B in lumped matrix can produce wrong results"
1535 if not self.getCoefficientOfGeneralPDE("C").isEmpty(): raise Warning,"Using coefficient C in lumped matrix can produce wrong results"
1536 mat=self.__getNewOperator()
1537 self.getDomain().addPDEToSystem(mat,escript.Data(), \
1538 self.getCoefficientOfGeneralPDE("A"), \
1539 self.getCoefficientOfGeneralPDE("B"), \
1540 self.getCoefficientOfGeneralPDE("C"), \
1541 self.getCoefficientOfGeneralPDE("D"), \
1542 escript.Data(), \
1543 escript.Data(), \
1544 self.getCoefficientOfGeneralPDE("d"), \
1545 escript.Data(),\
1546 self.getCoefficientOfGeneralPDE("d_contact"), \
1547 escript.Data())
1548 self.__operator=1./(mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True))
1549 del mat
1550 self.trace("New lumped operator has been built.")
1551 self.__operator_is_Valid=True
1552 if not self.__righthandside_isValid:
1553 self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1554 self.getCoefficientOfGeneralPDE("X"), \
1555 self.getCoefficientOfGeneralPDE("Y"),\
1556 self.getCoefficientOfGeneralPDE("y"),\
1557 self.getCoefficientOfGeneralPDE("y_contact"))
1558 self.trace("New right hand side as been built.")
1559 self.__righthandside_isValid=True
1560 else:
1561 if not self.__operator_is_Valid and not self.__righthandside_isValid:
1562 self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \
1563 self.getCoefficientOfGeneralPDE("A"), \
1564 self.getCoefficientOfGeneralPDE("B"), \
1565 self.getCoefficientOfGeneralPDE("C"), \
1566 self.getCoefficientOfGeneralPDE("D"), \
1567 self.getCoefficientOfGeneralPDE("X"), \
1568 self.getCoefficientOfGeneralPDE("Y"), \
1569 self.getCoefficientOfGeneralPDE("d"), \
1570 self.getCoefficientOfGeneralPDE("y"), \
1571 self.getCoefficientOfGeneralPDE("d_contact"), \
1572 self.getCoefficientOfGeneralPDE("y_contact"))
1573 self.__applyConstraint()
1574 self.__righthandside=self.copyConstraint(self.__righthandside)
1575 self.trace("New system has been built.")
1576 self.__operator_is_Valid=True
1577 self.__righthandside_isValid=True
1578 elif not self.__righthandside_isValid:
1579 self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1580 self.getCoefficientOfGeneralPDE("X"), \
1581 self.getCoefficientOfGeneralPDE("Y"),\
1582 self.getCoefficientOfGeneralPDE("y"),\
1583 self.getCoefficientOfGeneralPDE("y_contact"))
1584 self.__righthandside=self.copyConstraint(self.__righthandside)
1585 self.trace("New right hand side has been built.")
1586 self.__righthandside_isValid=True
1587 elif not self.__operator_is_Valid:
1588 self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \
1589 self.getCoefficientOfGeneralPDE("A"), \
1590 self.getCoefficientOfGeneralPDE("B"), \
1591 self.getCoefficientOfGeneralPDE("C"), \
1592 self.getCoefficientOfGeneralPDE("D"), \
1593 escript.Data(), \
1594 escript.Data(), \
1595 self.getCoefficientOfGeneralPDE("d"), \
1596 escript.Data(),\
1597 self.getCoefficientOfGeneralPDE("d_contact"), \
1598 escript.Data())
1599 self.__applyConstraint()
1600 self.trace("New operator has been built.")
1601 self.__operator_is_Valid=True
1602 return (self.__operator,self.__righthandside)
1603
1604
1605 class Poisson(LinearPDE):
1606 """
1607 Class to define a Poisson equation problem, which is genear L{LinearPDE} of the form
1608
1609 M{-grad(grad(u)[j])[j] = f}
1610
1611 with natural boundary conditons
1612
1613 M{n[j]*grad(u)[j] = 0 }
1614
1615 and constraints:
1616
1617 M{u=0} where M{q>0}
1618
1619 """
1620
1621 def __init__(self,domain,debug=False):
1622 """
1623 initializes a new Poisson equation
1624
1625 @param domain: domain of the PDE
1626 @type domain: L{Domain<escript.Domain>}
1627 @param debug: if True debug informations are printed.
1628
1629 """
1630 super(Poisson, self).__init__(domain,1,1,debug)
1631 self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1632 "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1633 self.setSymmetryOn()
1634
1635 def setValue(self,**coefficients):
1636 """
1637 sets new values to coefficients
1638
1639 @param coefficients: new values assigned to coefficients
1640 @keyword f: value for right hand side M{f}
1641 @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1642 @keyword q: mask for location of constraints
1643 @type q: any type that can be casted to rank zeo L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1644 depending of reduced order is used for the representation of the equation.
1645 @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1646 """
1647 super(Poisson, self).setValue(**coefficients)
1648
1649 def getCoefficientOfGeneralPDE(self,name):
1650 """
1651 return the value of the coefficient name of the general PDE
1652 @param name: name of the coefficient requested.
1653 @type name: C{string}
1654 @return: the value of the coefficient name
1655 @rtype: L{Data<escript.Data>}
1656 @raise IllegalCoefficient: if name is not one of coefficients
1657 M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.
1658 @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1659 """
1660 if name == "A" :
1661 return escript.Data(util.kronecker(self.getDim()),escript.Function(self.getDomain()))
1662 elif name == "B" :
1663 return escript.Data()
1664 elif name == "C" :
1665 return escript.Data()
1666 elif name == "D" :
1667 return escript.Data()
1668 elif name == "X" :
1669 return escript.Data()
1670 elif name == "Y" :
1671 return self.getCoefficient("f")
1672 elif name == "d" :
1673 return escript.Data()
1674 elif name == "y" :
1675 return escript.Data()
1676 elif name == "d_contact" :
1677 return escript.Data()
1678 elif name == "y_contact" :
1679 return escript.Data()
1680 elif name == "r" :
1681 return escript.Data()
1682 elif name == "q" :
1683 return self.getCoefficient("q")
1684 else:
1685 raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1686
1687 class Helmholtz(LinearPDE):
1688 """
1689 Class to define a Helmhotz equation problem, which is genear L{LinearPDE} of the form
1690
1691 M{S{omega}*u - grad(k*grad(u)[j])[j] = f}
1692
1693 with natural boundary conditons
1694
1695 M{k*n[j]*grad(u)[j] = g- S{alpha}u }
1696
1697 and constraints:
1698
1699 M{u=r} where M{q>0}
1700
1701 """
1702
1703 def __init__(self,domain,debug=False):
1704 """
1705 initializes a new Poisson equation
1706
1707 @param domain: domain of the PDE
1708 @type domain: L{Domain<escript.Domain>}
1709 @param debug: if True debug informations are printed.
1710
1711 """
1712 super(Helmholtz, self).__init__(domain,1,1,debug)
1713 self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1714 "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1715 "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1716 "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1717 "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1718 "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1719 "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1720 self.setSymmetryOn()
1721
1722 def setValue(self,**coefficients):
1723 """
1724 sets new values to coefficients
1725
1726 @param coefficients: new values assigned to coefficients
1727 @keyword omega: value for coefficient M{S{omega}}
1728 @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1729 @keyword k: value for coefficeint M{k}
1730 @type k: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1731 @keyword f: value for right hand side M{f}
1732 @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1733 @keyword alpha: value for right hand side M{S{alpha}}
1734 @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1735 @keyword g: value for right hand side M{g}
1736 @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1737 @keyword r: prescribed values M{r} for the solution in constraints.
1738 @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1739 depending of reduced order is used for the representation of the equation.
1740 @keyword q: mask for location of constraints
1741 @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1742 depending of reduced order is used for the representation of the equation.
1743 @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1744 """
1745 super(Helmholtz, self).setValue(**coefficients)
1746
1747 def getCoefficientOfGeneralPDE(self,name):
1748 """
1749 return the value of the coefficient name of the general PDE
1750
1751 @param name: name of the coefficient requested.
1752 @type name: C{string}
1753 @return: the value of the coefficient name
1754 @rtype: L{Data<escript.Data>}
1755 @raise IllegalCoefficient: if name is not one of coefficients
1756 "A", M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.
1757 @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1758 """
1759 if name == "A" :
1760 return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))*self.getCoefficient("k")
1761 elif name == "B" :
1762 return escript.Data()
1763 elif name == "C" :
1764 return escript.Data()
1765 elif name == "D" :
1766 return self.getCoefficient("omega")
1767 elif name == "X" :
1768 return escript.Data()
1769 elif name == "Y" :
1770 return self.getCoefficient("f")
1771 elif name == "d" :
1772 return self.getCoefficient("alpha")
1773 elif name == "y" :
1774 return self.getCoefficient("g")
1775 elif name == "d_contact" :
1776 return escript.Data()
1777 elif name == "y_contact" :
1778 return escript.Data()
1779 elif name == "r" :
1780 return self.getCoefficient("r")
1781 elif name == "q" :
1782 return self.getCoefficient("q")
1783 else:
1784 raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1785
1786 class LameEquation(LinearPDE):
1787 """
1788 Class to define a Lame equation problem:
1789
1790 M{-grad(S{mu}*(grad(u[i])[j]+grad(u[j])[i]))[j] - grad(S{lambda}*grad(u[j])[i])[j] = F_i -grad(S{sigma}[i,j])[j] }
1791
1792 with natural boundary conditons:
1793
1794 M{n[j]*(S{mu}*(grad(u[i])[j]+grad(u[j])[i]) - S{lambda}*grad(u[j])[i]) = f_i -n[j]*S{sigma}[i,j] }
1795
1796 and constraints:
1797
1798 M{u[i]=r[i]} where M{q[i]>0}
1799
1800 """
1801
1802 def __init__(self,domain,debug=False):
1803 super(LameEquation, self).__init__(domain,\
1804 domain.getDim(),domain.getDim(),debug)
1805 self.COEFFICIENTS={ "lame_lambda" : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
1806 "lame_mu" : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
1807 "F" : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1808 "sigma" : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
1809 "f" : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1810 "r" : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1811 "q" : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1812 self.setSymmetryOn()
1813
1814 def setValue(self,**coefficients):
1815 """
1816 sets new values to coefficients
1817
1818 @param coefficients: new values assigned to coefficients
1819 @keyword lame_mu: value for coefficient M{S{mu}}
1820 @type lame_mu: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1821 @keyword lame_lambda: value for coefficient M{S{lambda}}
1822 @type lame_lambda: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1823 @keyword F: value for internal force M{F}
1824 @type F: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}
1825 @keyword sigma: value for initial stress M{S{sigma}}
1826 @type sigma: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}
1827 @keyword f: value for extrenal force M{f}
1828 @type f: any type that can be casted to L{Vector<escript.Vector>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}
1829 @keyword r: prescribed values M{r} for the solution in constraints.
1830 @type r: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1831 depending of reduced order is used for the representation of the equation.
1832 @keyword q: mask for location of constraints
1833 @type q: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1834 depending of reduced order is used for the representation of the equation.
1835 @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1836 """
1837 super(LameEquation, self).setValue(**coefficients)
1838
1839 def getCoefficientOfGeneralPDE(self,name):
1840 """
1841 return the value of the coefficient name of the general PDE
1842
1843 @param name: name of the coefficient requested.
1844 @type name: C{string}
1845 @return: the value of the coefficient name
1846 @rtype: L{Data<escript.Data>}
1847 @raise IllegalCoefficient: if name is not one of coefficients
1848 "A", M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.
1849 @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1850 """
1851 if name == "A" :
1852 out =self.createCoefficientOfGeneralPDE("A")
1853 for i in range(self.getDim()):
1854 for j in range(self.getDim()):
1855 out[i,i,j,j] += self.getCoefficient("lame_lambda")
1856 out[i,j,j,i] += self.getCoefficient("lame_mu")
1857 out[i,j,i,j] += self.getCoefficient("lame_mu")
1858 return out
1859 elif name == "B" :
1860 return escript.Data()
1861 elif name == "C" :
1862 return escript.Data()
1863 elif name == "D" :
1864 return escript.Data()
1865 elif name == "X" :
1866 return self.getCoefficient("sigma")
1867 elif name == "Y" :
1868 return self.getCoefficient("F")
1869 elif name == "d" :
1870 return escript.Data()
1871 elif name == "y" :
1872 return self.getCoefficient("f")
1873 elif name == "d_contact" :
1874 return escript.Data()
1875 elif name == "y_contact" :
1876 return escript.Data()
1877 elif name == "r" :
1878 return self.getCoefficient("r")
1879 elif name == "q" :
1880 return self.getCoefficient("q")
1881 else:
1882 raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1883
1884 class AdvectivePDE(LinearPDE):
1885 """
1886 In cases of PDEs dominated by the advection terms M{B} and M{C} against the adevctive terms M{A}
1887 up-winding has been used. The L{AdvectivePDE} class applies SUPG upwinding to the advective terms.
1888
1889 In the following we set
1890
1891 M{Z[j]=C[j]-B[j]}
1892
1893 or
1894
1895 M{Z[i,k,l]=C[i,k,l]-B[i,l,k]}
1896
1897 To measure the dominance of the advective terms over the diffusive term M{A} the
1898 X{Pelclet number} M{P} is used. It is defined as
1899
1900 M{P=h|Z|/(2|A|)}
1901
1902 where M{|.|} denotes the L{length<util.length>} of the arument and M{h} is the local cell size
1903 from L{getSize<escript.Domain.getSize>}. Where M{|A|==0} M{P} is M{S{infinity}}.
1904
1905 From the X{Pelclet number} the stabilization parameters M{S{Xi}} and M{S{Xi}} are calculated:
1906
1907 M{S{Xi}=S{xi}(P) h/|Z|}
1908
1909 where M{S{xi}} is a suitable function of the Peclet number.
1910
1911 In the case of a single PDE the coefficient are up-dated in the following way:
1912 - M{A[i,j] S{<-} A[i,j] + S{Xi} * Z[j] * Z[l]}
1913 - M{B[j] S{<-} B[j] + S{Xi} * C[j] * D}
1914 - M{C[j] S{<-} C[j] + S{Xi} * B[j] * D}
1915 - M{X[j] S{<-} X[j] + S{Xi} * Z[j] * Y}
1916
1917 Similar for the case of a systems of PDEs:
1918 - M{A[i,j,k,l] S{<-} A[i,j,k,l]+ S{delta}[p,m] * S{Xi} * Z[p,i,j] * Z[m,k,l]}
1919 - M{B[i,j,k] S{<-} B[i,j,k] + S{delta}[p,m] * S{Xi} * D[p,k] * C[m,i,j]}
1920 - M{C[i,k,l] S{<-} C[i,k,l] + S{delta}[p,m] * S{Xi} * D[p,k] * B[m,l,i]}
1921 - M{X[i,j] S{<-} X[i,j] + S{delta}[p,m] * S{Xi} * Y[p] * Z[m,i,j]}
1922
1923 where M{S{delta}} is L{kronecker}.
1924 Using upwinding in this form, introduces an additonal error which is proprtional to the cell size M{h}
1925 but with the intension to stabilize the solution.
1926
1927 """
1928 def __init__(self,domain,numEquations=None,numSolutions=None,xi=None,debug=False):
1929 """
1930 creates a linear, steady, second order PDE on a L{Domain<escript.Domain>}
1931
1932 @param domain: domain of the PDE
1933 @type domain: L{Domain<escript.Domain>}
1934 @param numEquations: number of equations. If numEquations==None the number of equations
1935 is exracted from the PDE coefficients.
1936 @param numSolutions: number of solution components. If numSolutions==None the number of solution components
1937 is exracted from the PDE coefficients.
1938 @param xi: defines a function which returns for any given Preclet number as L{Scalar<escript.Scalar>} object the
1939 M{S{xi}}-value used to define the stabilization parameters. If equal to None, L{ELMAN_RAMAGE} is used.
1940 @type xi: callable object which returns a L{Scalar<escript.Scalar>} object.
1941 @param debug: if True debug informations are printed.
1942 """
1943 super(AdvectivePDE, self).__init__(domain,\
1944 numEquations,numSolutions,debug)
1945 if xi==None:
1946 self.__xi=AdvectivePDE.ELMAN_RAMAGE
1947 else:
1948 self.__xi=xi
1949 self.__Xi=escript.Data()
1950
1951 def setValue(**coefficients):
1952 """
1953 sets new values to coefficients
1954
1955 @param coefficients: new values assigned to coefficients
1956 @keyword A: value for coefficient A.
1957 @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1958 @keyword B: value for coefficient B
1959 @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1960 @keyword C: value for coefficient C
1961 @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1962 @keyword D: value for coefficient D
1963 @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1964 @keyword X: value for coefficient X
1965 @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1966 @keyword Y: value for coefficient Y
1967 @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1968 @keyword d: value for coefficient d
1969 @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1970 @keyword y: value for coefficient y
1971 @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1972 @keyword d_contact: value for coefficient d_contact
1973 @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1974 or L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1975 @keyword y_contact: value for coefficient y_contact
1976 @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1977 or L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1978 @keyword r: values prescribed to the solution at the locations of constraints
1979 @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1980 depending of reduced order is used for the solution.
1981 @keyword q: mask for location of constraints
1982 @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1983 depending of reduced order is used for the representation of the equation.
1984 @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1985
1986 """
1987 if "A" in coefficients.keys() or "B" in coefficients.keys() or "C" in coefficients.keys(): self.__Xi=escript.Data()
1988 super(AdvectivePDE, self).setValue(**coefficients)
1989
1990 def ELMAN_RAMAGE(self,P):
1991 """
1992 Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.
1993 This function uses the method suggested by H.C. Elman and A. Ramage, I{SIAM J. Numer. Anal.}, B{40} (2002)
1994 - M{S{xi}(P)=0} for M{P<1}
1995 - M{S{xi}(P)=(1-1/P)/2} otherwise
1996
1997 @param P: Preclet number
1998 @type P: L{Scalar<escript.Scalar>}
1999 @return: up-wind weightimg factor
2000 @rtype: L{Scalar<escript.Scalar>}
2001 """
2002 return util.wherePositive(P-1.)*0.5*(1.-1./(P+1.e-15))
2003
2004 def SIMPLIFIED_BROOK_HUGHES(self,P):
2005 """
2006 Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.
2007 The original methods is
2008
2009 M{S{xi}(P)=coth(P)-1/P}
2010
2011 As the evaluation of M{coth} is expensive we are using the approximation:
2012
2013 - M{S{xi}(P)=P/3} where M{P<3}
2014 - M{S{xi}(P)=1/2} otherwise
2015
2016 @param P: Preclet number
2017 @type P: L{Scalar<escript.Scalar>}
2018 @return: up-wind weightimg factor
2019 @rtype: L{Scalar<escript.Scalar>}
2020 """
2021 c=util.whereNegative(P-3.)
2022 return P/6.*c+1./2.*(1.-c)
2023
2024 def HALF(self,P):
2025 """
2026 Predefined function to set value M{1/2} for M{S{xi}}
2027
2028 @param P: Preclet number
2029 @type P: L{Scalar<escript.Scalar>}
2030 @return: up-wind weightimg factor
2031 @rtype: L{Scalar<escript.Scalar>}
2032 """
2033 return escript.Scalar(0.5,P.getFunctionSpace())
2034
2035 def __calculateXi(self,peclet_factor,flux,h):
2036 flux=util.Lsup(flux)
2037 if flux_max>0.:
2038 return h*self.__xi(flux*peclet_factor)/(flux+flux_max*self.__TOL)
2039 else:
2040 return 0.
2041
2042 def __getXi(self):
2043 if self.__Xi.isEmpty():
2044 B=self.getCoefficient("B")
2045 C=self.getCoefficient("C")
2046 A=self.getCoefficient("A")
2047 h=self.getDomain().getSize()
2048 self.__Xi=escript.Scalar(0.,self.getFunctionSpaceForCoefficient("A"))
2049 if not C.isEmpty() or not B.isEmpty():
2050 if not C.isEmpty() and not B.isEmpty():
2051 flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))
2052 if self.getNumEquations()>1:
2053 if self.getNumSolutions()>1:
2054 for i in range(self.getNumEquations()):
2055 for k in range(self.getNumSolutions()):
2056 for l in range(self.getDim()): flux2+=(C[i,k,l]-B[i,l,k])**2
2057 # flux=C-util.reorderComponents(B,[0,2,1])
2058 else:
2059 for i in range(self.getNumEquations()):
2060 for l in range(self.getDim()): flux2+=(C[i,l]-B[i,l])**2
2061 # flux=C-B
2062 else:
2063 if self.getNumSolutions()>1:
2064 for k in range(self.getNumSolutions()):
2065 for l in range(self.getDim()): flux2+=(C[k,l]-B[l,k])**2
2066 # flux=C-util.reorderComponents(B,[1,0])
2067 else:
2068 for l in range(self.getDim()): flux2+=(C[l]-B[l])**2
2069 #flux=C-B
2070 length_of_flux=util.sqrt(flux2)
2071 elif C.isEmpty():
2072 length_of_flux=util.length(B)
2073 #flux=B
2074 else:
2075 length_of_flux=util.length(C)
2076 #flux=C
2077
2078 #length_of_flux=util.length(flux)
2079 flux_max=util.Lsup(length_of_flux)
2080 if flux_max>0.:
2081 # length_of_A=util.inner(flux,util.tensormutiply(A,flux))
2082 length_of_A=util.length(A)
2083 A_max=util.Lsup(length_of_A)
2084 if A_max>0:
2085 inv_A=1./(length_of_A+A_max*self.__TOL)
2086 else:
2087 inv_A=1./self.__TOL
2088 peclet_number=length_of_flux*h/2*inv_A
2089 xi=self.__xi(peclet_number)
2090 self.__Xi=h*xi/(length_of_flux+flux_max*self.__TOL)
2091 self.trace("preclet number = %e"%util.Lsup(peclet_number))
2092 return self.__Xi
2093
2094
2095 def getCoefficientOfGeneralPDE(self,name):
2096 """
2097 return the value of the coefficient name of the general PDE
2098
2099 @param name: name of the coefficient requested.
2100 @type name: C{string}
2101 @return: the value of the coefficient name
2102 @rtype: L{Data<escript.Data>}
2103 @raise IllegalCoefficient: if name is not one of coefficients
2104 M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.
2105 @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2106 """
2107 if not self.getNumEquations() == self.getNumSolutions():
2108 raise ValueError,"AdvectivePDE expects the number of solution componets and the number of equations to be equal."
2109
2110 if name == "A" :
2111 A=self.getCoefficient("A")
2112 B=self.getCoefficient("B")
2113 C=self.getCoefficient("C")
2114 if B.isEmpty() and C.isEmpty():
2115 Aout=A
2116 else:
2117 if A.isEmpty():
2118 Aout=self.createNewCoefficient("A")
2119 else:
2120 Aout=A[:]
2121 Xi=self.__getXi()
2122 if self.getNumEquations()>1:
2123 for i in range(self.getNumEquations()):
2124 for j in range(self.getDim()):
2125 for k in range(self.getNumSolutions()):
2126 for l in range(self.getDim()):
2127 if not C.isEmpty() and not B.isEmpty():
2128 # tmp=C-util.reorderComponents(B,[0,2,1])
2129 # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(tmp,[1,2,0]),tmp,offset=1)
2130 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])
2131 elif C.isEmpty():
2132 for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*B[p,j,i]*B[p,l,k]
2133 # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(B,[2,1,0]),util.reorder(B,[0,2,1]),offset=1)
2134 else:
2135 for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*C[p,i,j]*C[p,k,l]
2136 # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),C,offset=1)
2137 else:
2138 for j in range(self.getDim()):
2139 for l in range(self.getDim()):
2140 if not C.isEmpty() and not B.isEmpty():
2141 Aout[j,l]+=Xi*(C[j]-B[j])*(C[l]-B[l])
2142 elif C.isEmpty():
2143 Aout[j,l]+=Xi*B[j]*B[l]
2144 else:
2145 Aout[j,l]+=Xi*C[j]*C[l]
2146 # if not C.isEmpty() and not B.isEmpty():
2147 # tmp=C-B
2148 # Aout=Aout+Xi*util.outer(tmp,tmp)
2149 # elif C.isEmpty():
2150 # Aout=Aout+Xi*util.outer(B,B)
2151 # else:
2152 # Aout=Aout+Xi*util.outer(C,C)
2153 return Aout
2154 elif name == "B" :
2155 B=self.getCoefficient("B")
2156 C=self.getCoefficient("C")
2157 D=self.getCoefficient("D")
2158 if C.isEmpty() or D.isEmpty():
2159 Bout=B
2160 else:
2161 Xi=self.__getXi()
2162 if B.isEmpty():
2163 Bout=self.createNewCoefficient("B")
2164 else:
2165 Bout=B[:]
2166 if self.getNumEquations()>1:
2167 for k in range(self.getNumSolutions()):
2168 for p in range(self.getNumEquations()):
2169 tmp=Xi*D[p,k]
2170 for i in range(self.getNumEquations()):
2171 for j in range(self.getDim()):
2172 Bout[i,j,k]+=tmp*C[p,i,j]
2173 # Bout=Bout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),D,offset=1)
2174 else:
2175 tmp=Xi*D
2176 for j in range(self.getDim()): Bout[j]+=tmp*C[j]
2177 # Bout=Bout+Xi*D*C
2178 return Bout
2179 elif name == "C" :
2180 B=self.getCoefficient("B")
2181 C=self.getCoefficient("C")
2182 D=self.getCoefficient("D")
2183 if B.isEmpty() or D.isEmpty():
2184 Cout=C
2185 else:
2186 Xi=self.__getXi()
2187 if C.isEmpty():
2188 Cout=self.createNewCoefficient("C")
2189 else:
2190 Cout=C[:]
2191 if self.getNumEquations()>1:
2192 for k in range(self.getNumSolutions()):
2193 for p in range(self.getNumEquations()):
2194 tmp=Xi*D[p,k]
2195 for i in range(self.getNumEquations()):
2196 for l in range(self.getDim()):
2197 Cout[i,k,l]+=tmp*B[p,l,i]
2198 # Cout=Cout+Xi*B[p,l,i]*D[p,k]
2199 else:
2200 tmp=Xi*D
2201 for j in range(self.getDim()): Cout[j]+=tmp*B[j]
2202 # Cout=Cout+tmp*D*B
2203 return Cout
2204 elif name == "D" :
2205 return self.getCoefficient("D")
2206 elif name == "X" :
2207 X=self.getCoefficient("X")
2208 Y=self.getCoefficient("Y")
2209 B=self.getCoefficient("B")
2210 C=self.getCoefficient("C")
2211 if Y.isEmpty() or (B.isEmpty() and C.isEmpty()):
2212 Xout=X
2213 else:
2214 if X.isEmpty():
2215 Xout=self.createNewCoefficient("X")
2216 else:
2217 Xout=X[:]
2218 Xi=self.__getXi()
2219 if self.getNumEquations()>1:
2220 for p in range(self.getNumEquations()):
2221 tmp=Xi*Y[p]
2222 for i in range(self.getNumEquations()):
2223 for j in range(self.getDim()):
2224 if not C.isEmpty() and not B.isEmpty():
2225 Xout[i,j]+=tmp*(C[p,i,j]-B[p,j,i])
2226 # Xout=X_out+Xi*util.inner(Y,C-util.reorderComponents(B,[0,2,1]),offset=1)
2227 elif C.isEmpty():
2228 Xout[i,j]-=tmp*B[p,j,i]
2229 # Xout=X_out-Xi*util.inner(Y,util.reorderComponents(B,[0,2,1]),offset=1)
2230 else:
2231 Xout[i,j]+=tmp*C[p,i,j]
2232 # Xout=X_out+Xi*util.inner(Y,C,offset=1)
2233 else:
2234 tmp=Xi*Y
2235 for j in range(self.getDim()):
2236 if not C.isEmpty() and not B.isEmpty():
2237 Xout[j]+=tmp*(C[j]-B[j])
2238 # Xout=Xout+Xi*Y*(C-B)
2239 elif C.isEmpty():
2240 Xout[j]-=tmp*B[j]
2241 # Xout=Xout-Xi*Y*B
2242 else:
2243 Xout[j]+=tmp*C[j]
2244 # Xout=Xout+Xi*Y*C
2245 return Xout
2246 elif name == "Y" :
2247 return self.getCoefficient("Y")
2248 elif name == "d" :
2249 return self.getCoefficient("d")
2250 elif name == "y" :
2251 return self.getCoefficient("y")
2252 elif name == "d_contact" :
2253 return self.getCoefficient("d_contact")
2254 elif name == "y_contact" :
2255 return self.getCoefficient("y_contact")
2256 elif name == "r" :
2257 return self.getCoefficient("r")
2258 elif name == "q" :
2259 return self.getCoefficient("q")
2260 else:
2261 raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2262
2263 class AdvectionDiffusion(LinearPDE):
2264 """
2265 Class to define PDE equation of the unisotropic advection-diffusion problem, which is genear L{LinearPDE} of the form
2266
2267 M{S{omega}*u + inner(v,grad(u))- grad(matrixmult(k_bar,grad(u))[j])[j] = f}
2268
2269 with natural boundary conditons
2270
2271 M{n[j]*matrixmult(k,grad(u))[j] = g- S{alpha}u }
2272
2273 and constraints:
2274
2275 M{u=r} where M{q>0}
2276
2277 and
2278
2279 M{k_bar[i,j]=k[i,j]+upwind[i]*upwind[j]}
2280
2281 """
2282
2283 def __init__(self,domain,debug=False):
2284 """
2285 initializes a new Poisson equation
2286
2287 @param domain: domain of the PDE
2288 @type domain: L{Domain<escript.Domain>}
2289 @param debug: if True debug informations are printed.
2290
2291 """
2292 super(AdvectionDiffusion, self).__init__(domain,1,1,debug)
2293 self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
2294 "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_DIM,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
2295 "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2296 "v": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_DIM,),PDECoefficient.OPERATOR),
2297 "upwind": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_DIM,),PDECoefficient.OPERATOR),
2298 "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
2299 "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2300 "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
2301 "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
2302
2303 def setValue(self,**coefficients):
2304 """
2305 sets new values to coefficients
2306
2307 @param coefficients: new values assigned to coefficients
2308 @keyword omega: value for coefficient M{S{omega}}
2309 @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2310 @keyword k: value for coefficient M{k}
2311 @type k: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}.
2312 @keyword v: value for coefficient M{v}
2313 @type v: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}.
2314 @keyword upwind: value for upwind term M{upwind}
2315 @type upwind: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}.
2316 @keyword f: value for right hand side M{f}
2317 @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2318 @keyword alpha: value for right hand side M{S{alpha}}
2319 @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2320 @keyword g: value for right hand side M{g}
2321 @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2322 @keyword r: prescribed values M{r} for the solution in constraints.
2323 @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2324 depending of reduced order is used for the representation of the equation.
2325 @keyword q: mask for location of constraints
2326 @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2327 depending of reduced order is used for the representation of the equation.
2328 @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2329 """
2330 super(AdvectionDiffusion, self).setValue(**coefficients)
2331
2332 def getCoefficientOfGeneralPDE(self,name):
2333 """
2334 return the value of the coefficient name of the general PDE
2335
2336 @param name: name of the coefficient requested.
2337 @type name: C{string}
2338 @return: the value of the coefficient name
2339 @rtype: L{Data<escript.Data>}
2340 @raise IllegalCoefficient: if name is not one of coefficients
2341 "A", M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.
2342 @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2343 """
2344 if name == "A" :
2345 return self.getCoefficient("k")+util.outer(self.getCoefficient("upwind"),self.getCoefficient("upwind"))
2346 elif name == "B" :
2347 return escript.Data()
2348 elif name == "C" :
2349 return self.getCoefficient("v")
2350 elif name == "D" :
2351 return self.getCoefficient("omega")
2352 elif name == "X" :
2353 return escript.Data()
2354 elif name == "Y" :
2355 return self.getCoefficient("f")
2356 elif name == "d" :
2357 return self.getCoefficient("alpha")
2358 elif name == "y" :
2359 return self.getCoefficient("g")
2360 elif name == "d_contact" :
2361 return escript.Data()
2362 elif name == "y_contact" :
2363 return escript.Data()
2364 elif name == "r" :
2365 return self.getCoefficient("r")
2366 elif name == "q" :
2367 return self.getCoefficient("q")
2368 else:
2369 raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2370
2371
2372 # $Log$
2373 # Revision 1.14 2005/09/22 01:54:57 jgs
2374 # Merge of development branch dev-02 back to main trunk on 2005-09-22
2375 #
2376 # Revision 1.13 2005/09/15 03:44:19 jgs
2377 # Merge of development branch dev-02 back to main trunk on 2005-09-15
2378 #
2379 # Revision 1.12 2005/09/01 03:31:28 jgs
2380 # Merge of development branch dev-02 back to main trunk on 2005-09-01
2381 #
2382 # Revision 1.11 2005/08/23 01:24:28 jgs
2383 # Merge of development branch dev-02 back to main trunk on 2005-08-23
2384 #
2385 # Revision 1.10 2005/08/12 01:45:36 jgs
2386 # erge of development branch dev-02 back to main trunk on 2005-08-12
2387 #
2388 # Revision 1.9.2.17 2005/09/21 07:03:33 matt
2389 # PDECoefficient and LinearPDE are now new style classes (introduced in Python
2390 # 2.2). Classes Poisson, Helmholtz, LameEquation and AdvectivePDE have been
2391 # modified to instead use portable/cooperative "super" calls to extend base
2392 # class methods.
2393 #
2394 # Revision 1.9.2.16 2005/09/16 01:54:37 matt
2395 # Removed redundant if-loop.
2396 #
2397 # Revision 1.9.2.15 2005/09/14 08:09:18 matt
2398 # Added "REDUCED" solution PDECoefficient descriptors for LinearPDEs.
2399 #
2400 # Revision 1.9.2.14 2005/09/07 06:26:16 gross
2401 # the solver from finley are put into the standalone package paso now
2402 #
2403 # Revision 1.9.2.13 2005/08/31 08:45:03 gross
2404 # in the case of lumping no new system is allocated if the constraint is changed.
2405 #
2406 # Revision 1.9.2.12 2005/08/31 07:10:23 gross
2407 # test for Lumping added
2408 #
2409 # Revision 1.9.2.11 2005/08/30 01:53:45 gross
2410 # bug in format fixed.
2411 #
2412 # Revision 1.9.2.10 2005/08/26 07:14:17 gross
2413 # a few more bugs in linearPDE fixed. remaining problem are finley problems
2414 #
2415 # Revision 1.9.2.9 2005/08/26 06:30:45 gross
2416 # fix for reported bug 0000004. test_linearPDE passes a few more tests
2417 #
2418 # Revision 1.9.2.8 2005/08/26 04:30:13 gross
2419 # gneric unit testing for linearPDE
2420 #
2421 # Revision 1.9.2.7 2005/08/25 07:06:50 gross
2422 # linearPDE documentation is parsed now by epydoc. there is still a problem with links into escriptcpp.so
2423 #
2424 # Revision 1.9.2.6 2005/08/24 05:01:24 gross
2425 # problem with resetting the matrix in case of resetting its values to 0 fixed.
2426 #
2427 # Revision 1.9.2.5 2005/08/24 02:03:28 gross
2428 # epydoc mark up partially fixed
2429 #
2430 # Revision 1.9.2.4 2005/08/22 07:11:09 gross
2431 # some problems with LinearPDEs fixed.
2432 #
2433 # Revision 1.9.2.3 2005/08/18 04:48:48 gross
2434 # the methods SetLumping*() are removed. Lumping is set trough setSolverMethod(LinearPDE.LUMPING)
2435 #
2436 # Revision 1.9.2.2 2005/08/18 04:39:32 gross
2437 # the constants have been removed from util.py as they not needed anymore. PDE related constants are accessed through LinearPDE attributes now
2438 #
2439 # Revision 1.9.2.1 2005/07/29 07:10:27 gross
2440 # new functions in util and a new pde type in linearPDEs
2441 #
2442 # Revision 1.1.2.25 2005/07/28 04:21:09 gross
2443 # Lame equation: (linear elastic, isotropic) added
2444 #
2445 # Revision 1.1.2.24 2005/07/22 06:37:11 gross
2446 # some extensions to modellib and linearPDEs
2447 #
2448 # Revision 1.1.2.23 2005/05/13 00:55:20 cochrane
2449 # Fixed up some docstrings. Moved module-level functions to top of file so
2450 # that epydoc and doxygen can pick them up properly.
2451 #
2452 # Revision 1.1.2.22 2005/05/12 11:41:30 gross
2453 # some basic Models have been added
2454 #
2455 # Revision 1.1.2.21 2005/05/12 07:16:12 cochrane
2456 # Moved ELMAN_RAMAGE, SIMPLIFIED_BROOK_HUGHES, and HALF functions to bottom of
2457 # file so that the AdvectivePDE class is picked up by doxygen. Some
2458 # reformatting of docstrings. Addition of code to make equations come out
2459 # as proper LaTeX.
2460 #
2461 # Revision 1.1.2.20 2005/04/15 07:09:08 gross
2462 # some problems with functionspace and linearPDEs fixed.
2463 #
2464 # Revision 1.1.2.19 2005/03/04 05:27:07 gross
2465 # bug in SystemPattern fixed.
2466 #
2467 # Revision 1.1.2.18 2005/02/08 06:16:45 gross
2468 # Bugs in AdvectivePDE fixed, AdvectiveTest is stable but more testing is needed
2469 #
2470 # Revision 1.1.2.17 2005/02/08 05:56:19 gross
2471 # Reference Number handling added
2472 #
2473 # Revision 1.1.2.16 2005/02/07 04:41:28 gross
2474 # some function exposed to python to make mesh merging running
2475 #
2476 # Revision 1.1.2.15 2005/02/03 00:14:44 gross
2477 # timeseries add and ESySParameter.py renames esysXML.py for consistence
2478 #
2479 # Revision 1.1.2.14 2005/02/01 06:44:10 gross
2480 # new implementation of AdvectivePDE which now also updates right hand side. systems of PDEs are still not working
2481 #
2482 # Revision 1.1.2.13 2005/01/25 00:47:07 gross
2483 # updates in the documentation
2484 #
2485 # Revision 1.1.2.12 2005/01/12 01:28:04 matt
2486 # Added createCoefficient method for linearPDEs.
2487 #
2488 # Revision 1.1.2.11 2005/01/11 01:55:34 gross
2489 # a problem in linearPDE class fixed
2490 #
2491 # Revision 1.1.2.10 2005/01/07 01:13:29 gross
2492 # some bugs in linearPDE fixed
2493 #
2494 # Revision 1.1.2.9 2005/01/06 06:24:58 gross
2495 # some bugs in slicing fixed
2496 #
2497 # Revision 1.1.2.8 2005/01/05 04:21:40 gross
2498 # FunctionSpace checking/matchig in slicing added
2499 #
2500 # Revision 1.1.2.7 2004/12/29 10:03:41 gross
2501 # bug in setValue fixed
2502 #
2503 # Revision 1.1.2.6 2004/12/29 05:29:59 gross
2504 # AdvectivePDE successfully tested for Peclet number 1000000. there is still a problem with setValue and Data()
2505 #
2506 # Revision 1.1.2.5 2004/12/29 00:18:41 gross
2507 # AdvectivePDE added
2508 #
2509 # Revision 1.1.2.4 2004/12/24 06:05:41 gross
2510 # some changes in linearPDEs to add AdevectivePDE
2511 #
2512 # Revision 1.1.2.3 2004/12/16 00:12:34 gross
2513 # __init__ of LinearPDE does not accept any coefficient anymore
2514 #
2515 # Revision 1.1.2.2 2004/12/14 03:55:01 jgs
2516 # *** empty log message ***
2517 #
2518 # Revision 1.1.2.1 2004/12/12 22:53:47 gross
2519 # linearPDE has been renamed LinearPDE
2520 #
2521 # Revision 1.1.1.1.2.7 2004/12/07 10:13:08 gross
2522 # GMRES added
2523 #
2524 # Revision 1.1.1.1.2.6 2004/12/07 03:19:50 gross
2525 # options for GMRES and PRES20 added
2526 #
2527 # Revision 1.1.1.1.2.5 2004/12/01 06:25:15 gross
2528 # some small changes
2529 #
2530 # Revision 1.1.1.1.2.4 2004/11/24 01:50:21 gross
2531 # Finley solves 4M unknowns now
2532 #
2533 # Revision 1.1.1.1.2.3 2004/11/15 06:05:26 gross
2534 # poisson solver added
2535 #
2536 # Revision 1.1.1.1.2.2 2004/11/12 06:58:15 gross
2537 # a lot of changes to get the linearPDE class running: most important change is that there is no matrix format exposed to the user anymore. the format is chosen by the Domain according to the solver and symmetry
2538 #
2539 # Revision 1.1.1.1.2.1 2004/10/28 22:59:22 gross
2540 # finley's RecTest.py is running now: problem in SystemMatrixAdapater fixed
2541 #
2542 # Revision 1.1.1.1 2004/10/26 06:53:56 jgs
2543 # initial import of project esys2
2544 #
2545 # Revision 1.3.2.3 2004/10/26 06:43:48 jgs
2546 # committing Lutz's and Paul's changes to brach jgs
2547 #
2548 # Revision 1.3.4.1 2004/10/20 05:32:51 cochrane
2549 # Added incomplete Doxygen comments to files, or merely put the docstrings that already exist into Doxygen form.
2550 #
2551 # Revision 1.3 2004/09/23 00:53:23 jgs
2552 # minor fixes
2553 #
2554 # Revision 1.1 2004/08/28 12:58:06 gross
2555 # SimpleSolve is not running yet: problem with == of functionsspace
2556 #

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