# Contents of /trunk/esys2/escript/py_src/linearPDEs.py

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Fri Mar 4 07:12:37 2005 UTC (15 years, 7 months ago) by jgs
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```Merge of development branch back to main trunk on 2005-03-04

```
 1 # \$Id\$ 2 3 ## @file linearPDEs.py 4 5 """ 6 @brief Functions and classes for linear PDEs 7 """ 8 9 import escript 10 import util 11 import numarray 12 13 14 def _CompTuple2(t1,t2): 15 """ 16 @brief 17 18 @param t1 19 @param t2 20 """ 21 dif=t1[0]+t1[1]-(t2[0]+t2[1]) 22 if dif<0: return 1 23 elif dif>0: return -1 24 else: return 0 25 26 class PDECoefficient: 27 """ 28 @brief 29 """ 30 # identifier for location of Data objects defining COEFFICIENTS 31 INTERIOR=0 32 BOUNDARY=1 33 CONTACT=2 34 CONTINUOUS=3 35 # identifier in the pattern of COEFFICIENTS: 36 # the pattern is a tuple of EQUATION,SOLUTION,DIM where DIM represents the spatial dimension, EQUATION the number of equations and SOLUTION the 37 # number of unknowns. 38 EQUATION=3 39 SOLUTION=4 40 DIM=5 41 # indicator for what is altered if the coefficient is altered: 42 OPERATOR=5 43 RIGHTHANDSIDE=6 44 BOTH=7 45 def __init__(self,where,pattern,altering): 46 """ 47 @brief Initialise a PDE Coefficient type 48 """ 49 self.what=where 50 self.pattern=pattern 51 self.altering=altering 52 self.resetValue() 53 54 def resetValue(self): 55 """ 56 @brief resets coefficient value to default 57 """ 58 self.value=escript.Data() 59 60 def getFunctionSpace(self,domain): 61 """ 62 @brief defines the FunctionSpace of the coefficient on the domain 63 64 @param domain 65 """ 66 if self.what==self.INTERIOR: return escript.Function(domain) 67 elif self.what==self.BOUNDARY: return escript.FunctionOnBoundary(domain) 68 elif self.what==self.CONTACT: return escript.FunctionOnContactZero(domain) 69 elif self.what==self.CONTINUOUS: return escript.ContinuousFunction(domain) 70 71 def getValue(self): 72 """ 73 @brief returns the value of the coefficient: 74 """ 75 return self.value 76 77 def setValue(self,newValue): 78 """ 79 @brief set the value of the coefficient to new value 80 """ 81 self.value=newValue 82 83 def isAlteringOperator(self): 84 """ 85 @brief return true if the operator of the PDE is changed when the coefficient is changed 86 """ 87 if self.altering==self.OPERATOR or self.altering==self.BOTH: 88 return not None 89 else: 90 return None 91 92 def isAlteringRightHandSide(self): 93 """ 94 @brief return true if the right hand side of the PDE is changed when the coefficient is changed 95 """ 96 if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH: 97 return not None 98 else: 99 return None 100 101 def estimateNumEquationsAndNumSolutions(self,shape=(),dim=3): 102 """ 103 @brief tries to estimate the number of equations in a given tensor shape for a given spatial dimension dim 104 105 @param shape 106 @param dim 107 """ 108 if len(shape)>0: 109 num=max(shape)+1 110 else: 111 num=1 112 search=[] 113 for u in range(num): 114 for e in range(num): 115 search.append((e,u)) 116 search.sort(_CompTuple2) 117 for item in search: 118 s=self.buildShape(item[0],item[1],dim) 119 if len(s)==0 and len(shape)==0: 120 return (1,1) 121 else: 122 if s==shape: return item 123 return None 124 125 def buildShape(self,e=1,u=1,dim=3): 126 """ 127 @brief builds the required shape for a given number of equations e, number of unknowns u and spatial dimension dim 128 129 @param e 130 @param u 131 @param dim 132 """ 133 s=() 134 for i in self.pattern: 135 if i==self.EQUATION: 136 if e>1: s=s+(e,) 137 elif i==self.SOLUTION: 138 if u>1: s=s+(u,) 139 else: 140 s=s+(dim,) 141 return s 142 143 class LinearPDE: 144 """ 145 @brief Class to handel a linear PDE 146 147 class to define a linear PDE of the form 148 149 -(A_{ijkl}u_{k,l})_{,j} -(B_{ijk}u_k)_{,j} + C_{ikl}u_{k,l} +D_{ik}u_k = - (X_{ij})_{,j} + Y_i 150 151 with boundary conditons: 152 153 n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i 154 155 and contact conditions 156 157 n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_contact_{ik}[u_k] = - n_j*X_{ij} + y_contact_i 158 159 and constraints: 160 161 u_i=r_i where q_i>0 162 163 """ 164 TOL=1.e-13 165 DEFAULT_METHOD=util.DEFAULT_METHOD 166 DIRECT=util.DIRECT 167 CHOLEVSKY=util.CHOLEVSKY 168 PCG=util.PCG 169 CR=util.CR 170 CGS=util.CGS 171 BICGSTAB=util.BICGSTAB 172 SSOR=util.SSOR 173 GMRES=util.GMRES 174 PRES20=util.PRES20 175 ILU0=util.ILU0 176 JACOBI=util.JACOBI 177 178 def __init__(self,domain,numEquations=0,numSolutions=0): 179 """ 180 @brief initializes a new linear PDE. 181 182 @param args 183 """ 184 # COEFFICIENTS can be overwritten by subclasses: 185 self.COEFFICIENTS={ 186 "A" : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM,PDECoefficient.SOLUTION,PDECoefficient.DIM),PDECoefficient.OPERATOR), 187 "B" : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR), 188 "C" : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION,PDECoefficient.DIM),PDECoefficient.OPERATOR), 189 "D" : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR), 190 "X" : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM),PDECoefficient.RIGHTHANDSIDE), 191 "Y" : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE), 192 "d" : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR), 193 "y" : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE), 194 "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR), 195 "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE), 196 "r" : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE), 197 "q" : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.SOLUTION,),PDECoefficient.BOTH)} 198 199 # initialize attributes 200 self.__debug=None 201 self.__domain=domain 202 self.__numEquations=numEquations 203 self.__numSolutions=numSolutions 204 self.cleanCoefficients() 205 206 self.__operator=escript.Operator() 207 self.__operator_isValid=False 208 self.__righthandside=escript.Data() 209 self.__righthandside_isValid=False 210 self.__solution=escript.Data() 211 self.__solution_isValid=False 212 213 # set some default values: 214 self.__homogeneous_constraint=True 215 self.__row_function_space=escript.Solution(self.__domain) 216 self.__column_function_space=escript.Solution(self.__domain) 217 self.__tolerance=1.e-8 218 self.__solver_method=util.DEFAULT_METHOD 219 self.__matrix_type=self.__domain.getSystemMatrixTypeId(util.DEFAULT_METHOD,False) 220 self.__sym=False 221 self.__lumping=False 222 223 def createCoefficient(self, name): 224 """ 225 @brief create a data object corresponding to coefficient name 226 @param name 227 """ 228 return escript.Data(shape = getShapeOfCoefficient(name), \ 229 what = getFunctionSpaceForCoefficient(name)) 230 231 def __del__(self): 232 pass 233 234 def getCoefficient(self,name): 235 """ 236 @brief return the value of the parameter name 237 238 @param name 239 """ 240 return self.COEFFICIENTS[name].getValue() 241 242 def getCoefficientOfPDE(self,name): 243 """ 244 @brief return the value of the coefficient name of the general PDE. This method is called by the assembling routine 245 it can be overwritten to map coefficients of a particualr PDE to the general PDE. 246 @param name 247 """ 248 return self.getCoefficient(name) 249 250 def hasCoefficient(self,name): 251 """ 252 @brief return true if name is the name of a coefficient 253 254 @param name 255 """ 256 return self.COEFFICIENTS.has_key(name) 257 258 def getFunctionSpaceForEquation(self): 259 """ 260 @brief return true if the test functions should use reduced order 261 """ 262 return self.__row_function_space 263 264 def getFunctionSpaceForSolution(self): 265 """ 266 @brief return true if the interpolation of the solution should use reduced order 267 """ 268 return self.__column_function_space 269 270 def setValue(self,**coefficients): 271 """ 272 @brief sets new values to coefficients 273 274 @param coefficients 275 """ 276 self._setValue(**coefficients) 277 278 279 def cleanCoefficients(self): 280 """ 281 @brief resets all coefficients to default values. 282 """ 283 for i in self.COEFFICIENTS.iterkeys(): 284 self.COEFFICIENTS[i].resetValue() 285 286 def createNewCoefficient(self,name): 287 """ 288 @brief returns a new coefficient appropriate for coefficient name: 289 """ 290 return escript.Data(0,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name)) 291 292 293 def getShapeOfCoefficient(self,name): 294 """ 295 @brief return the shape of the coefficient name 296 297 @param name 298 """ 299 if self.hasCoefficient(name): 300 return self.COEFFICIENTS[name].buildShape(self.getNumEquations(),self.getNumSolutions(),self.getDomain().getDim()) 301 else: 302 raise ValueError,"Solution coefficient %s requested"%name 303 304 def getFunctionSpaceForCoefficient(self,name): 305 """ 306 @brief return the atoms of the coefficient name 307 308 @param name 309 """ 310 if self.hasCoefficient(name): 311 return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain()) 312 else: 313 raise ValueError,"Solution coefficient %s requested"%name 314 315 def alteredCoefficient(self,name): 316 """ 317 @brief annonced that coefficient name has been changed 318 319 @param name 320 """ 321 if self.hasCoefficient(name): 322 if self.COEFFICIENTS[name].isAlteringOperator(): self.__rebuildOperator() 323 if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__rebuildRightHandSide() 324 else: 325 raise ValueError,"unknown coefficient %s requested"%name 326 327 # ===== debug ============================================================== 328 def setDebugOn(self): 329 """ 330 @brief 331 """ 332 self.__debug=not None 333 334 def setDebugOff(self): 335 """ 336 @brief 337 """ 338 self.__debug=None 339 340 def debug(self): 341 """ 342 @brief returns true if the PDE is in the debug mode 343 """ 344 return self.__debug 345 346 #===== Lumping =========================== 347 def setLumpingOn(self): 348 """ 349 @brief indicates to use matrix lumping 350 """ 351 if not self.isUsingLumping(): 352 if self.debug() : print "PDE Debug: lumping is set on" 353 self.__rebuildOperator() 354 self.__lumping=True 355 356 def setLumpingOff(self): 357 """ 358 @brief switches off matrix lumping 359 """ 360 if self.isUsingLumping(): 361 if self.debug() : print "PDE Debug: lumping is set off" 362 self.__rebuildOperator() 363 self.__lumping=False 364 365 def setLumping(self,flag=False): 366 """ 367 @brief set the matrix lumping flag to flag 368 """ 369 if flag: 370 self.setLumpingOn() 371 else: 372 self.setLumpingOff() 373 374 def isUsingLumping(self): 375 """ 376 @brief 377 """ 378 return self.__lumping 379 380 #============ method business ========================================================= 381 def setSolverMethod(self,solver=util.DEFAULT_METHOD): 382 """ 383 @brief sets a new solver 384 """ 385 if not solver==self.getSolverMethod(): 386 self.__solver_method=solver 387 if self.debug() : print "PDE Debug: New solver is %s"%solver 388 self.__checkMatrixType() 389 390 def getSolverMethod(self): 391 """ 392 @brief returns the solver method 393 """ 394 return self.__solver_method 395 396 #============ tolerance business ========================================================= 397 def setTolerance(self,tol=1.e-8): 398 """ 399 @brief resets the tolerance to tol. 400 """ 401 if not tol>0: 402 raise ValueException,"Tolerance as to be positive" 403 if tol0: 606 return self.__numEquations 607 else: 608 raise ValueError,"Number of equations is undefined. Please specify argument numEquations." 609 610 def getNumSolutions(self): 611 """ 612 @brief returns the number of unknowns 613 """ 614 if self.__numSolutions>0: 615 return self.__numSolutions 616 else: 617 raise ValueError,"Number of solution is undefined. Please specify argument numSolutions." 618 619 620 def checkSymmetry(self,verbose=True): 621 """ 622 @brief returns if the Operator is symmetric. This is a very expensive operation!!! The symmetry flag is not altered. 623 """ 624 verbose=verbose or self.debug() 625 out=True 626 if self.getNumSolutions()!=self.getNumEquations(): 627 if verbose: print "non-symmetric PDE because of different number of equations and solutions" 628 out=False 629 else: 630 A=self.getCoefficientOfPDE("A") 631 if not A.isEmpty(): 632 tol=util.Lsup(A)*self.TOL 633 if self.getNumSolutions()>1: 634 for i in range(self.getNumEquations()): 635 for j in range(self.getDim()): 636 for k in range(self.getNumSolutions()): 637 for l in range(self.getDim()): 638 if util.Lsup(A[i,j,k,l]-A[k,l,i,j])>tol: 639 if verbose: print "non-symmetric PDE because A[%d,%d,%d,%d]!=A[%d,%d,%d,%d]"%(i,j,k,l,k,l,i,j) 640 out=False 641 else: 642 for j in range(self.getDim()): 643 for l in range(self.getDim()): 644 if util.Lsup(A[j,l]-A[l,j])>tol: 645 if verbose: print "non-symmetric PDE because A[%d,%d]!=A[%d,%d]"%(j,l,l,j) 646 out=False 647 B=self.getCoefficientOfPDE("B") 648 C=self.getCoefficientOfPDE("C") 649 if B.isEmpty() and not C.isEmpty(): 650 if verbose: print "non-symmetric PDE because B is not present but C is" 651 out=False 652 elif not B.isEmpty() and C.isEmpty(): 653 if verbose: print "non-symmetric PDE because C is not present but B is" 654 out=False 655 elif not B.isEmpty() and not C.isEmpty(): 656 tol=(util.Lsup(B)+util.Lsup(C))*self.TOL/2. 657 if self.getNumSolutions()>1: 658 for i in range(self.getNumEquations()): 659 for j in range(self.getDim()): 660 for k in range(self.getNumSolutions()): 661 if util.Lsup(B[i,j,k]-C[k,i,j])>tol: 662 if verbose: print "non-symmetric PDE because B[%d,%d,%d]!=C[%d,%d,%d]"%(i,j,k,k,i,j) 663 out=False 664 else: 665 for j in range(self.getDim()): 666 if util.Lsup(B[j]-C[j])>tol: 667 if verbose: print "non-symmetric PDE because B[%d]!=C[%d]"%(j,j) 668 out=False 669 if self.getNumSolutions()>1: 670 D=self.getCoefficientOfPDE("D") 671 if not D.isEmpty(): 672 tol=util.Lsup(D)*self.TOL 673 for i in range(self.getNumEquations()): 674 for k in range(self.getNumSolutions()): 675 if util.Lsup(D[i,k]-D[k,i])>tol: 676 if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i) 677 out=False 678 679 return out 680 681 def getFlux(self,u): 682 """ 683 @brief returns the flux J_ij for a given u 684 685 J_ij=A_{ijkl}u_{k,l}+B_{ijk}u_k-X_{ij} 686 687 @param u argument of the operator 688 689 """ 690 raise SystemError,"getFlux is not implemented yet" 691 return None 692 693 def applyOperator(self,u): 694 """ 695 @brief applies the operator of the PDE to a given solution u in weak from 696 697 @param u argument of the operator 698 699 """ 700 return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution()) 701 702 def getResidual(self,u): 703 """ 704 @brief return the residual of u in the weak from 705 706 @param u 707 """ 708 return self.applyOperator(u)-self.getRightHandSide() 709 710 def _setValue(self,**coefficients): 711 """ 712 @brief sets new values to coefficient 713 714 @param coefficients 715 """ 716 # check if the coefficients are legal: 717 for i in coefficients.iterkeys(): 718 if not self.hasCoefficient(i): 719 raise ValueError,"Attempt to set unknown coefficient %s"%i 720 # if the number of unknowns or equations is still unknown we try to estimate them: 721 if self.__numEquations<1 or self.__numSolutions<1: 722 for i,d in coefficients.iteritems(): 723 if hasattr(d,"shape"): 724 s=d.shape 725 elif hasattr(d,"getShape"): 726 s=d.getShape() 727 else: 728 s=numarray.array(d).shape 729 if s!=None: 730 # get number of equations and number of unknowns: 731 res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(s,self.getDim()) 732 if res==None: 733 raise ValueError,"Illegal shape %s of coefficient %s"%(s,i) 734 else: 735 if self.__numEquations<1: self.__numEquations=res[0] 736 if self.__numSolutions<1: self.__numSolutions=res[1] 737 if self.__numEquations<1: raise ValueError,"unidententified number of equations" 738 if self.__numSolutions<1: raise ValueError,"unidententified number of solutions" 739 # now we check the shape of the coefficient if numEquations and numSolutions are set: 740 for i,d in coefficients.iteritems(): 741 if d==None: 742 d2=escript.Data() 743 elif isinstance(d,escript.Data): 744 if d.isEmpty(): 745 d2=d 746 else: 747 d2=escript.Data(d,self.getFunctionSpaceForCoefficient(i)) 748 else: 749 d2=escript.Data(d,self.getFunctionSpaceForCoefficient(i)) 750 if not d2.isEmpty(): 751 if not self.getShapeOfCoefficient(i)==d2.getShape(): 752 raise ValueError,"Expected shape for coefficient %s is %s but actual shape is %s."%(i,self.getShapeOfCoefficient(i),d2.getShape()) 753 # overwrite new values: 754 if self.debug(): print "PDE Debug: Coefficient %s has been altered."%i 755 self.COEFFICIENTS[i].setValue(d2) 756 self.alteredCoefficient(i) 757 758 # reset the HomogeneousConstraintFlag: 759 self.__setHomogeneousConstraintFlag() 760 if len(coefficients)>0 and not self.isUsingLumping() and not self.__homogeneous_constraint: self.__rebuildSystem() 761 762 def __setHomogeneousConstraintFlag(self): 763 """ 764 @brief checks if the constraints are homogeneous and sets self.__homogeneous_constraint accordingly. 765 """ 766 self.__homogeneous_constraint=True 767 q=self.getCoefficientOfPDE("q") 768 r=self.getCoefficientOfPDE("r") 769 if not q.isEmpty() and not r.isEmpty(): 770 if (q*r).Lsup()>=1.e-13*r.Lsup(): self.__homogeneous_constraint=False 771 if self.debug(): 772 if self.__homogeneous_constraint: 773 print "PDE Debug: Constraints are homogeneous." 774 else: 775 print "PDE Debug: Constraints are inhomogeneous." 776 777 778 # ==== rebuild switches ===================================================================== 779 def __rebuildSolution(self,deep=False): 780 """ 781 @brief indicates the PDE has to be reolved if the solution is requested 782 """ 783 if self.__solution_isValid and self.debug() : print "PDE Debug: PDE has to be resolved." 784 self.__solution_isValid=False 785 if deep: self.__solution=escript.Data() 786 787 788 def __rebuildOperator(self,deep=False): 789 """ 790 @brief indicates the operator has to be rebuilt next time it is used 791 """ 792 if self.__operator_isValid and self.debug() : print "PDE Debug: Operator has to be rebuilt." 793 self.__rebuildSolution(deep) 794 self.__operator_isValid=False 795 if deep: self.__operator=escript.Operator() 796 797 def __rebuildRightHandSide(self,deep=False): 798 """ 799 @brief indicates the right hand side has to be rebuild next time it is used 800 """ 801 if self.__righthandside_isValid and self.debug() : print "PDE Debug: Right hand side has to be rebuilt." 802 self.__rebuildSolution(deep) 803 self.__righthandside_isValid=False 804 if deep: self.__righthandside=escript.Data() 805 806 def __rebuildSystem(self,deep=False): 807 """ 808 @brief annonced that all coefficient name has been changed 809 """ 810 self.__rebuildSolution(deep) 811 self.__rebuildOperator(deep) 812 self.__rebuildRightHandSide(deep) 813 814 def __checkMatrixType(self): 815 """ 816 @brief reassess the matrix type and, if needed, initiates an operator rebuild 817 """ 818 new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod(),self.isSymmetric()) 819 if not new_matrix_type==self.__matrix_type: 820 if self.debug() : print "PDE Debug: Matrix type is now %d."%new_matrix_type 821 self.__matrix_type=new_matrix_type 822 self.__rebuildOperator(deep=True) 823 824 #============ assembling ======================================================= 825 def __copyConstraint(self): 826 """ 827 @brief copies the constrint condition into u 828 """ 829 if not self.__righthandside.isEmpty(): 830 q=self.getCoefficientOfPDE("q") 831 r=self.getCoefficientOfPDE("r") 832 if not q.isEmpty(): 833 if r.isEmpty(): 834 r2=escript.Data(0,self.__righthandside.getShape(),self.__righthandside.getFunctionSpace()) 835 else: 836 r2=escript.Data(r,self.__righthandside.getFunctionSpace()) 837 self.__righthandside.copyWithMask(r2,escript.Data(q,self.__righthandside.getFunctionSpace())) 838 839 def __applyConstraint(self): 840 """ 841 @brief applies the constraints defined by q and r to the system 842 """ 843 q=self.getCoefficientOfPDE("q") 844 r=self.getCoefficientOfPDE("r") 845 if not q.isEmpty() and not self.__operator.isEmpty(): 846 # q is the row and column mask to indicate where constraints are set: 847 row_q=escript.Data(q,self.getFunctionSpaceForEquation()) 848 col_q=escript.Data(q,self.getFunctionSpaceForSolution()) 849 u=self.__makeNewSolution() 850 if r.isEmpty(): 851 r_s=self.__makeNewSolution() 852 else: 853 r_s=escript.Data(r,self.getFunctionSpaceForSolution()) 854 u.copyWithMask(r_s,col_q) 855 if self.isUsingLumping(): 856 self.__operator.copyWithMask(escript.Data(1,q.getShape(),self.getFunctionSpaceForEquation()),row_q) 857 else: 858 if not self.__righthandside.isEmpty(): self.__righthandside-=self.__operator*u 859 self.__operator.nullifyRowsAndCols(row_q,col_q,1.) 860 861 def getSystem(self): 862 """ 863 @brief return the operator and right hand side of the PDE 864 """ 865 if not self.__operator_isValid or not self.__righthandside_isValid: 866 if self.isUsingLumping(): 867 if not self.__operator_isValid: 868 if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution(): 869 raise TypeError,"Lumped matrix requires same order for equations and unknowns" 870 if not self.getCoefficientOfPDE("A").isEmpty(): 871 raise Warning,"Lumped matrix does not allow coefficient A" 872 if not self.getCoefficientOfPDE("B").isEmpty(): 873 raise Warning,"Lumped matrix does not allow coefficient B" 874 if not self.getCoefficientOfPDE("C").isEmpty(): 875 raise Warning,"Lumped matrix does not allow coefficient C" 876 if self.debug() : print "PDE Debug: New lumped operator is built." 877 mat=self.__makeNewOperator() 878 self.getDomain().addPDEToSystem(mat,escript.Data(), \ 879 self.getCoefficientOfPDE("A"), \ 880 self.getCoefficientOfPDE("B"), \ 881 self.getCoefficientOfPDE("C"), \ 882 self.getCoefficientOfPDE("D"), \ 883 escript.Data(), \ 884 escript.Data(), \ 885 self.getCoefficientOfPDE("d"), \ 886 escript.Data(),\ 887 self.getCoefficientOfPDE("d_contact"), \ 888 escript.Data()) 889 self.__operator=mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True) 890 self.__applyConstraint() 891 self.__operator_isValid=True 892 if not self.__righthandside_isValid: 893 if self.debug() : print "PDE Debug: New right hand side is built." 894 self.getDomain().addPDEToRHS(self.__getFreshRightHandSide(), \ 895 self.getCoefficientOfPDE("X"), \ 896 self.getCoefficientOfPDE("Y"),\ 897 self.getCoefficientOfPDE("y"),\ 898 self.getCoefficientOfPDE("y_contact")) 899 self.__copyConstraint() 900 self.__righthandside_isValid=True 901 else: 902 if not self.__operator_isValid and not self.__righthandside_isValid: 903 if self.debug() : print "PDE Debug: New system is built." 904 self.getDomain().addPDEToSystem(self.__getFreshOperator(),self.__getFreshRightHandSide(), \ 905 self.getCoefficientOfPDE("A"), \ 906 self.getCoefficientOfPDE("B"), \ 907 self.getCoefficientOfPDE("C"), \ 908 self.getCoefficientOfPDE("D"), \ 909 self.getCoefficientOfPDE("X"), \ 910 self.getCoefficientOfPDE("Y"), \ 911 self.getCoefficientOfPDE("d"), \ 912 self.getCoefficientOfPDE("y"), \ 913 self.getCoefficientOfPDE("d_contact"), \ 914 self.getCoefficientOfPDE("y_contact")) 915 self.__applyConstraint() 916 self.__copyConstraint() 917 self.__operator_isValid=True 918 self.__righthandside_isValid=True 919 elif not self.__righthandside_isValid: 920 if self.debug() : print "PDE Debug: New right hand side is built." 921 self.getDomain().addPDEToRHS(self.__getFreshRightHandSide(), \ 922 self.getCoefficientOfPDE("X"), \ 923 self.getCoefficientOfPDE("Y"),\ 924 self.getCoefficientOfPDE("y"),\ 925 self.getCoefficientOfPDE("y_contact")) 926 self.__copyConstraint() 927 self.__righthandside_isValid=True 928 elif not self.__operator_isValid: 929 if self.debug() : print "PDE Debug: New operator is built." 930 self.getDomain().addPDEToSystem(self.__getFreshOperator(),escript.Data(), \ 931 self.getCoefficientOfPDE("A"), \ 932 self.getCoefficientOfPDE("B"), \ 933 self.getCoefficientOfPDE("C"), \ 934 self.getCoefficientOfPDE("D"), \ 935 escript.Data(), \ 936 escript.Data(), \ 937 self.getCoefficientOfPDE("d"), \ 938 escript.Data(),\ 939 self.getCoefficientOfPDE("d_contact"), \ 940 escript.Data()) 941 self.__applyConstraint() 942 self.__operator_isValid=True 943 return (self.__operator,self.__righthandside) 944 def getOperator(self): 945 """ 946 @brief returns the operator of the PDE 947 """ 948 return self.getSystem()[0] 949 950 def getRightHandSide(self): 951 """ 952 @brief returns the right hand side of the PDE 953 """ 954 return self.getSystem()[1] 955 956 def solve(self,**options): 957 """ 958 @brief solve the PDE 959 960 @param options 961 """ 962 mat,f=self.getSystem() 963 if self.isUsingLumping(): 964 out=f/mat 965 else: 966 options[util.TOLERANCE_KEY]=self.getTolerance() 967 options[util.METHOD_KEY]=self.getSolverMethod() 968 options[util.SYMMETRY_KEY]=self.isSymmetric() 969 if self.debug() : print "PDE Debug: solver options: ",options 970 out=mat.solve(f,options) 971 return out 972 973 def getSolution(self,**options): 974 """ 975 @brief returns the solution of the PDE 976 977 @param options 978 """ 979 if not self.__solution_isValid: 980 if self.debug() : print "PDE Debug: PDE is resolved." 981 self.__solution=self.solve(**options) 982 self.__solution_isValid=True 983 return self.__solution 984 985 986 987 def ELMAN_RAMAGE(P): return (P-1.).wherePositive()*0.5*(1.-1./(P+1.e-15)) 988 def SIMPLIFIED_BROOK_HUGHES(P): 989 c=(P-3.).whereNegative() 990 return P/6.*c+1./2.*(1.-c) 991 def HALF(P): return escript.Scalar(0.5,P.getFunctionSpace()) 992 993 994 class AdvectivePDE(LinearPDE): 995 """ 996 @brief Class to handel a linear PDE domineated by advective terms: 997 998 class to define a linear PDE of the form 999 1000 -(A_{ijkl}u_{k,l})_{,j} -(B_{ijk}u_k)_{,j} + C_{ikl}u_{k,l} +D_{ik}u_k = - (X_{ij})_{,j} + Y_i 1001 1002 with boundary conditons: 1003 1004 n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i 1005 1006 and contact conditions 1007 1008 n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_contact_{ik}[u_k] = - n_j*X_{ij} + y_contact_i 1009 1010 and constraints: 1011 1012 u_i=r_i where q_i>0 1013 1014 """ 1015 def __init__(self,domain,numEquations=0,numSolutions=0,xi=ELMAN_RAMAGE): 1016 LinearPDE.__init__(self,domain,numEquations,numSolutions) 1017 self.__xi=xi 1018 self.__Xi=escript.Data() 1019 1020 def __calculateXi(self,peclet_factor,Z,h): 1021 Z_max=util.Lsup(Z) 1022 if Z_max>0.: 1023 return h*self.__xi(Z*peclet_factor)/(Z+Z_max*self.TOL) 1024 else: 1025 return 0. 1026 1027 def setValue(self,**args): 1028 if "A" in args.keys() or "B" in args.keys() or "C" in args.keys(): self.__Xi=escript.Data() 1029 self._setValue(**args) 1030 1031 def getXi(self): 1032 if self.__Xi.isEmpty(): 1033 B=self.getCoefficient("B") 1034 C=self.getCoefficient("C") 1035 A=self.getCoefficient("A") 1036 h=self.getDomain().getSize() 1037 self.__Xi=escript.Scalar(0.,self.getFunctionSpaceForCoefficient("A")) 1038 if not C.isEmpty() or not B.isEmpty(): 1039 if not C.isEmpty() and not B.isEmpty(): 1040 Z2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A")) 1041 if self.getNumEquations()>1: 1042 if self.getNumSolutions()>1: 1043 for i in range(self.getNumEquations()): 1044 for k in range(self.getNumSolutions()): 1045 for l in range(self.getDim()): Z2+=(C[i,k,l]-B[i,l,k])**2 1046 else: 1047 for i in range(self.getNumEquations()): 1048 for l in range(self.getDim()): Z2+=(C[i,l]-B[i,l])**2 1049 else: 1050 if self.getNumSolutions()>1: 1051 for k in range(self.getNumSolutions()): 1052 for l in range(self.getDim()): Z2+=(C[k,l]-B[l,k])**2 1053 else: 1054 for l in range(self.getDim()): Z2+=(C[l]-B[l])**2 1055 length_of_Z=util.sqrt(Z2) 1056 elif C.isEmpty(): 1057 length_of_Z=util.length(B) 1058 else: 1059 length_of_Z=util.length(C) 1060 1061 Z_max=util.Lsup(length_of_Z) 1062 if Z_max>0.: 1063 length_of_A=util.length(A) 1064 A_max=util.Lsup(length_of_A) 1065 if A_max>0: 1066 inv_A=1./(length_of_A+A_max*self.TOL) 1067 else: 1068 inv_A=1./self.TOL 1069 peclet_number=length_of_Z*h/2*inv_A 1070 xi=self.__xi(peclet_number) 1071 self.__Xi=h*xi/(length_of_Z+Z_max*self.TOL) 1072 print "@ preclet number = %e"%util.Lsup(peclet_number),util.Lsup(xi),util.Lsup(length_of_Z) 1073 return self.__Xi 1074 1075 1076 def getCoefficientOfPDE(self,name): 1077 """ 1078 @brief return the value of the coefficient name of the general PDE 1079 @param name 1080 """ 1081 if not self.getNumEquations() == self.getNumSolutions(): 1082 raise ValueError,"AdvectivePDE expects the number of solution componets and the number of equations to be equal." 1083 1084 if name == "A" : 1085 A=self.getCoefficient("A") 1086 B=self.getCoefficient("B") 1087 C=self.getCoefficient("C") 1088 if B.isEmpty() and C.isEmpty(): 1089 Aout=A 1090 else: 1091 if A.isEmpty(): 1092 Aout=self.createNewCoefficient("A") 1093 else: 1094 Aout=A[:] 1095 Xi=self.getXi() 1096 if self.getNumEquations()>1: 1097 for i in range(self.getNumEquations()): 1098 for j in range(self.getDim()): 1099 for k in range(self.getNumSolutions()): 1100 for l in range(self.getDim()): 1101 if not C.isEmpty() and not B.isEmpty(): 1102 for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*(C[p,i,j]-B[p,j,i])*(C[p,k,l]-B[p,l,k]) 1103 elif C.isEmpty(): 1104 for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*B[p,j,i]*B[p,l,k] 1105 else: 1106 for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*C[p,i,j]*C[p,k,l] 1107 else: 1108 for j in range(self.getDim()): 1109 for l in range(self.getDim()): 1110 if not C.isEmpty() and not B.isEmpty(): 1111 Aout[j,l]+=Xi*(C[j]-B[j])*(C[l]-B[l]) 1112 elif C.isEmpty(): 1113 Aout[j,l]+=Xi*B[j]*B[l] 1114 else: 1115 Aout[j,l]+=Xi*C[j]*C[l] 1116 return Aout 1117 elif name == "B" : 1118 B=self.getCoefficient("B") 1119 C=self.getCoefficient("C") 1120 D=self.getCoefficient("D") 1121 if C.isEmpty() or D.isEmpty(): 1122 Bout=B 1123 else: 1124 Xi=self.getXi() 1125 if B.isEmpty(): 1126 Bout=self.createNewCoefficient("B") 1127 else: 1128 Bout=B[:] 1129 if self.getNumEquations()>1: 1130 for k in range(self.getNumSolutions()): 1131 for p in range(self.getNumEquations()): 1132 tmp=Xi*D[p,k] 1133 for i in range(self.getNumEquations()): 1134 for j in range(self.getDim()): 1135 Bout[i,j,k]+=tmp*C[p,i,j] 1136 else: 1137 tmp=Xi*D 1138 for j in range(self.getDim()): Bout[j]+=tmp*C[j] 1139 return Bout 1140 elif name == "C" : 1141 B=self.getCoefficient("B") 1142 C=self.getCoefficient("C") 1143 D=self.getCoefficient("D") 1144 if B.isEmpty() or D.isEmpty(): 1145 Cout=C 1146 else: 1147 Xi=self.getXi() 1148 if C.isEmpty(): 1149 Cout=self.createNewCoefficient("C") 1150 else: 1151 Cout=C[:] 1152 if self.getNumEquations()>1: 1153 for k in range(self.getNumSolutions()): 1154 for p in range(self.getNumEquations()): 1155 tmp=Xi*D[p,k] 1156 for i in range(self.getNumEquations()): 1157 for l in range(self.getDim()): 1158 Cout[i,k,l]+=tmp*B[p,l,i] 1159 else: 1160 tmp=Xi*D 1161 for j in range(self.getDim()): Cout[j]+=tmp*B[j] 1162 return Cout 1163 elif name == "D" : 1164 return self.getCoefficient("D") 1165 elif name == "X" : 1166 X=self.getCoefficient("X") 1167 Y=self.getCoefficient("Y") 1168 B=self.getCoefficient("B") 1169 C=self.getCoefficient("C") 1170 if Y.isEmpty() or (B.isEmpty() and C.isEmpty()): 1171 Xout=X 1172 else: 1173 if X.isEmpty(): 1174 Xout=self.createNewCoefficient("X") 1175 else: 1176 Xout=X[:] 1177 Xi=self.getXi() 1178 if self.getNumEquations()>1: 1179 for p in range(self.getNumEquations()): 1180 tmp=Xi*Y[p] 1181 for i in range(self.getNumEquations()): 1182 for j in range(self.getDim()): 1183 if not C.isEmpty() and not B.isEmpty(): 1184 Xout[i,j]+=tmp*(C[p,i,j]-B[p,j,i]) 1185 elif C.isEmpty(): 1186 Xout[i,j]-=tmp*B[p,j,i] 1187 else: 1188 Xout[i,j]+=tmp*C[p,i,j] 1189 else: 1190 tmp=Xi*Y 1191 for j in range(self.getDim()): 1192 if not C.isEmpty() and not B.isEmpty(): 1193 Xout[j]+=tmp*(C[j]-B[j]) 1194 elif C.isEmpty(): 1195 Xout[j]-=tmp*B[j] 1196 else: 1197 Xout[j]+=tmp*C[j] 1198 return Xout 1199 elif name == "Y" : 1200 return self.getCoefficient("Y") 1201 elif name == "d" : 1202 return self.getCoefficient("d") 1203 elif name == "y" : 1204 return self.getCoefficient("y") 1205 elif name == "d_contact" : 1206 return self.getCoefficient("d_contact") 1207 elif name == "y_contact" : 1208 return self.getCoefficient("y_contact") 1209 elif name == "r" : 1210 return self.getCoefficient("r") 1211 elif name == "q" : 1212 return self.getCoefficient("q") 1213 else: 1214 raise SystemError,"unknown PDE coefficient %s",name 1215 1216 1217 class Poisson(LinearPDE): 1218 """ 1219 @brief Class to define a Poisson equstion problem: 1220 1221 class to define a linear PDE of the form 1222 1223 -u_{,jj} = f 1224 1225 with boundary conditons: 1226 1227 n_j*u_{,j} = 0 1228 1229 and constraints: 1230 1231 u=0 where q>0 1232 1233 """ 1234 1235 def __init__(self,domain,f=escript.Data(),q=escript.Data()): 1236 LinearPDE.__init__(self,domain,1,1) 1237 self.COEFFICIENTS={ 1238 "f" : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE), 1239 "q" : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.BOTH)} 1240 self.setSymmetryOn() 1241 self.setValue(f,q) 1242 1243 def setValue(self,f=escript.Data(),q=escript.Data()): 1244 self._setValue(f=f,q=q) 1245 1246 def getCoefficientOfPDE(self,name): 1247 """ 1248 @brief return the value of the coefficient name of the general PDE 1249 @param name 1250 """ 1251 if name == "A" : 1252 return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain())) 1253 elif name == "B" : 1254 return escript.Data() 1255 elif name == "C" : 1256 return escript.Data() 1257 elif name == "D" : 1258 return escript.Data() 1259 elif name == "X" : 1260 return escript.Data() 1261 elif name == "Y" : 1262 return self.getCoefficient("f") 1263 elif name == "d" : 1264 return escript.Data() 1265 elif name == "y" : 1266 return escript.Data() 1267 elif name == "d_contact" : 1268 return escript.Data() 1269 elif name == "y_contact" : 1270 return escript.Data() 1271 elif name == "r" : 1272 return escript.Data() 1273 elif name == "q" : 1274 return self.getCoefficient("q") 1275 else: 1276 raise SystemError,"unknown PDE coefficient %s",name

## Properties

Name Value
svn:eol-style native
svn:keywords Author Date Id Revision