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1 #
2 # $Id$
3 #
4 #######################################################
5 #
6 # Copyright 2003-2007 by ACceSS MNRF
7 # Copyright 2007 by University of Queensland
8 #
9 # http://esscc.uq.edu.au
10 # Primary Business: Queensland, Australia
11 # Licensed under the Open Software License version 3.0
12 # http://www.opensource.org/licenses/osl-3.0.php
13 #
14 #######################################################
15 #
16
17 """
18 The module provides an interface to define and solve linear partial
19 differential equations (PDEs) within L{escript}. L{linearPDEs} does not provide any
20 solver capabilities in itself but hands the PDE over to
21 the PDE solver library defined through the L{Domain<escript.Domain>} of the PDE.
22 The general interface is provided through the L{LinearPDE} class. The
23 L{AdvectivePDE} which is derived from the L{LinearPDE} class
24 provides an interface to PDE dominated by its advective terms. The L{Poisson},
25 L{Helmholtz}, L{LameEquation}, L{AdvectivePDE}
26 classs which are also derived form the L{LinearPDE} class should be used
27 to define of solve these sepecial PDEs.
28
29 @var __author__: name of author
30 @var __copyright__: copyrights
31 @var __license__: licence agreement
32 @var __url__: url entry point on documentation
33 @var __version__: version
34 @var __date__: date of the version
35 """
36
37 import escript
38 import util
39 import numarray
40
41 __author__="Lutz Gross, l.gross@uq.edu.au"
42 __copyright__=""" Copyright (c) 2006 by ACcESS MNRF
43 http://www.access.edu.au
44 Primary Business: Queensland, Australia"""
45 __license__="""Licensed under the Open Software License version 3.0
46 http://www.opensource.org/licenses/osl-3.0.php"""
47 __url__="http://www.iservo.edu.au/esys"
48 __version__="$Revision$"
49 __date__="$Date$"
50
51
52 class IllegalCoefficient(ValueError):
53 """
54 raised if an illegal coefficient of the general ar particular PDE is requested.
55 """
56 pass
57
58 class IllegalCoefficientValue(ValueError):
59 """
60 raised if an incorrect value for a coefficient is used.
61 """
62 pass
63
64 class IllegalCoefficientFunctionSpace(ValueError):
65 """
66 raised if an incorrect function space for a coefficient is used.
67 """
68
69 class UndefinedPDEError(ValueError):
70 """
71 raised if a PDE is not fully defined yet.
72 """
73 pass
74
75 class PDECoefficient(object):
76 """
77 A class for describing a PDE coefficient
78
79 @cvar INTERIOR: indicator that coefficient is defined on the interior of the PDE domain
80 @cvar BOUNDARY: indicator that coefficient is defined on the boundary of the PDE domain
81 @cvar CONTACT: indicator that coefficient is defined on the contact region within the PDE domain
82 @cvar INTERIOR_REDUCED: indicator that coefficient is defined on the interior of the PDE domain using a reduced integration order
83 @cvar BOUNDARY_REDUCED: indicator that coefficient is defined on the boundary of the PDE domain using a reduced integration order
84 @cvar CONTACT_REDUCED: indicator that coefficient is defined on the contact region within the PDE domain using a reduced integration order
85 @cvar SOLUTION: indicator that coefficient is defined trough a solution of the PDE
86 @cvar REDUCED: indicator that coefficient is defined trough a reduced solution of the PDE
87 @cvar BY_EQUATION: indicator that the dimension of the coefficient shape is defined by the number PDE equations
88 @cvar BY_SOLUTION: indicator that the dimension of the coefficient shape is defined by the number PDE solutions
89 @cvar BY_DIM: indicator that the dimension of the coefficient shape is defined by the spatial dimension
90 @cvar OPERATOR: indicator that the the coefficient alters the operator of the PDE
91 @cvar RIGHTHANDSIDE: indicator that the the coefficient alters the right hand side of the PDE
92 @cvar BOTH: indicator that the the coefficient alters the operator as well as the right hand side of the PDE
93
94 """
95 INTERIOR=0
96 BOUNDARY=1
97 CONTACT=2
98 SOLUTION=3
99 REDUCED=4
100 BY_EQUATION=5
101 BY_SOLUTION=6
102 BY_DIM=7
103 OPERATOR=10
104 RIGHTHANDSIDE=11
105 BOTH=12
106 INTERIOR_REDUCED=13
107 BOUNDARY_REDUCED=14
108 CONTACT_REDUCED=15
109
110 def __init__(self, where, pattern, altering):
111 """
112 Initialise a PDE Coefficient type
113
114 @param where: describes where the coefficient lives
115 @type where: one of L{INTERIOR}, L{BOUNDARY}, L{CONTACT}, L{SOLUTION}, L{REDUCED},
116 L{INTERIOR_REDUCED}, L{BOUNDARY_REDUCED}, L{CONTACT_REDUCED}.
117 @param pattern: describes the shape of the coefficient and how the shape is build for a given
118 spatial dimension and numbers of equation and solution in then PDE. For instance,
119 (L{BY_EQUATION},L{BY_SOLUTION},L{BY_DIM}) descrbes a rank 3 coefficient which
120 is instanciated as shape (3,2,2) in case of a three equations and two solution components
121 on a 2-dimensional domain. In the case of single equation and a single solution component
122 the shape compoments marked by L{BY_EQUATION} or L{BY_SOLUTION} are dropped. In this case
123 the example would be read as (2,).
124 @type pattern: C{tuple} of L{BY_EQUATION}, L{BY_SOLUTION}, L{BY_DIM}
125 @param altering: indicates what part of the PDE is altered if the coefficiennt is altered
126 @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}
127 @param reduced: indicates if reduced
128 @type reduced: C{bool}
129 """
130 super(PDECoefficient, self).__init__()
131 self.what=where
132 self.pattern=pattern
133 self.altering=altering
134 self.resetValue()
135
136 def resetValue(self):
137 """
138 resets coefficient value to default
139 """
140 self.value=escript.Data()
141
142 def getFunctionSpace(self,domain,reducedEquationOrder=False,reducedSolutionOrder=False):
143 """
144 defines the L{FunctionSpace<escript.FunctionSpace>} of the coefficient
145
146 @param domain: domain on which the PDE uses the coefficient
147 @type domain: L{Domain<escript.Domain>}
148 @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
149 @type reducedEquationOrder: C{bool}
150 @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
151 @type reducedSolutionOrder: C{bool}
152 @return: L{FunctionSpace<escript.FunctionSpace>} of the coefficient
153 @rtype: L{FunctionSpace<escript.FunctionSpace>}
154 """
155 if self.what==self.INTERIOR:
156 return escript.Function(domain)
157 elif self.what==self.INTERIOR_REDUCED:
158 return escript.ReducedFunction(domain)
159 elif self.what==self.BOUNDARY:
160 return escript.FunctionOnBoundary(domain)
161 elif self.what==self.BOUNDARY_REDUCED:
162 return escript.ReducedFunctionOnBoundary(domain)
163 elif self.what==self.CONTACT:
164 return escript.FunctionOnContactZero(domain)
165 elif self.what==self.CONTACT_REDUCED:
166 return escript.ReducedFunctionOnContactZero(domain)
167 elif self.what==self.SOLUTION:
168 if reducedEquationOrder and reducedSolutionOrder:
169 return escript.ReducedSolution(domain)
170 else:
171 return escript.Solution(domain)
172 elif self.what==self.REDUCED:
173 return escript.ReducedSolution(domain)
174
175 def getValue(self):
176 """
177 returns the value of the coefficient
178
179 @return: value of the coefficient
180 @rtype: L{Data<escript.Data>}
181 """
182 return self.value
183
184 def setValue(self,domain,numEquations=1,numSolutions=1,reducedEquationOrder=False,reducedSolutionOrder=False,newValue=None):
185 """
186 set the value of the coefficient to a new value
187
188 @param domain: domain on which the PDE uses the coefficient
189 @type domain: L{Domain<escript.Domain>}
190 @param numEquations: number of equations of the PDE
191 @type numEquations: C{int}
192 @param numSolutions: number of components of the PDE solution
193 @type numSolutions: C{int}
194 @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
195 @type reducedEquationOrder: C{bool}
196 @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
197 @type reducedSolutionOrder: C{bool}
198 @param newValue: number of components of the PDE solution
199 @type newValue: any object that can be converted into a L{Data<escript.Data>} object with the appropriate shape and L{FunctionSpace<escript.FunctionSpace>}
200 @raise IllegalCoefficientValue: if the shape of the assigned value does not match the shape of the coefficient
201 @raise IllegalCoefficientFunctionSpace: if unable to interploate value to appropriate function space
202 """
203 if newValue==None:
204 newValue=escript.Data()
205 elif isinstance(newValue,escript.Data):
206 if not newValue.isEmpty():
207 if not newValue.getFunctionSpace() == self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder):
208 try:
209 newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
210 except:
211 raise IllegalCoefficientFunctionSpace,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)
212 else:
213 newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
214 if not newValue.isEmpty():
215 if not self.getShape(domain,numEquations,numSolutions)==newValue.getShape():
216 raise IllegalCoefficientValue,"Expected shape of coefficient is %s but actual shape is %s."%(self.getShape(domain,numEquations,numSolutions),newValue.getShape())
217 self.value=newValue
218
219 def isAlteringOperator(self):
220 """
221 checks if the coefficient alters the operator of the PDE
222
223 @return: True if the operator of the PDE is changed when the coefficient is changed
224 @rtype: C{bool}
225 """
226 if self.altering==self.OPERATOR or self.altering==self.BOTH:
227 return not None
228 else:
229 return None
230
231 def isAlteringRightHandSide(self):
232 """
233 checks if the coefficeint alters the right hand side of the PDE
234
235 @rtype: C{bool}
236 @return: True if the right hand side of the PDE is changed when the coefficient is changed
237 """
238 if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:
239 return not None
240 else:
241 return None
242
243 def estimateNumEquationsAndNumSolutions(self,domain,shape=()):
244 """
245 tries to estimate the number of equations and number of solutions if the coefficient has the given shape
246
247 @param domain: domain on which the PDE uses the coefficient
248 @type domain: L{Domain<escript.Domain>}
249 @param shape: suggested shape of the coefficient
250 @type shape: C{tuple} of C{int} values
251 @return: the number of equations and number of solutions of the PDE is the coefficient has shape s.
252 If no appropriate numbers could be identified, C{None} is returned
253 @rtype: C{tuple} of two C{int} values or C{None}
254 """
255 dim=domain.getDim()
256 if len(shape)>0:
257 num=max(shape)+1
258 else:
259 num=1
260 search=[]
261 if self.definesNumEquation() and self.definesNumSolutions():
262 for u in range(num):
263 for e in range(num):
264 search.append((e,u))
265 search.sort(self.__CompTuple2)
266 for item in search:
267 s=self.getShape(domain,item[0],item[1])
268 if len(s)==0 and len(shape)==0:
269 return (1,1)
270 else:
271 if s==shape: return item
272 elif self.definesNumEquation():
273 for e in range(num,0,-1):
274 s=self.getShape(domain,e,0)
275 if len(s)==0 and len(shape)==0:
276 return (1,None)
277 else:
278 if s==shape: return (e,None)
279
280 elif self.definesNumSolutions():
281 for u in range(num,0,-1):
282 s=self.getShape(domain,0,u)
283 if len(s)==0 and len(shape)==0:
284 return (None,1)
285 else:
286 if s==shape: return (None,u)
287 return None
288 def definesNumSolutions(self):
289 """
290 checks if the coefficient allows to estimate the number of solution components
291
292 @return: True if the coefficient allows an estimate of the number of solution components
293 @rtype: C{bool}
294 """
295 for i in self.pattern:
296 if i==self.BY_SOLUTION: return True
297 return False
298
299 def definesNumEquation(self):
300 """
301 checks if the coefficient allows to estimate the number of equations
302
303 @return: True if the coefficient allows an estimate of the number of equations
304 @rtype: C{bool}
305 """
306 for i in self.pattern:
307 if i==self.BY_EQUATION: return True
308 return False
309
310 def __CompTuple2(self,t1,t2):
311 """
312 Compare two tuples of possible number of equations and number of solutions
313
314 @param t1: The first tuple
315 @param t2: The second tuple
316
317 """
318
319 dif=t1[0]+t1[1]-(t2[0]+t2[1])
320 if dif<0: return 1
321 elif dif>0: return -1
322 else: return 0
323
324 def getShape(self,domain,numEquations=1,numSolutions=1):
325 """
326 builds the required shape of the coefficient
327
328 @param domain: domain on which the PDE uses the coefficient
329 @type domain: L{Domain<escript.Domain>}
330 @param numEquations: number of equations of the PDE
331 @type numEquations: C{int}
332 @param numSolutions: number of components of the PDE solution
333 @type numSolutions: C{int}
334 @return: shape of the coefficient
335 @rtype: C{tuple} of C{int} values
336 """
337 dim=domain.getDim()
338 s=()
339 for i in self.pattern:
340 if i==self.BY_EQUATION:
341 if numEquations>1: s=s+(numEquations,)
342 elif i==self.BY_SOLUTION:
343 if numSolutions>1: s=s+(numSolutions,)
344 else:
345 s=s+(dim,)
346 return s
347
348 class LinearPDE(object):
349 """
350 This class is used to define a general linear, steady, second order PDE
351 for an unknown function M{u} on a given domain defined through a L{Domain<escript.Domain>} object.
352
353 For a single PDE with a solution with a single component the linear PDE is defined in the following form:
354
355 M{-(grad(A[j,l]+A_reduced[j,l])*grad(u)[l]+(B[j]+B_reduced[j])u)[j]+(C[l]+C_reduced[l])*grad(u)[l]+(D+D_reduced)=-grad(X+X_reduced)[j,j]+(Y+Y_reduced)}
356
357
358 where M{grad(F)} denotes the spatial derivative of M{F}. Einstein's summation convention,
359 ie. summation over indexes appearing twice in a term of a sum is performed, is used.
360 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
361 L{Function<escript.Function>} and the coefficients M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced} and M{Y_reduced} have to be specified through L{Data<escript.Data>} objects in the
362 L{ReducedFunction<escript.ReducedFunction>}. It is also allowd to use objects that can be converted into
363 such L{Data<escript.Data>} objects. M{A} and M{A_reduced} are rank two, M{B_reduced}, M{C_reduced}, M{X_reduced}
364 M{B_reduced}, M{C_reduced} and M{X_reduced} are rank one and M{D}, M{D_reduced} and M{Y_reduced} are scalar.
365
366 The following natural boundary conditions are considered:
367
368 M{n[j]*((A[i,j]+A_reduced[i,j])*grad(u)[l]+(B+B_reduced)[j]*u)+(d+d_reduced)*u=n[j]*(X[j]+X_reduced[j])+y}
369
370 where M{n} is the outer normal field. Notice that the coefficients M{A}, M{A_reduced}, M{B}, M{B_reduced}, M{X} and M{X_reduced} are defined in the PDE. The coefficients M{d} and M{y} and are each a scalar in the L{FunctionOnBoundary<escript.FunctionOnBoundary>} and the coefficients M{d_reduced} and M{y_reduced} and are each a scalar in the L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
371
372
373 Constraints for the solution prescribing the value of the solution at certain locations in the domain. They have the form
374
375 M{u=r} where M{q>0}
376
377 M{r} and M{q} are each scalar where M{q} is the characteristic function defining where the constraint is applied.
378 The constraints override any other condition set by the PDE or the boundary condition.
379
380 The PDE is symmetrical if
381
382 M{A[i,j]=A[j,i]} and M{B[j]=C[j]} and M{A_reduced[i,j]=A_reduced[j,i]} and M{B_reduced[j]=C_reduced[j]}
383
384 For a system of PDEs and a solution with several components the PDE has the form
385
386 M{-grad((A[i,j,k,l]+A_reduced[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k])[j]+(C[i,k,l]+C_reduced[i,k,l])*grad(u[k])[l]+(D[i,k]+D_reduced[i,k]*u[k] =-grad(X[i,j]+X_reduced[i,j])[j]+Y[i]+Y_reduced[i] }
387
388 M{A} and M{A_reduced} are of rank four, M{B}, M{B_reduced}, M{C} and M{C_reduced} are each of rank three, M{D}, M{D_reduced}, M{X_reduced} and M{X} are each a rank two and M{Y} and M{Y_reduced} are of rank one.
389 The natural boundary conditions take the form:
390
391 M{n[j]*((A[i,j,k,l]+A_reduced[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k])+(d[i,k]+d_reduced[i,k])*u[k]=n[j]*(X[i,j]+X_reduced[i,j])+y[i]+y_reduced[i]}
392
393
394 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 and the coefficients M{d_reduced} is a rank two and M{y_reduced} is a rank one both in the L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
395
396 Constraints take the form
397
398 M{u[i]=r[i]} where M{q[i]>0}
399
400 M{r} and M{q} are each rank one. Notice that at some locations not necessarily all components must have a constraint.
401
402 The system of PDEs is symmetrical if
403
404 - M{A[i,j,k,l]=A[k,l,i,j]}
405 - M{A_reduced[i,j,k,l]=A_reduced[k,l,i,j]}
406 - M{B[i,j,k]=C[k,i,j]}
407 - M{B_reduced[i,j,k]=C_reduced[k,i,j]}
408 - M{D[i,k]=D[i,k]}
409 - M{D_reduced[i,k]=D_reduced[i,k]}
410 - M{d[i,k]=d[k,i]}
411 - M{d_reduced[i,k]=d_reduced[k,i]}
412
413 L{LinearPDE} also supports solution discontinuities over a contact region in the domain. To specify the conditions across the
414 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
415 defined as
416
417 M{J[i,j]=(A[i,j,k,l]+A_reduced[[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k]-X[i,j]-X_reduced[i,j]}
418
419 For the case of single solution component and single PDE M{J} is defined
420
421 M{J_{j}=(A[i,j]+A_reduced[i,j])*grad(u)[j]+(B[i]+B_reduced[i])*u-X[i]-X_reduced[i]}
422
423 In the context of discontinuities M{n} denotes the normal on the discontinuity pointing from side 0 towards side 1
424 calculated from L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnContactZero<escript.FunctionOnContactZero>}. For a system of PDEs
425 the contact condition takes the form
426
427 M{n[j]*J0[i,j]=n[j]*J1[i,j]=(y_contact[i]+y_contact_reduced[i])- (d_contact[i,k]+d_contact_reduced[i,k])*jump(u)[k]}
428
429 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
430 of the solution at side 1 and at side 0, denotes the jump of M{u} across discontinuity along the normal calcualted by
431 L{jump<util.jump>}.
432 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>}.
433 The coefficient M{d_contact_reduced} is a rank two and M{y_contact_reduced} is a rank one both in the L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>} or L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>}.
434 In case of a single PDE and a single component solution the contact condition takes the form
435
436 M{n[j]*J0_{j}=n[j]*J1_{j}=(y_contact+y_contact_reduced)-(d_contact+y_contact_reduced)*jump(u)}
437
438 In this case the coefficient M{d_contact} and M{y_contact} are each scalar both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>} and the coefficient M{d_contact_reduced} and M{y_contact_reduced} are each scalar both in the L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>} or L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>}
439
440 @cvar DEFAULT: The default method used to solve the system of linear equations
441 @cvar DIRECT: The direct solver based on LDU factorization
442 @cvar CHOLEVSKY: The direct solver based on LDLt factorization (can only be applied for symmetric PDEs)
443 @cvar PCG: The preconditioned conjugate gradient method (can only be applied for symmetric PDEs)
444 @cvar CR: The conjugate residual method
445 @cvar CGS: The conjugate gardient square method
446 @cvar BICGSTAB: The stabilized BiConjugate Gradient method.
447 @cvar SSOR: The symmetric overrealaxtion method
448 @cvar ILU0: The incomplete LU factorization preconditioner with no fill in
449 @cvar ILUT: The incomplete LU factorization preconditioner with will in
450 @cvar JACOBI: The Jacobi preconditioner
451 @cvar GMRES: The Gram-Schmidt minimum residual method
452 @cvar PRES20: Special GMRES with restart after 20 steps and truncation after 5 residuals
453 @cvar LUMPING: Matrix lumping.
454 @cvar NO_REORDERING: No matrix reordering allowed
455 @cvar MINIMUM_FILL_IN: Reorder matrix to reduce fill-in during factorization
456 @cvar NESTED_DISSECTION: Reorder matrix to improve load balancing during factorization
457 @cvar PASO: PASO solver package
458 @cvar SCSL: SGI SCSL solver library
459 @cvar MKL: Intel's MKL solver library
460 @cvar UMFPACK: the UMFPACK library
461 @cvar TRILINOS: the TRILINOS parallel solver class library from Sandia Natl Labs
462 @cvar ITERATIVE: The default iterative solver
463 @cvar AMG: algebraic multi grid
464 @cvar RILU: recursive ILU
465
466 """
467 DEFAULT= 0
468 DIRECT= 1
469 CHOLEVSKY= 2
470 PCG= 3
471 CR= 4
472 CGS= 5
473 BICGSTAB= 6
474 SSOR= 7
475 ILU0= 8
476 ILUT= 9
477 JACOBI= 10
478 GMRES= 11
479 PRES20= 12
480 LUMPING= 13
481 NO_REORDERING= 17
482 MINIMUM_FILL_IN= 18
483 NESTED_DISSECTION= 19
484 SCSL= 14
485 MKL= 15
486 UMFPACK= 16
487 ITERATIVE= 20
488 PASO= 21
489 AMG= 22
490 RILU = 23
491 TRILINOS = 24
492
493 SMALL_TOLERANCE=1.e-13
494 __PACKAGE_KEY="package"
495 __METHOD_KEY="method"
496 __SYMMETRY_KEY="symmetric"
497 __TOLERANCE_KEY="tolerance"
498 __PRECONDITIONER_KEY="preconditioner"
499
500
501 def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):
502 """
503 initializes a new linear PDE
504
505 @param domain: domain of the PDE
506 @type domain: L{Domain<escript.Domain>}
507 @param numEquations: number of equations. If numEquations==None the number of equations
508 is exracted from the PDE coefficients.
509 @param numSolutions: number of solution components. If numSolutions==None the number of solution components
510 is exracted from the PDE coefficients.
511 @param debug: if True debug informations are printed.
512
513 """
514 super(LinearPDE, self).__init__()
515 #
516 # the coefficients of the general PDE:
517 #
518 self.__COEFFICIENTS_OF_GENEARL_PDE={
519 "A" : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
520 "B" : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
521 "C" : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
522 "D" : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
523 "X" : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
524 "Y" : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
525 "d" : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
526 "y" : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
527 "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
528 "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
529 "A_reduced" : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
530 "B_reduced" : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
531 "C_reduced" : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
532 "D_reduced" : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
533 "X_reduced" : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
534 "Y_reduced" : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
535 "d_reduced" : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
536 "y_reduced" : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
537 "d_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
538 "y_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
539 "r" : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
540 "q" : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
541
542 # COEFFICIENTS can be overwritten by subclasses:
543 self.COEFFICIENTS=self.__COEFFICIENTS_OF_GENEARL_PDE
544 self.__altered_coefficients=False
545 # initialize attributes
546 self.__debug=debug
547 self.__domain=domain
548 self.__numEquations=numEquations
549 self.__numSolutions=numSolutions
550 self.__resetSystem()
551
552 # set some default values:
553 self.__reduce_equation_order=False
554 self.__reduce_solution_order=False
555 self.__tolerance=1.e-8
556 self.__solver_method=self.DEFAULT
557 self.__solver_package=self.DEFAULT
558 self.__preconditioner=self.DEFAULT
559 self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT,self.DEFAULT,False)
560 self.__sym=False
561
562 self.resetCoefficients()
563 self.trace("PDE Coeffients are %s"%str(self.COEFFICIENTS.keys()))
564 # =============================================================================
565 # general stuff:
566 # =============================================================================
567 def __str__(self):
568 """
569 returns string representation of the PDE
570
571 @return: a simple representation of the PDE
572 @rtype: C{str}
573 """
574 return "<LinearPDE %d>"%id(self)
575 # =============================================================================
576 # debug :
577 # =============================================================================
578 def setDebugOn(self):
579 """
580 switches on debugging
581 """
582 self.__debug=not None
583
584 def setDebugOff(self):
585 """
586 switches off debugging
587 """
588 self.__debug=None
589
590 def trace(self,text):
591 """
592 print the text message if debugging is swiched on.
593 @param text: message
594 @type text: C{string}
595 """
596 if self.__debug: print "%s: %s"%(str(self),text)
597
598 # =============================================================================
599 # some service functions:
600 # =============================================================================
601 def getDomain(self):
602 """
603 returns the domain of the PDE
604
605 @return: the domain of the PDE
606 @rtype: L{Domain<escript.Domain>}
607 """
608 return self.__domain
609
610 def getDim(self):
611 """
612 returns the spatial dimension of the PDE
613
614 @return: the spatial dimension of the PDE domain
615 @rtype: C{int}
616 """
617 return self.getDomain().getDim()
618
619 def getNumEquations(self):
620 """
621 returns the number of equations
622
623 @return: the number of equations
624 @rtype: C{int}
625 @raise UndefinedPDEError: if the number of equations is not be specified yet.
626 """
627 if self.__numEquations==None:
628 raise UndefinedPDEError,"Number of equations is undefined. Please specify argument numEquations."
629 else:
630 return self.__numEquations
631
632 def getNumSolutions(self):
633 """
634 returns the number of unknowns
635
636 @return: the number of unknowns
637 @rtype: C{int}
638 @raise UndefinedPDEError: if the number of unknowns is not be specified yet.
639 """
640 if self.__numSolutions==None:
641 raise UndefinedPDEError,"Number of solution is undefined. Please specify argument numSolutions."
642 else:
643 return self.__numSolutions
644
645 def reduceEquationOrder(self):
646 """
647 return status for order reduction for equation
648
649 @return: return True is reduced interpolation order is used for the represenation of the equation
650 @rtype: L{bool}
651 """
652 return self.__reduce_equation_order
653
654 def reduceSolutionOrder(self):
655 """
656 return status for order reduction for the solution
657
658 @return: return True is reduced interpolation order is used for the represenation of the solution
659 @rtype: L{bool}
660 """
661 return self.__reduce_solution_order
662
663 def getFunctionSpaceForEquation(self):
664 """
665 returns the L{FunctionSpace<escript.FunctionSpace>} used to discretize the equation
666
667 @return: representation space of equation
668 @rtype: L{FunctionSpace<escript.FunctionSpace>}
669 """
670 if self.reduceEquationOrder():
671 return escript.ReducedSolution(self.getDomain())
672 else:
673 return escript.Solution(self.getDomain())
674
675 def getFunctionSpaceForSolution(self):
676 """
677 returns the L{FunctionSpace<escript.FunctionSpace>} used to represent the solution
678
679 @return: representation space of solution
680 @rtype: L{FunctionSpace<escript.FunctionSpace>}
681 """
682 if self.reduceSolutionOrder():
683 return escript.ReducedSolution(self.getDomain())
684 else:
685 return escript.Solution(self.getDomain())
686
687
688 def getOperator(self):
689 """
690 provides access to the operator of the PDE
691
692 @return: the operator of the PDE
693 @rtype: L{Operator<escript.Operator>}
694 """
695 m=self.getSystem()[0]
696 if self.isUsingLumping():
697 return self.copyConstraint(1./m)
698 else:
699 return m
700
701 def getRightHandSide(self):
702 """
703 provides access to the right hand side of the PDE
704 @return: the right hand side of the PDE
705 @rtype: L{Data<escript.Data>}
706 """
707 r=self.getSystem()[1]
708 if self.isUsingLumping():
709 return self.copyConstraint(r)
710 else:
711 return r
712
713 def applyOperator(self,u=None):
714 """
715 applies the operator of the PDE to a given u or the solution of PDE if u is not present.
716
717 @param u: argument of the operator. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
718 the current solution is used.
719 @type u: L{Data<escript.Data>} or None
720 @return: image of u
721 @rtype: L{Data<escript.Data>}
722 """
723 if u==None:
724 return self.getOperator()*self.getSolution()
725 else:
726 return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
727
728 def getResidual(self,u=None):
729 """
730 return the residual of u or the current solution if u is not present.
731
732 @param u: argument in the residual calculation. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
733 the current solution is used.
734 @type u: L{Data<escript.Data>} or None
735 @return: residual of u
736 @rtype: L{Data<escript.Data>}
737 """
738 return self.applyOperator(u)-self.getRightHandSide()
739
740 def checkSymmetry(self,verbose=True):
741 """
742 test the PDE for symmetry.
743
744 @param verbose: if equal to True or not present a report on coefficients which are breaking the symmetry is printed.
745 @type verbose: C{bool}
746 @return: True if the PDE is symmetric.
747 @rtype: L{Data<escript.Data>}
748 @note: This is a very expensive operation. It should be used for degugging only! The symmetry flag is not altered.
749 """
750 verbose=verbose or self.__debug
751 out=True
752 if self.getNumSolutions()!=self.getNumEquations():
753 if verbose: print "non-symmetric PDE because of different number of equations and solutions"
754 out=False
755 else:
756 A=self.getCoefficientOfGeneralPDE("A")
757 if not A.isEmpty():
758 tol=util.Lsup(A)*self.SMALL_TOLERANCE
759 if self.getNumSolutions()>1:
760 for i in range(self.getNumEquations()):
761 for j in range(self.getDim()):
762 for k in range(self.getNumSolutions()):
763 for l in range(self.getDim()):
764 if util.Lsup(A[i,j,k,l]-A[k,l,i,j])>tol:
765 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)
766 out=False
767 else:
768 for j in range(self.getDim()):
769 for l in range(self.getDim()):
770 if util.Lsup(A[j,l]-A[l,j])>tol:
771 if verbose: print "non-symmetric PDE because A[%d,%d]!=A[%d,%d]"%(j,l,l,j)
772 out=False
773 B=self.getCoefficientOfGeneralPDE("B")
774 C=self.getCoefficientOfGeneralPDE("C")
775 if B.isEmpty() and not C.isEmpty():
776 if verbose: print "non-symmetric PDE because B is not present but C is"
777 out=False
778 elif not B.isEmpty() and C.isEmpty():
779 if verbose: print "non-symmetric PDE because C is not present but B is"
780 out=False
781 elif not B.isEmpty() and not C.isEmpty():
782 tol=(util.Lsup(B)+util.Lsup(C))*self.SMALL_TOLERANCE/2.
783 if self.getNumSolutions()>1:
784 for i in range(self.getNumEquations()):
785 for j in range(self.getDim()):
786 for k in range(self.getNumSolutions()):
787 if util.Lsup(B[i,j,k]-C[k,i,j])>tol:
788 if verbose: print "non-symmetric PDE because B[%d,%d,%d]!=C[%d,%d,%d]"%(i,j,k,k,i,j)
789 out=False
790 else:
791 for j in range(self.getDim()):
792 if util.Lsup(B[j]-C[j])>tol:
793 if verbose: print "non-symmetric PDE because B[%d]!=C[%d]"%(j,j)
794 out=False
795 if self.getNumSolutions()>1:
796 D=self.getCoefficientOfGeneralPDE("D")
797 if not D.isEmpty():
798 tol=util.Lsup(D)*self.SMALL_TOLERANCE
799 for i in range(self.getNumEquations()):
800 for k in range(self.getNumSolutions()):
801 if util.Lsup(D[i,k]-D[k,i])>tol:
802 if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)
803 out=False
804 d=self.getCoefficientOfGeneralPDE("d")
805 if not d.isEmpty():
806 tol=util.Lsup(d)*self.SMALL_TOLERANCE
807 for i in range(self.getNumEquations()):
808 for k in range(self.getNumSolutions()):
809 if util.Lsup(d[i,k]-d[k,i])>tol:
810 if verbose: print "non-symmetric PDE because d[%d,%d]!=d[%d,%d]"%(i,k,k,i)
811 out=False
812 d_contact=self.getCoefficientOfGeneralPDE("d_contact")
813 if not d_contact.isEmpty():
814 tol=util.Lsup(d_contact)*self.SMALL_TOLERANCE
815 for i in range(self.getNumEquations()):
816 for k in range(self.getNumSolutions()):
817 if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
818 if verbose: print "non-symmetric PDE because d_contact[%d,%d]!=d_contact[%d,%d]"%(i,k,k,i)
819 out=False
820 # and now the reduced coefficients
821 A_reduced=self.getCoefficientOfGeneralPDE("A_reduced")
822 if not A_reduced.isEmpty():
823 tol=util.Lsup(A_reduced)*self.SMALL_TOLERANCE
824 if self.getNumSolutions()>1:
825 for i in range(self.getNumEquations()):
826 for j in range(self.getDim()):
827 for k in range(self.getNumSolutions()):
828 for l in range(self.getDim()):
829 if util.Lsup(A_reduced[i,j,k,l]-A_reduced[k,l,i,j])>tol:
830 if verbose: print "non-symmetric PDE because A_reduced[%d,%d,%d,%d]!=A_reduced[%d,%d,%d,%d]"%(i,j,k,l,k,l,i,j)
831 out=False
832 else:
833 for j in range(self.getDim()):
834 for l in range(self.getDim()):
835 if util.Lsup(A_reduced[j,l]-A_reduced[l,j])>tol:
836 if verbose: print "non-symmetric PDE because A_reduced[%d,%d]!=A_reduced[%d,%d]"%(j,l,l,j)
837 out=False
838 B_reduced=self.getCoefficientOfGeneralPDE("B_reduced")
839 C_reduced=self.getCoefficientOfGeneralPDE("C_reduced")
840 if B_reduced.isEmpty() and not C_reduced.isEmpty():
841 if verbose: print "non-symmetric PDE because B_reduced is not present but C_reduced is"
842 out=False
843 elif not B_reduced.isEmpty() and C_reduced.isEmpty():
844 if verbose: print "non-symmetric PDE because C_reduced is not present but B_reduced is"
845 out=False
846 elif not B_reduced.isEmpty() and not C_reduced.isEmpty():
847 tol=(util.Lsup(B_reduced)+util.Lsup(C_reduced))*self.SMALL_TOLERANCE/2.
848 if self.getNumSolutions()>1:
849 for i in range(self.getNumEquations()):
850 for j in range(self.getDim()):
851 for k in range(self.getNumSolutions()):
852 if util.Lsup(B_reduced[i,j,k]-C_reduced[k,i,j])>tol:
853 if verbose: print "non-symmetric PDE because B_reduced[%d,%d,%d]!=C_reduced[%d,%d,%d]"%(i,j,k,k,i,j)
854 out=False
855 else:
856 for j in range(self.getDim()):
857 if util.Lsup(B_reduced[j]-C_reduced[j])>tol:
858 if verbose: print "non-symmetric PDE because B_reduced[%d]!=C_reduced[%d]"%(j,j)
859 out=False
860 if self.getNumSolutions()>1:
861 D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
862 if not D_reduced.isEmpty():
863 tol=util.Lsup(D_reduced)*self.SMALL_TOLERANCE
864 for i in range(self.getNumEquations()):
865 for k in range(self.getNumSolutions()):
866 if util.Lsup(D_reduced[i,k]-D_reduced[k,i])>tol:
867 if verbose: print "non-symmetric PDE because D_reduced[%d,%d]!=D_reduced[%d,%d]"%(i,k,k,i)
868 out=False
869 d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
870 if not d_reduced.isEmpty():
871 tol=util.Lsup(d_reduced)*self.SMALL_TOLERANCE
872 for i in range(self.getNumEquations()):
873 for k in range(self.getNumSolutions()):
874 if util.Lsup(d_reduced[i,k]-d_reduced[k,i])>tol:
875 if verbose: print "non-symmetric PDE because d_reduced[%d,%d]!=d_reduced[%d,%d]"%(i,k,k,i)
876 out=False
877 d_contact_reduced=self.getCoefficientOfGeneralPDE("d_contact_reduced")
878 if not d_contact_reduced.isEmpty():
879 tol=util.Lsup(d_contact_reduced)*self.SMALL_TOLERANCE
880 for i in range(self.getNumEquations()):
881 for k in range(self.getNumSolutions()):
882 if util.Lsup(d_contact_reduced[i,k]-d_contact_reduced[k,i])>tol:
883 if verbose: print "non-symmetric PDE because d_contact_reduced[%d,%d]!=d_contact_reduced[%d,%d]"%(i,k,k,i)
884 out=False
885 return out
886
887 def getSolution(self,**options):
888 """
889 returns the solution of the PDE. If the solution is not valid the PDE is solved.
890
891 @return: the solution
892 @rtype: L{Data<escript.Data>}
893 @param options: solver options
894 @keyword verbose: True to get some information during PDE solution
895 @type verbose: C{bool}
896 @keyword reordering: reordering scheme to be used during elimination. Allowed values are
897 L{NO_REORDERING}, L{MINIMUM_FILL_IN}, L{NESTED_DISSECTION}
898 @keyword iter_max: maximum number of iteration steps allowed.
899 @keyword drop_tolerance: threshold for drupping in L{ILUT}
900 @keyword drop_storage: maximum of allowed memory in L{ILUT}
901 @keyword truncation: maximum number of residuals in L{GMRES}
902 @keyword restart: restart cycle length in L{GMRES}
903 """
904 if not self.__solution_isValid:
905 mat,f=self.getSystem()
906 if self.isUsingLumping():
907 self.__solution=self.copyConstraint(f*mat)
908 else:
909 options[self.__TOLERANCE_KEY]=self.getTolerance()
910 options[self.__METHOD_KEY]=self.getSolverMethod()[0]
911 options[self.__PRECONDITIONER_KEY]=self.getSolverMethod()[1]
912 options[self.__PACKAGE_KEY]=self.getSolverPackage()
913 options[self.__SYMMETRY_KEY]=self.isSymmetric()
914 self.trace("PDE is resolved.")
915 self.trace("solver options: %s"%str(options))
916 self.__solution=mat.solve(f,options)
917 self.__solution_isValid=True
918 return self.__solution
919
920 def getFlux(self,u=None):
921 """
922 returns the flux M{J} for a given M{u}
923
924 M{J[i,j]=(A[i,j,k,l]+A_reduced[A[i,j,k,l]]*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])u[k]-X[i,j]-X_reduced[i,j]}
925
926 or
927
928 M{J[j]=(A[i,j]+A_reduced[i,j])*grad(u)[l]+(B[j]+B_reduced[j])u-X[j]-X_reduced[j]}
929
930 @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.
931 @type u: L{Data<escript.Data>} or None
932 @return: flux
933 @rtype: L{Data<escript.Data>}
934 """
935 if u==None: u=self.getSolution()
936 return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u,Funtion(self.getDomain))) \
937 +util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u) \
938 -util.self.getCoefficientOfGeneralPDE("X") \
939 +util.tensormult(self.getCoefficientOfGeneralPDE("A_reduced"),util.grad(u,ReducedFuntion(self.getDomain))) \
940 +util.matrixmult(self.getCoefficientOfGeneralPDE("B_reduced"),u) \
941 -util.self.getCoefficientOfGeneralPDE("X_reduced")
942 # =============================================================================
943 # solver settings:
944 # =============================================================================
945 def setSolverMethod(self,solver=None,preconditioner=None):
946 """
947 sets a new solver
948
949 @param solver: sets a new solver method.
950 @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}, L{AMG}
951 @param preconditioner: sets a new solver method.
952 @type preconditioner: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}, L{RILU}
953 """
954 if solver==None: solver=self.__solver_method
955 if preconditioner==None: preconditioner=self.__preconditioner
956 if solver==None: solver=self.DEFAULT
957 if preconditioner==None: preconditioner=self.DEFAULT
958 if not (solver,preconditioner)==self.getSolverMethod():
959 self.__solver_method=solver
960 self.__preconditioner=preconditioner
961 self.__checkMatrixType()
962 self.trace("New solver is %s"%self.getSolverMethodName())
963
964 def getSolverMethodName(self):
965 """
966 returns the name of the solver currently used
967
968 @return: the name of the solver currently used.
969 @rtype: C{string}
970 """
971
972 m=self.getSolverMethod()
973 p=self.getSolverPackage()
974 method=""
975 if m[0]==self.DEFAULT: method="DEFAULT"
976 elif m[0]==self.DIRECT: method= "DIRECT"
977 elif m[0]==self.ITERATIVE: method= "ITERATIVE"
978 elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
979 elif m[0]==self.PCG: method= "PCG"
980 elif m[0]==self.CR: method= "CR"
981 elif m[0]==self.CGS: method= "CGS"
982 elif m[0]==self.BICGSTAB: method= "BICGSTAB"
983 elif m[0]==self.SSOR: method= "SSOR"
984 elif m[0]==self.GMRES: method= "GMRES"
985 elif m[0]==self.PRES20: method= "PRES20"
986 elif m[0]==self.LUMPING: method= "LUMPING"
987 elif m[0]==self.AMG: method= "AMG"
988 if m[1]==self.DEFAULT: method+="+DEFAULT"
989 elif m[1]==self.JACOBI: method+= "+JACOBI"
990 elif m[1]==self.ILU0: method+= "+ILU0"
991 elif m[1]==self.ILUT: method+= "+ILUT"
992 elif m[1]==self.SSOR: method+= "+SSOR"
993 elif m[1]==self.AMG: method+= "+AMG"
994 elif m[1]==self.RILU: method+= "+RILU"
995 if p==self.DEFAULT: package="DEFAULT"
996 elif p==self.PASO: package= "PASO"
997 elif p==self.MKL: package= "MKL"
998 elif p==self.SCSL: package= "SCSL"
999 elif p==self.UMFPACK: package= "UMFPACK"
1000 elif p==self.TRILINOS: package= "TRILINOS"
1001 else : method="unknown"
1002 return "%s solver of %s package"%(method,package)
1003
1004
1005 def getSolverMethod(self):
1006 """
1007 returns the solver method
1008
1009 @return: the solver method currently be used.
1010 @rtype: C{int}
1011 """
1012 return self.__solver_method,self.__preconditioner
1013
1014 def setSolverPackage(self,package=None):
1015 """
1016 sets a new solver package
1017
1018 @param package: sets a new solver method.
1019 @type package: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMFPACK}, L{TRILINOS}
1020 """
1021 if package==None: package=self.DEFAULT
1022 if not package==self.getSolverPackage():
1023 self.__solver_package=package
1024 self.__checkMatrixType()
1025 self.trace("New solver is %s"%self.getSolverMethodName())
1026
1027 def getSolverPackage(self):
1028 """
1029 returns the package of the solver
1030
1031 @return: the solver package currently being used.
1032 @rtype: C{int}
1033 """
1034 return self.__solver_package
1035
1036 def isUsingLumping(self):
1037 """
1038 checks if matrix lumping is used a solver method
1039
1040 @return: True is lumping is currently used a solver method.
1041 @rtype: C{bool}
1042 """
1043 return self.getSolverMethod()[0]==self.LUMPING
1044
1045 def setTolerance(self,tol=1.e-8):
1046 """
1047 resets the tolerance for the solver method to tol where for an appropriate norm M{|.|}
1048
1049 M{|L{getResidual}()|<tol*|L{getRightHandSide}()|}
1050
1051 defines the stopping criterion.
1052
1053 @param tol: new tolerance for the solver. If the tol is lower then the current tolerence
1054 the system will be resolved.
1055 @type tol: positive C{float}
1056 @raise ValueError: if tolerance is not positive.
1057 """
1058 if not tol>0:
1059 raise ValueError,"Tolerance as to be positive"
1060 if tol<self.getTolerance(): self.__invalidateSolution()
1061 self.trace("New tolerance %e"%tol)
1062 self.__tolerance=tol
1063 return
1064
1065 def getTolerance(self):
1066 """
1067 returns the tolerance set for the solution
1068
1069 @return: tolerance currently used.
1070 @rtype: C{float}
1071 """
1072 return self.__tolerance
1073
1074 # =============================================================================
1075 # symmetry flag:
1076 # =============================================================================
1077 def isSymmetric(self):
1078 """
1079 checks if symmetry is indicated.
1080
1081 @return: True is a symmetric PDE is indicated, otherwise False is returned
1082 @rtype: C{bool}
1083 """
1084 return self.__sym
1085
1086 def setSymmetryOn(self):
1087 """
1088 sets the symmetry flag.
1089 """
1090 if not self.isSymmetric():
1091 self.trace("PDE is set to be symmetric")
1092 self.__sym=True
1093 self.__checkMatrixType()
1094
1095 def setSymmetryOff(self):
1096 """
1097 removes the symmetry flag.
1098 """
1099 if self.isSymmetric():
1100 self.trace("PDE is set to be unsymmetric")
1101 self.__sym=False
1102 self.__checkMatrixType()
1103
1104 def setSymmetryTo(self,flag=False):
1105 """
1106 sets the symmetry flag to flag
1107
1108 @param flag: If flag, the symmetry flag is set otherwise the symmetry flag is released.
1109 @type flag: C{bool}
1110 """
1111 if flag:
1112 self.setSymmetryOn()
1113 else:
1114 self.setSymmetryOff()
1115
1116 # =============================================================================
1117 # function space handling for the equation as well as the solution
1118 # =============================================================================
1119 def setReducedOrderOn(self):
1120 """
1121 switches on reduced order for solution and equation representation
1122
1123 @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1124 """
1125 self.setReducedOrderForSolutionOn()
1126 self.setReducedOrderForEquationOn()
1127
1128 def setReducedOrderOff(self):
1129 """
1130 switches off reduced order for solution and equation representation
1131
1132 @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1133 """
1134 self.setReducedOrderForSolutionOff()
1135 self.setReducedOrderForEquationOff()
1136
1137 def setReducedOrderTo(self,flag=False):
1138 """
1139 sets order reduction for both solution and equation representation according to flag.
1140 @param flag: if flag is True, the order reduction is switched on for both solution and equation representation, otherwise or
1141 if flag is not present order reduction is switched off
1142 @type flag: C{bool}
1143 @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1144 """
1145 self.setReducedOrderForSolutionTo(flag)
1146 self.setReducedOrderForEquationTo(flag)
1147
1148
1149 def setReducedOrderForSolutionOn(self):
1150 """
1151 switches on reduced order for solution representation
1152
1153 @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1154 """
1155 if not self.__reduce_solution_order:
1156 if self.__altered_coefficients:
1157 raise RuntimeError,"order cannot be altered after coefficients have been defined."
1158 self.trace("Reduced order is used to solution representation.")
1159 self.__reduce_solution_order=True
1160 self.__resetSystem()
1161
1162 def setReducedOrderForSolutionOff(self):
1163 """
1164 switches off reduced order for solution representation
1165
1166 @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1167 """
1168 if self.__reduce_solution_order:
1169 if self.__altered_coefficients:
1170 raise RuntimeError,"order cannot be altered after coefficients have been defined."
1171 self.trace("Full order is used to interpolate solution.")
1172 self.__reduce_solution_order=False
1173 self.__resetSystem()
1174
1175 def setReducedOrderForSolutionTo(self,flag=False):
1176 """
1177 sets order for test functions according to flag
1178
1179 @param flag: if flag is True, the order reduction is switched on for solution representation, otherwise or
1180 if flag is not present order reduction is switched off
1181 @type flag: C{bool}
1182 @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1183 """
1184 if flag:
1185 self.setReducedOrderForSolutionOn()
1186 else:
1187 self.setReducedOrderForSolutionOff()
1188
1189 def setReducedOrderForEquationOn(self):
1190 """
1191 switches on reduced order for equation representation
1192
1193 @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1194 """
1195 if not self.__reduce_equation_order:
1196 if self.__altered_coefficients:
1197 raise RuntimeError,"order cannot be altered after coefficients have been defined."
1198 self.trace("Reduced order is used for test functions.")
1199 self.__reduce_equation_order=True
1200 self.__resetSystem()
1201
1202 def setReducedOrderForEquationOff(self):
1203 """
1204 switches off reduced order for equation representation
1205
1206 @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1207 """
1208 if self.__reduce_equation_order:
1209 if self.__altered_coefficients:
1210 raise RuntimeError,"order cannot be altered after coefficients have been defined."
1211 self.trace("Full order is used for test functions.")
1212 self.__reduce_equation_order=False
1213 self.__resetSystem()
1214
1215 def setReducedOrderForEquationTo(self,flag=False):
1216 """
1217 sets order for test functions according to flag
1218
1219 @param flag: if flag is True, the order reduction is switched on for equation representation, otherwise or
1220 if flag is not present order reduction is switched off
1221 @type flag: C{bool}
1222 @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1223 """
1224 if flag:
1225 self.setReducedOrderForEquationOn()
1226 else:
1227 self.setReducedOrderForEquationOff()
1228
1229 # =============================================================================
1230 # private method:
1231 # =============================================================================
1232 def __checkMatrixType(self):
1233 """
1234 reassess the matrix type and, if a new matrix is needed, resets the system.
1235 """
1236 new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod()[0],self.getSolverPackage(),self.isSymmetric())
1237 if not new_matrix_type==self.__matrix_type:
1238 self.trace("Matrix type is now %d."%new_matrix_type)
1239 self.__matrix_type=new_matrix_type
1240 self.__resetSystem()
1241 #
1242 # rebuild switches :
1243 #
1244 def __invalidateSolution(self):
1245 """
1246 indicates the PDE has to be resolved if the solution is requested
1247 """
1248 if self.__solution_isValid: self.trace("PDE has to be resolved.")
1249 self.__solution_isValid=False
1250
1251 def __invalidateOperator(self):
1252 """
1253 indicates the operator has to be rebuilt next time it is used
1254 """
1255 if self.__operator_is_Valid: self.trace("Operator has to be rebuilt.")
1256 self.__invalidateSolution()
1257 self.__operator_is_Valid=False
1258
1259 def __invalidateRightHandSide(self):
1260 """
1261 indicates the right hand side has to be rebuild next time it is used
1262 """
1263 if self.__righthandside_isValid: self.trace("Right hand side has to be rebuilt.")
1264 self.__invalidateSolution()
1265 self.__righthandside_isValid=False
1266
1267 def __invalidateSystem(self):
1268 """
1269 annonced that everthing has to be rebuild:
1270 """
1271 if self.__righthandside_isValid: self.trace("System has to be rebuilt.")
1272 self.__invalidateSolution()
1273 self.__invalidateOperator()
1274 self.__invalidateRightHandSide()
1275
1276 def __resetSystem(self):
1277 """
1278 annonced that everthing has to be rebuild:
1279 """
1280 self.trace("New System is built from scratch.")
1281 self.__operator=escript.Operator()
1282 self.__operator_is_Valid=False
1283 self.__righthandside=escript.Data()
1284 self.__righthandside_isValid=False
1285 self.__solution=escript.Data()
1286 self.__solution_isValid=False
1287 #
1288 # system initialization:
1289 #
1290 def __getNewOperator(self):
1291 """
1292 returns an instance of a new operator
1293 """
1294 self.trace("New operator is allocated.")
1295 return self.getDomain().newOperator( \
1296 self.getNumEquations(), \
1297 self.getFunctionSpaceForEquation(), \
1298 self.getNumSolutions(), \
1299 self.getFunctionSpaceForSolution(), \
1300 self.__matrix_type)
1301
1302 def __getNewRightHandSide(self):
1303 """
1304 returns an instance of a new right hand side
1305 """
1306 self.trace("New right hand side is allocated.")
1307 if self.getNumEquations()>1:
1308 return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)
1309 else:
1310 return escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)
1311
1312 def __getNewSolution(self):
1313 """
1314 returns an instance of a new solution
1315 """
1316 self.trace("New solution is allocated.")
1317 if self.getNumSolutions()>1:
1318 return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)
1319 else:
1320 return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)
1321
1322 def __makeFreshSolution(self):
1323 """
1324 makes sure that the solution is instantiated and returns it initialized by zeros
1325 """
1326 if self.__solution.isEmpty():
1327 self.__solution=self.__getNewSolution()
1328 else:
1329 self.__solution*=0
1330 self.trace("Solution is reset to zero.")
1331 return self.__solution
1332
1333 def __makeFreshRightHandSide(self):
1334 """
1335 makes sure that the right hand side is instantiated and returns it initialized by zeros
1336 """
1337 if self.__righthandside.isEmpty():
1338 self.__righthandside=self.__getNewRightHandSide()
1339 else:
1340 self.__righthandside.setToZero()
1341 self.trace("Right hand side is reset to zero.")
1342 return self.__righthandside
1343
1344 def __makeFreshOperator(self):
1345 """
1346 makes sure that the operator is instantiated and returns it initialized by zeros
1347 """
1348 if self.__operator.isEmpty():
1349 self.__operator=self.__getNewOperator()
1350 else:
1351 self.__operator.resetValues()
1352 self.trace("Operator reset to zero")
1353 return self.__operator
1354
1355 def __applyConstraint(self):
1356 """
1357 applies the constraints defined by q and r to the system
1358 """
1359 if not self.isUsingLumping():
1360 q=self.getCoefficientOfGeneralPDE("q")
1361 r=self.getCoefficientOfGeneralPDE("r")
1362 if not q.isEmpty() and not self.__operator.isEmpty():
1363 # q is the row and column mask to indicate where constraints are set:
1364 row_q=escript.Data(q,self.getFunctionSpaceForEquation())
1365 col_q=escript.Data(q,self.getFunctionSpaceForSolution())
1366 u=self.__getNewSolution()
1367 if r.isEmpty():
1368 r_s=self.__getNewSolution()
1369 else:
1370 r_s=escript.Data(r,self.getFunctionSpaceForSolution())
1371 u.copyWithMask(r_s,col_q)
1372 if not self.__righthandside.isEmpty():
1373 self.__righthandside-=self.__operator*u
1374 self.__righthandside=self.copyConstraint(self.__righthandside)
1375 self.__operator.nullifyRowsAndCols(row_q,col_q,1.)
1376 # =============================================================================
1377 # function giving access to coefficients of the general PDE:
1378 # =============================================================================
1379 def getCoefficientOfGeneralPDE(self,name):
1380 """
1381 return the value of the coefficient name of the general PDE.
1382
1383 @note: This method is called by the assembling routine it can be overwritten
1384 to map coefficients of a particular PDE to the general PDE.
1385 @param name: name of the coefficient requested.
1386 @type name: C{string}
1387 @return: the value of the coefficient name
1388 @rtype: L{Data<escript.Data>}
1389 @raise IllegalCoefficient: if name is not one of coefficients
1390 M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1391 M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1392 """
1393 if self.hasCoefficientOfGeneralPDE(name):
1394 return self.getCoefficient(name)
1395 else:
1396 raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1397
1398 def hasCoefficientOfGeneralPDE(self,name):
1399 """
1400 checks if name is a the name of a coefficient of the general PDE.
1401
1402 @param name: name of the coefficient enquired.
1403 @type name: C{string}
1404 @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1405 @rtype: C{bool}
1406
1407 """
1408 return self.__COEFFICIENTS_OF_GENEARL_PDE.has_key(name)
1409
1410 def createCoefficientOfGeneralPDE(self,name):
1411 """
1412 returns a new instance of a coefficient for coefficient name of the general PDE
1413
1414 @param name: name of the coefficient requested.
1415 @type name: C{string}
1416 @return: a coefficient name initialized to 0.
1417 @rtype: L{Data<escript.Data>}
1418 @raise IllegalCoefficient: if name is not one of coefficients
1419 M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1420 M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1421 """
1422 if self.hasCoefficientOfGeneralPDE(name):
1423 return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
1424 else:
1425 raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1426
1427 def getFunctionSpaceForCoefficientOfGeneralPDE(self,name):
1428 """
1429 return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name of the general PDE
1430
1431 @param name: name of the coefficient enquired.
1432 @type name: C{string}
1433 @return: the function space to be used for coefficient name
1434 @rtype: L{FunctionSpace<escript.FunctionSpace>}
1435 @raise IllegalCoefficient: if name is not one of coefficients
1436 M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1437 M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1438 """
1439 if self.hasCoefficientOfGeneralPDE(name):
1440 return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
1441 else:
1442 raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1443
1444 def getShapeOfCoefficientOfGeneralPDE(self,name):
1445 """
1446 return the shape of the coefficient name of the general PDE
1447
1448 @param name: name of the coefficient enquired.
1449 @type name: C{string}
1450 @return: the shape of the coefficient name
1451 @rtype: C{tuple} of C{int}
1452 @raise IllegalCoefficient: if name is not one of coefficients
1453 M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1454 M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1455 """
1456 if self.hasCoefficientOfGeneralPDE(name):
1457 return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1458 else:
1459 raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1460
1461 # =============================================================================
1462 # functions giving access to coefficients of a particular PDE implementation:
1463 # =============================================================================
1464 def getCoefficient(self,name):
1465 """
1466 returns the value of the coefficient name
1467
1468 @param name: name of the coefficient requested.
1469 @type name: C{string}
1470 @return: the value of the coefficient name
1471 @rtype: L{Data<escript.Data>}
1472 @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1473 """
1474 if self.hasCoefficient(name):
1475 return self.COEFFICIENTS[name].getValue()
1476 else:
1477 raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1478
1479 def hasCoefficient(self,name):
1480 """
1481 return True if name is the name of a coefficient
1482
1483 @param name: name of the coefficient enquired.
1484 @type name: C{string}
1485 @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1486 @rtype: C{bool}
1487 """
1488 return self.COEFFICIENTS.has_key(name)
1489
1490 def createCoefficient(self, name):
1491 """
1492 create a L{Data<escript.Data>} object corresponding to coefficient name
1493
1494 @return: a coefficient name initialized to 0.
1495 @rtype: L{Data<escript.Data>}
1496 @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1497 """
1498 if self.hasCoefficient(name):
1499 return escript.Data(0.,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))
1500 else:
1501 raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1502
1503 def getFunctionSpaceForCoefficient(self,name):
1504 """
1505 return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name
1506
1507 @param name: name of the coefficient enquired.
1508 @type name: C{string}
1509 @return: the function space to be used for coefficient name
1510 @rtype: L{FunctionSpace<escript.FunctionSpace>}
1511 @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1512 """
1513 if self.hasCoefficient(name):
1514 return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())
1515 else:
1516 raise ValueError,"unknown coefficient %s requested"%name
1517 def getShapeOfCoefficient(self,name):
1518 """
1519 return the shape of the coefficient name
1520
1521 @param name: name of the coefficient enquired.
1522 @type name: C{string}
1523 @return: the shape of the coefficient name
1524 @rtype: C{tuple} of C{int}
1525 @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1526 """
1527 if self.hasCoefficient(name):
1528 return self.COEFFICIENTS[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1529 else:
1530 raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1531
1532 def resetCoefficients(self):
1533 """
1534 resets all coefficients to there default values.
1535 """
1536 for i in self.COEFFICIENTS.iterkeys():
1537 self.COEFFICIENTS[i].resetValue()
1538
1539 def alteredCoefficient(self,name):
1540 """
1541 announce that coefficient name has been changed
1542
1543 @param name: name of the coefficient enquired.
1544 @type name: C{string}
1545 @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1546 @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.
1547 """
1548 if self.hasCoefficient(name):
1549 self.trace("Coefficient %s has been altered."%name)
1550 if not ((name=="q" or name=="r") and self.isUsingLumping()):
1551 if self.COEFFICIENTS[name].isAlteringOperator(): self.__invalidateOperator()
1552 if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__invalidateRightHandSide()
1553 else:
1554 raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1555
1556 def copyConstraint(self,u):
1557 """
1558 copies the constraint into u and returns u.
1559
1560 @param u: a function of rank 0 is a single PDE is solved and of shape (numSolution,) for a system of PDEs
1561 @type u: L{Data<escript.Data>}
1562 @return: the input u modified by the constraints.
1563 @rtype: L{Data<escript.Data>}
1564 @warning: u is altered if it has the appropriate L{FunctionSpace<escript.FunctionSpace>}
1565 """
1566 q=self.getCoefficientOfGeneralPDE("q")
1567 r=self.getCoefficientOfGeneralPDE("r")
1568 if not q.isEmpty():
1569 if u.isEmpty(): u=escript.Data(0.,q.getShape(),q.getFunctionSpace())
1570 if r.isEmpty():
1571 r=escript.Data(0,u.getShape(),u.getFunctionSpace())
1572 else:
1573 r=escript.Data(r,u.getFunctionSpace())
1574 u.copyWithMask(r,escript.Data(q,u.getFunctionSpace()))
1575 return u
1576
1577 def setValue(self,**coefficients):
1578 """
1579 sets new values to coefficients
1580
1581 @param coefficients: new values assigned to coefficients
1582 @keyword A: value for coefficient A.
1583 @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1584 @keyword A_reduced: value for coefficient A_reduced.
1585 @type A_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1586 @keyword B: value for coefficient B
1587 @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1588 @keyword B_reduced: value for coefficient B_reduced
1589 @type B_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1590 @keyword C: value for coefficient C
1591 @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1592 @keyword C_reduced: value for coefficient C_reduced
1593 @type C_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1594 @keyword D: value for coefficient D
1595 @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1596 @keyword D_reduced: value for coefficient D_reduced
1597 @type D_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1598 @keyword X: value for coefficient X
1599 @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1600 @keyword X_reduced: value for coefficient X_reduced
1601 @type X_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1602 @keyword Y: value for coefficient Y
1603 @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1604 @keyword Y_reduced: value for coefficient Y_reduced
1605 @type Y_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.Function>}.
1606 @keyword d: value for coefficient d
1607 @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1608 @keyword d_reduced: value for coefficient d_reduced
1609 @type d_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
1610 @keyword y: value for coefficient y
1611 @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1612 @keyword d_contact: value for coefficient d_contact
1613 @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>} or L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1614 @keyword d_contact_reduced: value for coefficient d_contact_reduced
1615 @type d_contact_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>} or L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>}.
1616 @keyword y_contact: value for coefficient y_contact
1617 @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>} or L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1618 @keyword y_contact_reduced: value for coefficient y_contact_reduced
1619 @type y_contact_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnContactOne<escript.FunctionOnContactOne>} or L{ReducedFunctionOnContactZero<escript.FunctionOnContactZero>}.
1620 @keyword r: values prescribed to the solution at the locations of constraints
1621 @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1622 depending of reduced order is used for the solution.
1623 @keyword q: mask for location of constraints
1624 @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1625 depending of reduced order is used for the representation of the equation.
1626 @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1627 """
1628 # check if the coefficients are legal:
1629 for i in coefficients.iterkeys():
1630 if not self.hasCoefficient(i):
1631 raise IllegalCoefficient,"Attempt to set unknown coefficient %s"%i
1632 # if the number of unknowns or equations is still unknown we try to estimate them:
1633 if self.__numEquations==None or self.__numSolutions==None:
1634 for i,d in coefficients.iteritems():
1635 if hasattr(d,"shape"):
1636 s=d.shape
1637 elif hasattr(d,"getShape"):
1638 s=d.getShape()
1639 else:
1640 s=numarray.array(d).shape
1641 if s!=None:
1642 # get number of equations and number of unknowns:
1643 res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(self.getDomain(),s)
1644 if res==None:
1645 raise IllegalCoefficientValue,"Illegal shape %s of coefficient %s"%(s,i)
1646 else:
1647 if self.__numEquations==None: self.__numEquations=res[0]
1648 if self.__numSolutions==None: self.__numSolutions=res[1]
1649 if self.__numEquations==None: raise UndefinedPDEError,"unidententified number of equations"
1650 if self.__numSolutions==None: raise UndefinedPDEError,"unidententified number of solutions"
1651 # now we check the shape of the coefficient if numEquations and numSolutions are set:
1652 for i,d in coefficients.iteritems():
1653 try:
1654 self.COEFFICIENTS[i].setValue(self.getDomain(),
1655 self.getNumEquations(),self.getNumSolutions(),
1656 self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1657 self.alteredCoefficient(i)
1658 except IllegalCoefficientFunctionSpace,m:
1659 # if the function space is wrong then we try the reduced version:
1660 i_red=i+"_reduced"
1661 if (not i_red in coefficients.keys()) and i_red in self.COEFFICIENTS.keys():
1662 try:
1663 self.COEFFICIENTS[i_red].setValue(self.getDomain(),
1664 self.getNumEquations(),self.getNumSolutions(),
1665 self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1666 self.alteredCoefficient(i_red)
1667 except IllegalCoefficientValue,m:
1668 raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1669 except IllegalCoefficientFunctionSpace,m:
1670 raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1671 else:
1672 raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1673 except IllegalCoefficientValue,m:
1674 raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1675 self.__altered_coefficients=True
1676 # check if the systrem is inhomogeneous:
1677 if len(coefficients)>0 and not self.isUsingLumping():
1678 q=self.getCoefficientOfGeneralPDE("q")
1679 r=self.getCoefficientOfGeneralPDE("r")
1680 homogeneous_constraint=True
1681 if not q.isEmpty() and not r.isEmpty():
1682 if util.Lsup(q*r)>0.:
1683 self.trace("Inhomogeneous constraint detected.")
1684 self.__invalidateSystem()
1685
1686 def getSystem(self):
1687 """
1688 return the operator and right hand side of the PDE
1689
1690 @return: the discrete version of the PDE
1691 @rtype: C{tuple} of L{Operator,<escript.Operator>} and L{Data<escript.Data>}.
1692 """
1693 if not self.__operator_is_Valid or not self.__righthandside_isValid:
1694 if self.isUsingLumping():
1695 if not self.__operator_is_Valid:
1696 if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():
1697 raise TypeError,"Lumped matrix requires same order for equations and unknowns"
1698 if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1699 raise ValueError,"coefficient A in lumped matrix may not be present."
1700 if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1701 raise ValueError,"coefficient B in lumped matrix may not be present."
1702 if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1703 raise ValueError,"coefficient C in lumped matrix may not be present."
1704 if not self.getCoefficientOfGeneralPDE("d_contact").isEmpty():
1705 raise ValueError,"coefficient d_contact in lumped matrix may not be present."
1706 if not self.getCoefficientOfGeneralPDE("A_reduced").isEmpty():
1707 raise ValueError,"coefficient A_reduced in lumped matrix may not be present."
1708 if not self.getCoefficientOfGeneralPDE("B_reduced").isEmpty():
1709 raise ValueError,"coefficient B_reduced in lumped matrix may not be present."
1710 if not self.getCoefficientOfGeneralPDE("C_reduced").isEmpty():
1711 raise ValueError,"coefficient C_reduced in lumped matrix may not be present."
1712 if not self.getCoefficientOfGeneralPDE("d_contact_reduced").isEmpty():
1713 raise ValueError,"coefficient d_contact_reduced in lumped matrix may not be present."
1714 D=self.getCoefficientOfGeneralPDE("D")
1715 d=self.getCoefficientOfGeneralPDE("d")
1716 D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
1717 d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
1718 if not D.isEmpty():
1719 if self.getNumSolutions()>1:
1720 D_times_e=util.matrix_mult(D,numarray.ones((self.getNumSolutions(),)))
1721 else:
1722 D_times_e=D
1723 else:
1724 D_times_e=escript.Data()
1725 if not d.isEmpty():
1726 if self.getNumSolutions()>1:
1727 d_times_e=util.matrix_mult(d,numarray.ones((self.getNumSolutions(),)))
1728 else:
1729 d_times_e=d
1730 else:
1731 d_times_e=escript.Data()
1732
1733 if not D_reduced.isEmpty():
1734 if self.getNumSolutions()>1:
1735 D_reduced_times_e=util.matrix_mult(D_reduced,numarray.ones((self.getNumSolutions(),)))
1736 else:
1737 D_reduced_times_e=D_reduced
1738 else:
1739 D_reduced_times_e=escript.Data()
1740 if not d_reduced.isEmpty():
1741 if self.getNumSolutions()>1:
1742 d_reduced_times_e=util.matrix_mult(d_reduced,numarray.ones((self.getNumSolutions(),)))
1743 else:
1744 d_reduced_times_e=d_reduced
1745 else:
1746 d_reduced_times_e=escript.Data()
1747
1748 self.__operator=self.__getNewRightHandSide()
1749 if hasattr(self.getDomain(), "addPDEToLumpedSystem") :
1750 self.getDomain().addPDEToLumpedSystem(self.__operator, D_times_e, d_times_e)
1751 self.getDomain().addPDEToLumpedSystem(self.__operator, D_reduced_times_e, d_reduced_times_e)
1752 else:
1753 self.getDomain().addPDEToRHS(self.__operator, \
1754 escript.Data(), \
1755 D_times_e, \
1756 d_times_e,\
1757 escript.Data())
1758 self.getDomain().addPDEToRHS(self.__operator, \
1759 escript.Data(), \
1760 D_reduced_times_e, \
1761 d_reduced_times_e,\
1762 escript.Data())
1763 self.__operator=1./self.__operator
1764 self.trace("New lumped operator has been built.")
1765 self.__operator_is_Valid=True
1766 if not self.__righthandside_isValid:
1767 self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1768 self.getCoefficientOfGeneralPDE("X"), \
1769 self.getCoefficientOfGeneralPDE("Y"),\
1770 self.getCoefficientOfGeneralPDE("y"),\
1771 self.getCoefficientOfGeneralPDE("y_contact"))
1772 self.getDomain().addPDEToRHS(self.__righthandside, \
1773 self.getCoefficientOfGeneralPDE("X_reduced"), \
1774 self.getCoefficientOfGeneralPDE("Y_reduced"),\
1775 self.getCoefficientOfGeneralPDE("y_reduced"),\
1776 self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1777 self.trace("New right hand side as been built.")
1778 self.__righthandside_isValid=True
1779 else:
1780 if not self.__operator_is_Valid and not self.__righthandside_isValid:
1781 self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \
1782 self.getCoefficientOfGeneralPDE("A"), \
1783 self.getCoefficientOfGeneralPDE("B"), \
1784 self.getCoefficientOfGeneralPDE("C"), \
1785 self.getCoefficientOfGeneralPDE("D"), \
1786 self.getCoefficientOfGeneralPDE("X"), \
1787 self.getCoefficientOfGeneralPDE("Y"), \
1788 self.getCoefficientOfGeneralPDE("d"), \
1789 self.getCoefficientOfGeneralPDE("y"), \
1790 self.getCoefficientOfGeneralPDE("d_contact"), \
1791 self.getCoefficientOfGeneralPDE("y_contact"))
1792 self.getDomain().addPDEToSystem(self.__operator,self.__righthandside, \
1793 self.getCoefficientOfGeneralPDE("A_reduced"), \
1794 self.getCoefficientOfGeneralPDE("B_reduced"), \
1795 self.getCoefficientOfGeneralPDE("C_reduced"), \
1796 self.getCoefficientOfGeneralPDE("D_reduced"), \
1797 self.getCoefficientOfGeneralPDE("X_reduced"), \
1798 self.getCoefficientOfGeneralPDE("Y_reduced"), \
1799 self.getCoefficientOfGeneralPDE("d_reduced"), \
1800 self.getCoefficientOfGeneralPDE("y_reduced"), \
1801 self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1802 self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1803 self.__applyConstraint()
1804 self.__righthandside=self.copyConstraint(self.__righthandside)
1805 self.trace("New system has been built.")
1806 self.__operator_is_Valid=True
1807 self.__righthandside_isValid=True
1808 elif not self.__righthandside_isValid:
1809 self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1810 self.getCoefficientOfGeneralPDE("X"), \
1811 self.getCoefficientOfGeneralPDE("Y"),\
1812 self.getCoefficientOfGeneralPDE("y"),\
1813 self.getCoefficientOfGeneralPDE("y_contact"))
1814 self.getDomain().addPDEToRHS(self.__righthandside, \
1815 self.getCoefficientOfGeneralPDE("X_reduced"), \
1816 self.getCoefficientOfGeneralPDE("Y_reduced"),\
1817 self.getCoefficientOfGeneralPDE("y_reduced"),\
1818 self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1819 self.__righthandside=self.copyConstraint(self.__righthandside)
1820 self.trace("New right hand side has been built.")
1821 self.__righthandside_isValid=True
1822 elif not self.__operator_is_Valid:
1823 self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \
1824 self.getCoefficientOfGeneralPDE("A"), \
1825 self.getCoefficientOfGeneralPDE("B"), \
1826 self.getCoefficientOfGeneralPDE("C"), \
1827 self.getCoefficientOfGeneralPDE("D"), \
1828 escript.Data(), \
1829 escript.Data(), \
1830 self.getCoefficientOfGeneralPDE("d"), \
1831 escript.Data(),\
1832 self.getCoefficientOfGeneralPDE("d_contact"), \
1833 escript.Data())
1834 self.getDomain().addPDEToSystem(self.__operator,escript.Data(), \
1835 self.getCoefficientOfGeneralPDE("A_reduced"), \
1836 self.getCoefficientOfGeneralPDE("B_reduced"), \
1837 self.getCoefficientOfGeneralPDE("C_reduced"), \
1838 self.getCoefficientOfGeneralPDE("D_reduced"), \
1839 escript.Data(), \
1840 escript.Data(), \
1841 self.getCoefficientOfGeneralPDE("d_reduced"), \
1842 escript.Data(),\
1843 self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1844 escript.Data())
1845 self.__applyConstraint()
1846 self.trace("New operator has been built.")
1847 self.__operator_is_Valid=True
1848 return (self.__operator,self.__righthandside)
1849
1850
1851 class Poisson(LinearPDE):
1852 """
1853 Class to define a Poisson equation problem, which is genear L{LinearPDE} of the form
1854
1855 M{-grad(grad(u)[j])[j] = f}
1856
1857 with natural boundary conditons
1858
1859 M{n[j]*grad(u)[j] = 0 }
1860
1861 and constraints:
1862
1863 M{u=0} where M{q>0}
1864
1865 """
1866
1867 def __init__(self,domain,debug=False):
1868 """
1869 initializes a new Poisson equation
1870
1871 @param domain: domain of the PDE
1872 @type domain: L{Domain<escript.Domain>}
1873 @param debug: if True debug informations are printed.
1874
1875 """
1876 super(Poisson, self).__init__(domain,1,1,debug)
1877 self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1878 "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1879 "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1880 self.setSymmetryOn()
1881
1882 def setValue(self,**coefficients):
1883 """
1884 sets new values to coefficients
1885
1886 @param coefficients: new values assigned to coefficients
1887 @keyword f: value for right hand side M{f}
1888 @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1889 @keyword q: mask for location of constraints
1890 @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>}
1891 depending of reduced order is used for the representation of the equation.
1892 @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1893 """
1894 super(Poisson, self).setValue(**coefficients)
1895
1896 def getCoefficientOfGeneralPDE(self,name):
1897 """
1898 return the value of the coefficient name of the general PDE
1899 @param name: name of the coefficient requested.
1900 @type name: C{string}
1901 @return: the value of the coefficient name
1902 @rtype: L{Data<escript.Data>}
1903 @raise IllegalCoefficient: if name is not one of coefficients
1904 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}.
1905 @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1906 """
1907 if name == "A" :
1908 return escript.Data(util.kronecker(self.getDim()),escript.Function(self.getDomain()))
1909 elif name == "B" :
1910 return escript.Data()
1911 elif name == "C" :
1912 return escript.Data()
1913 elif name == "D" :
1914 return escript.Data()
1915 elif name == "X" :
1916 return escript.Data()
1917 elif name == "Y" :
1918 return self.getCoefficient("f")
1919 elif name == "d" :
1920 return escript.Data()
1921 elif name == "y" :
1922 return escript.Data()
1923 elif name == "d_contact" :
1924 return escript.Data()
1925 elif name == "y_contact" :
1926 return escript.Data()
1927 elif name == "A_reduced" :
1928 return escript.Data()
1929 elif name == "B_reduced" :
1930 return escript.Data()
1931 elif name == "C_reduced" :
1932 return escript.Data()
1933 elif name == "D_reduced" :
1934 return escript.Data()
1935 elif name == "X_reduced" :
1936 return escript.Data()
1937 elif name == "Y_reduced" :
1938 return self.getCoefficient("f_reduced")
1939 elif name == "d_reduced" :
1940 return escript.Data()
1941 elif name == "y_reduced" :
1942 return escript.Data()
1943 elif name == "d_contact_reduced" :
1944 return escript.Data()
1945 elif name == "y_contact_reduced" :
1946 return escript.Data()
1947 elif name == "r" :
1948 return escript.Data()
1949 elif name == "q" :
1950 return self.getCoefficient("q")
1951 else:
1952 raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1953
1954 class Helmholtz(LinearPDE):
1955 """
1956 Class to define a Helmhotz equation problem, which is genear L{LinearPDE} of the form
1957
1958 M{S{omega}*u - grad(k*grad(u)[j])[j] = f}
1959
1960 with natural boundary conditons
1961
1962 M{k*n[j]*grad(u)[j] = g- S{alpha}u }
1963
1964 and constraints:
1965
1966 M{u=r} where M{q>0}
1967
1968 """
1969
1970 def __init__(self,domain,debug=False):
1971 """
1972 initializes a new Poisson equation
1973
1974 @param domain: domain of the PDE
1975 @type domain: L{Domain<escript.Domain>}
1976 @param debug: if True debug informations are printed.
1977
1978 """
1979 super(Helmholtz, self).__init__(domain,1,1,debug)
1980 self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1981 "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1982 "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1983 "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1984 "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1985 "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1986 "g_reduced": PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1987 "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1988 "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1989 self.setSymmetryOn()
1990
1991 def setValue(self,**coefficients):
1992 """
1993 sets new values to coefficients
1994
1995 @param coefficients: new values assigned to coefficients
1996 @keyword omega: value for coefficient M{S{omega}}
1997 @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1998 @keyword k: value for coefficeint M{k}
1999 @type k: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2000 @keyword f: value for right hand side M{f}
2001 @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2002 @keyword alpha: value for right hand side M{S{alpha}}
2003 @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2004 @keyword g: value for right hand side M{g}
2005 @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2006 @keyword r: prescribed values M{r} for the solution in constraints.
2007 @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2008 depending of reduced order is used for the representation of the equation.
2009 @keyword q: mask for location of constraints
2010 @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2011 depending of reduced order is used for the representation of the equation.
2012 @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2013 """
2014 super(Helmholtz, self).setValue(**coefficients)
2015
2016 def getCoefficientOfGeneralPDE(self,name):
2017 """
2018 return the value of the coefficient name of the general PDE
2019
2020 @param name: name of the coefficient requested.
2021 @type name: C{string}
2022 @return: the value of the coefficient name
2023 @rtype: L{Data<escript.Data>}
2024 @raise IllegalCoefficient: if name is not one of coefficients
2025 "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}.
2026 @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2027 """
2028 if name == "A" :
2029 return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))*self.getCoefficient("k")
2030 elif name == "B" :
2031 return escript.Data()
2032 elif name == "C" :
2033 return escript.Data()
2034 elif name == "D" :
2035 return self.getCoefficient("omega")
2036 elif name == "X" :
2037 return escript.Data()
2038 elif name == "Y" :
2039 return self.getCoefficient("f")
2040 elif name == "d" :
2041 return self.getCoefficient("alpha")
2042 elif name == "y" :
2043 return self.getCoefficient("g")
2044 elif name == "d_contact" :
2045 return escript.Data()
2046 elif name == "y_contact" :
2047 return escript.Data()
2048 elif name == "A_reduced" :
2049 return escript.Data()
2050 elif name == "B_reduced" :
2051 return escript.Data()
2052 elif name == "C_reduced" :
2053 return escript.Data()
2054 elif name == "D_reduced" :
2055 return escript.Data()
2056 elif name == "X_reduced" :
2057 return escript.Data()
2058 elif name == "Y_reduced" :
2059 return self.getCoefficient("f_reduced")
2060 elif name == "d_reduced" :
2061 return escript.Data()
2062 elif name == "y_reduced" :
2063 return self.getCoefficient("g_reduced")
2064 elif name == "d_contact_reduced" :
2065 return escript.Data()
2066 elif name == "y_contact_reduced" :
2067 return escript.Data()
2068 elif name == "r" :
2069 return self.getCoefficient("r")
2070 elif name == "q" :
2071 return self.getCoefficient("q")
2072 else:
2073 raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2074
2075 class LameEquation(LinearPDE):
2076 """
2077 Class to define a Lame equation problem:
2078
2079 M{-grad(S{mu}*(grad(u[i])[j]+grad(u[j])[i]))[j] - grad(S{lambda}*grad(u[k])[k])[j] = F_i -grad(S{sigma}[ij])[j] }
2080
2081 with natural boundary conditons:
2082
2083 M{n[j]*(S{mu}*(grad(u[i])[j]+grad(u[j])[i]) + S{lambda}*grad(u[k])[k]) = f_i +n[j]*S{sigma}[ij] }
2084
2085 and constraints:
2086
2087 M{u[i]=r[i]} where M{q[i]>0}
2088
2089 """
2090
2091 def __init__(self,domain,debug=False):
2092 super(LameEquation, self).__init__(domain,\
2093 domain.getDim(),domain.getDim(),debug)
2094 self.COEFFICIENTS={ "lame_lambda" : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2095 "lame_mu" : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2096 "F" : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2097 "sigma" : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
2098 "f" : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2099 "r" : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
2100 "q" : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
2101 self.setSymmetryOn()
2102
2103 def setValues(self,**coefficients):
2104 """
2105 sets new values to coefficients
2106
2107 @param coefficients: new values assigned to coefficients
2108 @keyword lame_mu: value for coefficient M{S{mu}}
2109 @type lame_mu: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2110 @keyword lame_lambda: value for coefficient M{S{lambda}}
2111 @type lame_lambda: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2112 @keyword F: value for internal force M{F}
2113 @type F: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}
2114 @keyword sigma: value for initial stress M{S{sigma}}
2115 @type sigma: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}
2116 @keyword f: value for extrenal force M{f}
2117 @type f: any type that can be casted to L{Vector<escript.Vector>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}
2118 @keyword r: prescribed values M{r} for the solution in constraints.
2119 @type r: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2120 depending of reduced order is used for the representation of the equation.
2121 @keyword q: mask for location of constraints
2122 @type q: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2123 depending of reduced order is used for the representation of the equation.
2124 @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2125 """
2126 super(LameEquation, self).setValues(**coefficients)
2127
2128 def getCoefficientOfGeneralPDE(self,name):
2129 """
2130 return the value of the coefficient name of the general PDE
2131
2132 @param name: name of the coefficient requested.
2133 @type name: C{string}
2134 @return: the value of the coefficient name
2135 @rtype: L{Data<escript.Data>}
2136 @raise IllegalCoefficient: if name is not one of coefficients
2137 "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}.
2138 @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2139 """
2140 if name == "A" :
2141 out =self.createCoefficientOfGeneralPDE("A")
2142 for i in range(self.getDim()):
2143 for j in range(self.getDim()):
2144 out[i,i,j,j] += self.getCoefficient("lame_lambda")
2145 out[i,j,j,i] += self.getCoefficient("lame_mu")
2146 out[i,j,i,j] += self.getCoefficient("lame_mu")
2147 return out
2148 elif name == "B" :
2149 return escript.Data()
2150 elif name == "C" :
2151 return escript.Data()
2152 elif name == "D" :
2153 return escript.Data()
2154 elif name == "X" :
2155 return self.getCoefficient("sigma")
2156 elif name == "Y" :
2157 return self.getCoefficient("F")
2158 elif name == "d" :
2159 return escript.Data()
2160 elif name == "y" :
2161 return self.getCoefficient("f")
2162 elif name == "d_contact" :
2163 return escript.Data()
2164 elif name == "y_contact" :
2165 return escript.Data()
2166 elif name == "A_reduced" :
2167 return escript.Data()
2168 elif name == "B_reduced" :
2169 return escript.Data()
2170 elif name == "C_reduced" :
2171 return escript.Data()
2172 elif name == "D_reduced" :
2173 return escript.Data()
2174 elif name == "X_reduced" :
2175 return escript.Data()
2176 elif name == "Y_reduced" :
2177 return escript.Data()
2178 elif name == "d_reduced" :
2179 return escript.Data()
2180 elif name == "y_reduced" :
2181 return escript.Data()
2182 elif name == "d_contact_reduced" :
2183 return escript.Data()
2184 elif name == "y_contact_reduced" :
2185 return escript.Data()
2186 elif name == "r" :
2187 return self.getCoefficient("r")
2188 elif name == "q" :
2189 return self.getCoefficient("q")
2190 else:
2191 raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2192

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