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trunk/esys2/escript/py_src/linearPDEs.py revision 148 by jgs, Tue Aug 23 01:24:31 2005 UTC trunk/escript/py_src/linearPDEs.py revision 1809 by ksteube, Thu Sep 25 06:43:44 2008 UTC
# Line 1  Line 1 
 # $Id$  
1    
2  ## @file linearPDEs.py  ########################################################
3    #
4    # Copyright (c) 2003-2008 by University of Queensland
5    # Earth Systems Science Computational Center (ESSCC)
6    # http://www.uq.edu.au/esscc
7    #
8    # Primary Business: Queensland, Australia
9    # Licensed under the Open Software License version 3.0
10    # http://www.opensource.org/licenses/osl-3.0.php
11    #
12    ########################################################
13    
14    __copyright__="""Copyright (c) 2003-2008 by University of Queensland
15    Earth Systems Science Computational Center (ESSCC)
16    http://www.uq.edu.au/esscc
17    Primary Business: Queensland, Australia"""
18    __license__="""Licensed under the Open Software License version 3.0
19    http://www.opensource.org/licenses/osl-3.0.php"""
20    __url__="http://www.uq.edu.au/esscc/escript-finley"
21    
22  """  """
23  Functions and classes for linear PDEs  The module provides an interface to define and solve linear partial
24    differential equations (PDEs) within L{escript}. L{linearPDEs} does not provide any
25    solver capabilities in itself but hands the PDE over to
26    the PDE solver library defined through the L{Domain<escript.Domain>} of the PDE.
27    The general interface is provided through the L{LinearPDE} class. The
28    L{AdvectivePDE} which is derived from the L{LinearPDE} class
29    provides an interface to PDE dominated by its advective terms. The L{Poisson},
30    L{Helmholtz}, L{LameEquation}, L{AdvectivePDE}
31    classs which are also derived form the L{LinearPDE} class should be used
32    to define of solve these sepecial PDEs.
33    
34    @var __author__: name of author
35    @var __copyright__: copyrights
36    @var __license__: licence agreement
37    @var __url__: url entry point on documentation
38    @var __version__: version
39    @var __date__: date of the version
40  """  """
41    
42    import math
43  import escript  import escript
44  import util  import util
45  import numarray  import numarray
46    
47    __author__="Lutz Gross, l.gross@uq.edu.au"
48    
49    
50  class IllegalCoefficient(ValueError):  class IllegalCoefficient(ValueError):
51     """     """
52     raised if an illegal coefficient of the general ar particular PDE is requested.     raised if an illegal coefficient of the general ar particular PDE is requested.
53     """     """
54       pass
55    
56  class IllegalCoefficientValue(ValueError):  class IllegalCoefficientValue(ValueError):
57     """     """
58     raised if an incorrect value for a coefficient is used.     raised if an incorrect value for a coefficient is used.
59     """     """
60       pass
61    
62    class IllegalCoefficientFunctionSpace(ValueError):
63       """
64       raised if an incorrect function space for a coefficient is used.
65       """
66    
67  class UndefinedPDEError(ValueError):  class UndefinedPDEError(ValueError):
68     """     """
69     raised if a PDE is not fully defined yet.     raised if a PDE is not fully defined yet.
70     """     """
71       pass
72    
73  def _CompTuple2(t1,t2):  class PDECoefficient(object):
       """  
       Compare two tuples  
     
       @param t1 The first tuple  
       @param t2 The second tuple  
     
       """  
     
       dif=t1[0]+t1[1]-(t2[0]+t2[1])  
       if dif<0: return 1  
       elif dif>0: return -1  
       else: return 0  
     
 class PDECoefficient:  
74      """      """
75      A class for PDE coefficients      A class for describing a PDE coefficient
76    
77        @cvar INTERIOR: indicator that coefficient is defined on the interior of the PDE domain
78        @cvar BOUNDARY: indicator that coefficient is defined on the boundary of the PDE domain
79        @cvar CONTACT: indicator that coefficient is defined on the contact region within the PDE domain
80        @cvar INTERIOR_REDUCED: indicator that coefficient is defined on the interior of the PDE domain using a reduced integration order
81        @cvar BOUNDARY_REDUCED: indicator that coefficient is defined on the boundary of the PDE domain using a reduced integration order
82        @cvar CONTACT_REDUCED: indicator that coefficient is defined on the contact region within the PDE domain using a reduced integration order
83        @cvar SOLUTION: indicator that coefficient is defined trough a solution of the PDE
84        @cvar REDUCED: indicator that coefficient is defined trough a reduced solution of the PDE
85        @cvar BY_EQUATION: indicator that the dimension of the coefficient shape is defined by the number PDE equations
86        @cvar BY_SOLUTION: indicator that the dimension of the coefficient shape is defined by the number PDE solutions
87        @cvar BY_DIM: indicator that the dimension of the coefficient shape is defined by the spatial dimension
88        @cvar OPERATOR: indicator that the the coefficient alters the operator of the PDE
89        @cvar RIGHTHANDSIDE: indicator that the the coefficient alters the right hand side of the PDE
90        @cvar BOTH: indicator that the the coefficient alters the operator as well as the right hand side of the PDE
91    
92      """      """
     # identifier for location of Data objects defining COEFFICIENTS  
93      INTERIOR=0      INTERIOR=0
94      BOUNDARY=1      BOUNDARY=1
95      CONTACT=2      CONTACT=2
96      CONTINUOUS=3      SOLUTION=3
97      # identifier in the pattern of COEFFICIENTS:      REDUCED=4
98      # the pattern is a tuple of EQUATION,SOLUTION,DIM where DIM represents the spatial dimension, EQUATION the number of equations and SOLUTION the      BY_EQUATION=5
99      # number of unknowns.      BY_SOLUTION=6
100      EQUATION=3      BY_DIM=7
101      SOLUTION=4      OPERATOR=10
102      DIM=5      RIGHTHANDSIDE=11
103      # indicator for what is altered if the coefficient is altered:      BOTH=12
104      OPERATOR=5      INTERIOR_REDUCED=13
105      RIGHTHANDSIDE=6      BOUNDARY_REDUCED=14
106      BOTH=7      CONTACT_REDUCED=15
107      def __init__(self,where,pattern,altering):  
108        def __init__(self, where, pattern, altering):
109         """         """
110         Initialise a PDE Coefficient type         Initialise a PDE Coefficient type
111    
112           @param where: describes where the coefficient lives
113           @type where: one of L{INTERIOR}, L{BOUNDARY}, L{CONTACT}, L{SOLUTION}, L{REDUCED},
114                               L{INTERIOR_REDUCED}, L{BOUNDARY_REDUCED}, L{CONTACT_REDUCED}.
115           @param pattern: describes the shape of the coefficient and how the shape is build for a given
116                  spatial dimension and numbers of equation and solution in then PDE. For instance,
117                  (L{BY_EQUATION},L{BY_SOLUTION},L{BY_DIM}) descrbes a rank 3 coefficient which
118                  is instanciated as shape (3,2,2) in case of a three equations and two solution components
119                  on a 2-dimensional domain. In the case of single equation and a single solution component
120                  the shape compoments marked by L{BY_EQUATION} or L{BY_SOLUTION} are dropped. In this case
121                  the example would be read as (2,).
122           @type pattern: C{tuple} of L{BY_EQUATION}, L{BY_SOLUTION}, L{BY_DIM}
123           @param altering: indicates what part of the PDE is altered if the coefficiennt is altered
124           @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}
125           @param reduced: indicates if reduced
126           @type reduced: C{bool}
127         """         """
128           super(PDECoefficient, self).__init__()
129         self.what=where         self.what=where
130         self.pattern=pattern         self.pattern=pattern
131         self.altering=altering         self.altering=altering
# Line 74  class PDECoefficient: Line 137  class PDECoefficient:
137         """         """
138         self.value=escript.Data()         self.value=escript.Data()
139    
140      def getFunctionSpace(self,domain):      def getFunctionSpace(self,domain,reducedEquationOrder=False,reducedSolutionOrder=False):
141         """         """
142         defines the FunctionSpace of the coefficient on the domain         defines the L{FunctionSpace<escript.FunctionSpace>} of the coefficient
143    
144         @param domain:         @param domain: domain on which the PDE uses the coefficient
145         """         @type domain: L{Domain<escript.Domain>}
146         if self.what==self.INTERIOR: return escript.Function(domain)         @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
147         elif self.what==self.BOUNDARY: return escript.FunctionOnBoundary(domain)         @type reducedEquationOrder: C{bool}
148         elif self.what==self.CONTACT: return escript.FunctionOnContactZero(domain)         @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
149         elif self.what==self.CONTINUOUS: return escript.ContinuousFunction(domain)         @type reducedSolutionOrder: C{bool}
150           @return:  L{FunctionSpace<escript.FunctionSpace>} of the coefficient
151           @rtype:  L{FunctionSpace<escript.FunctionSpace>}
152           """
153           if self.what==self.INTERIOR:
154                return escript.Function(domain)
155           elif self.what==self.INTERIOR_REDUCED:
156                return escript.ReducedFunction(domain)
157           elif self.what==self.BOUNDARY:
158                return escript.FunctionOnBoundary(domain)
159           elif self.what==self.BOUNDARY_REDUCED:
160                return escript.ReducedFunctionOnBoundary(domain)
161           elif self.what==self.CONTACT:
162                return escript.FunctionOnContactZero(domain)
163           elif self.what==self.CONTACT_REDUCED:
164                return escript.ReducedFunctionOnContactZero(domain)
165           elif self.what==self.SOLUTION:
166                if reducedEquationOrder and reducedSolutionOrder:
167                    return escript.ReducedSolution(domain)
168                else:
169                    return escript.Solution(domain)
170           elif self.what==self.REDUCED:
171                return escript.ReducedSolution(domain)
172    
173      def getValue(self):      def getValue(self):
174         """         """
175         returns the value of the coefficient:         returns the value of the coefficient
176    
177           @return:  value of the coefficient
178           @rtype:  L{Data<escript.Data>}
179         """         """
180         return self.value         return self.value
181    
182      def setValue(self,domain,numEquations=1,numSolutions=1,newValue=None):      def setValue(self,domain,numEquations=1,numSolutions=1,reducedEquationOrder=False,reducedSolutionOrder=False,newValue=None):
183         """         """
184         set the value of the coefficient to new value         set the value of the coefficient to a new value
185    
186           @param domain: domain on which the PDE uses the coefficient
187           @type domain: L{Domain<escript.Domain>}
188           @param numEquations: number of equations of the PDE
189           @type numEquations: C{int}
190           @param numSolutions: number of components of the PDE solution
191           @type numSolutions: C{int}
192           @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
193           @type reducedEquationOrder: C{bool}
194           @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
195           @type reducedSolutionOrder: C{bool}
196           @param newValue: number of components of the PDE solution
197           @type newValue: any object that can be converted into a L{Data<escript.Data>} object with the appropriate shape and L{FunctionSpace<escript.FunctionSpace>}
198           @raise IllegalCoefficientValue: if the shape of the assigned value does not match the shape of the coefficient
199           @raise IllegalCoefficientFunctionSpace: if unable to interploate value to appropriate function space
200         """         """
201         if newValue==None:         if newValue==None:
202             newValue=escript.Data()             newValue=escript.Data()
203         elif isinstance(newValue,escript.Data):         elif isinstance(newValue,escript.Data):
204             if not newValue.isEmpty():             if not newValue.isEmpty():
205                newValue=escript.Data(newValue,self.getFunctionSpace(domain))                if not newValue.getFunctionSpace() == self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder):
206                    try:
207                      newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
208                    except:
209                      raise IllegalCoefficientFunctionSpace,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)
210         else:         else:
211             newValue=escript.Data(newValue,self.getFunctionSpace(domain))             newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
212         if not newValue.isEmpty():         if not newValue.isEmpty():
213             if not self.getShape(domain,numEquations,numSolutions)==newValue.getShape():             if not self.getShape(domain,numEquations,numSolutions)==newValue.getShape():
214                 raise IllegalCoefficientValue,"Expected shape for coefficient %s is %s but actual shape is %s."%(self.getShape(domain,numEquations,numSolutions),newValue.getShape())                 raise IllegalCoefficientValue,"Expected shape of coefficient is %s but actual shape is %s."%(self.getShape(domain,numEquations,numSolutions),newValue.getShape())
215         self.value=newValue         self.value=newValue
216    
217      def isAlteringOperator(self):      def isAlteringOperator(self):
218          """          """
219      return true if the operator of the PDE is changed when the coefficient is changed          checks if the coefficient alters the operator of the PDE
220    
221            @return:  True if the operator of the PDE is changed when the coefficient is changed
222            @rtype:  C{bool}
223      """      """
224          if self.altering==self.OPERATOR or self.altering==self.BOTH:          if self.altering==self.OPERATOR or self.altering==self.BOTH:
225              return not None              return not None
# Line 118  class PDECoefficient: Line 228  class PDECoefficient:
228    
229      def isAlteringRightHandSide(self):      def isAlteringRightHandSide(self):
230          """          """
231      return true if the right hand side of the PDE is changed when the coefficient is changed          checks if the coefficeint alters the right hand side of the PDE
232    
233        @rtype:  C{bool}
234            @return:  True if the right hand side of the PDE is changed when the coefficient is changed
235      """      """
236          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:
237              return not None              return not None
# Line 127  class PDECoefficient: Line 240  class PDECoefficient:
240    
241      def estimateNumEquationsAndNumSolutions(self,domain,shape=()):      def estimateNumEquationsAndNumSolutions(self,domain,shape=()):
242         """         """
243         tries to estimate the number of equations in a given tensor shape for a given spatial dimension dim         tries to estimate the number of equations and number of solutions if the coefficient has the given shape
244    
245         @param shape:         @param domain: domain on which the PDE uses the coefficient
246         @param dim:         @type domain: L{Domain<escript.Domain>}
247           @param shape: suggested shape of the coefficient
248           @type shape: C{tuple} of C{int} values
249           @return: the number of equations and number of solutions of the PDE is the coefficient has shape s.
250                     If no appropriate numbers could be identified, C{None} is returned
251           @rtype: C{tuple} of two C{int} values or C{None}
252         """         """
253         dim=domain.getDim()         dim=domain.getDim()
254         if len(shape)>0:         if len(shape)>0:
# Line 138  class PDECoefficient: Line 256  class PDECoefficient:
256         else:         else:
257             num=1             num=1
258         search=[]         search=[]
259         for u in range(num):         if self.definesNumEquation() and self.definesNumSolutions():
260            for e in range(num):            for u in range(num):
261               search.append((e,u))               for e in range(num):
262         search.sort(_CompTuple2)                  search.append((e,u))
263         for item in search:            search.sort(self.__CompTuple2)
264              for item in search:
265               s=self.getShape(domain,item[0],item[1])               s=self.getShape(domain,item[0],item[1])
266               if len(s)==0 and len(shape)==0:               if len(s)==0 and len(shape)==0:
267                   return (1,1)                   return (1,1)
268               else:               else:
269                   if s==shape: return item                   if s==shape: return item
270           elif self.definesNumEquation():
271              for e in range(num,0,-1):
272                 s=self.getShape(domain,e,0)
273                 if len(s)==0 and len(shape)==0:
274                     return (1,None)
275                 else:
276                     if s==shape: return (e,None)
277    
278           elif self.definesNumSolutions():
279              for u in range(num,0,-1):
280                 s=self.getShape(domain,0,u)
281                 if len(s)==0 and len(shape)==0:
282                     return (None,1)
283                 else:
284                     if s==shape: return (None,u)
285         return None         return None
286        def definesNumSolutions(self):
287           """
288           checks if the coefficient allows to estimate the number of solution components
289    
290           @return: True if the coefficient allows an estimate of the number of solution components
291           @rtype: C{bool}
292           """
293           for i in self.pattern:
294                 if i==self.BY_SOLUTION: return True
295           return False
296    
297        def definesNumEquation(self):
298           """
299           checks if the coefficient allows to estimate the number of equations
300    
301           @return: True if the coefficient allows an estimate of the number of equations
302           @rtype: C{bool}
303           """
304           for i in self.pattern:
305                 if i==self.BY_EQUATION: return True
306           return False
307    
308        def __CompTuple2(self,t1,t2):
309          """
310          Compare two tuples of possible number of equations and number of solutions
311    
312          @param t1: The first tuple
313          @param t2: The second tuple
314    
315          """
316    
317          dif=t1[0]+t1[1]-(t2[0]+t2[1])
318          if dif<0: return 1
319          elif dif>0: return -1
320          else: return 0
321    
322      def getShape(self,domain,numEquations=1,numSolutions=1):      def getShape(self,domain,numEquations=1,numSolutions=1):
323          """         """
324      builds the required shape for a given number of equations e, number of unknowns u and spatial dimension dim         builds the required shape of the coefficient
325    
326      @param e:         @param domain: domain on which the PDE uses the coefficient
327      @param u:         @type domain: L{Domain<escript.Domain>}
328      @param dim:         @param numEquations: number of equations of the PDE
329      """         @type numEquations: C{int}
330          dim=domain.getDim()         @param numSolutions: number of components of the PDE solution
331          s=()         @type numSolutions: C{int}
332          for i in self.pattern:         @return: shape of the coefficient
333               if i==self.EQUATION:         @rtype: C{tuple} of C{int} values
334           """
335           dim=domain.getDim()
336           s=()
337           for i in self.pattern:
338                 if i==self.BY_EQUATION:
339                  if numEquations>1: s=s+(numEquations,)                  if numEquations>1: s=s+(numEquations,)
340               elif i==self.SOLUTION:               elif i==self.BY_SOLUTION:
341                  if numSolutions>1: s=s+(numSolutions,)                  if numSolutions>1: s=s+(numSolutions,)
342               else:               else:
343                  s=s+(dim,)                  s=s+(dim,)
344          return s         return s
345    
346  class LinearPDE:  class LinearPDE(object):
347     """     """
348     Class to define a linear PDE of the form     This class is used to define a general linear, steady, second order PDE
349       for an unknown function M{u} on a given domain defined through a L{Domain<escript.Domain>} object.
350    
351     \f[     For a single PDE with a solution with a single component the linear PDE is defined in the following form:
      -(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  
    \f]  
352    
353     with boundary conditons:     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)}
354    
    \f[  
    n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i  
    \f]  
355    
356     and contact conditions     where M{grad(F)} denotes the spatial derivative of M{F}. Einstein's summation convention,
357       ie. summation over indexes appearing twice in a term of a sum is performed, is used.
358       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
359       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
360       L{ReducedFunction<escript.ReducedFunction>}. It is also allowd to use objects that can be converted into
361       such L{Data<escript.Data>} objects. M{A} and M{A_reduced} are rank two, M{B_reduced}, M{C_reduced}, M{X_reduced}
362       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.
363    
364     \f[     The following natural boundary conditions are considered:
    n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_contact_{ik}[u_k] = - n_j*X_{ij} + y_contact_i  
    \f]  
365    
366     and constraints:     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}
367    
368       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>}.
369    
370    
371       Constraints for the solution prescribing the value of the solution at certain locations in the domain. They have the form
372    
373       M{u=r}  where M{q>0}
374    
375       M{r} and M{q} are each scalar where M{q} is the characteristic function defining where the constraint is applied.
376       The constraints override any other condition set by the PDE or the boundary condition.
377    
378       The PDE is symmetrical if
379    
380       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]}
381    
382       For a system of PDEs and a solution with several components the PDE has the form
383    
384       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] }
385    
386       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.
387       The natural boundary conditions take the form:
388    
389       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]}
390    
391    
392       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>}.
393    
394       Constraints take the form
395    
396       M{u[i]=r[i]}  where  M{q[i]>0}
397    
398       M{r} and M{q} are each rank one. Notice that at some locations not necessarily all components must have a constraint.
399    
400       The system of PDEs is symmetrical if
401    
402            - M{A[i,j,k,l]=A[k,l,i,j]}
403            - M{A_reduced[i,j,k,l]=A_reduced[k,l,i,j]}
404            - M{B[i,j,k]=C[k,i,j]}
405            - M{B_reduced[i,j,k]=C_reduced[k,i,j]}
406            - M{D[i,k]=D[i,k]}
407            - M{D_reduced[i,k]=D_reduced[i,k]}
408            - M{d[i,k]=d[k,i]}
409            - M{d_reduced[i,k]=d_reduced[k,i]}
410    
411       L{LinearPDE} also supports solution discontinuities over a contact region in the domain. To specify the conditions across the
412       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
413       defined as
414    
415       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]}
416    
417       For the case of single solution component and single PDE M{J} is defined
418    
419       M{J_{j}=(A[i,j]+A_reduced[i,j])*grad(u)[j]+(B[i]+B_reduced[i])*u-X[i]-X_reduced[i]}
420    
421     \f[     In the context of discontinuities M{n} denotes the normal on the discontinuity pointing from side 0 towards side 1
422     u_i=r_i \quad \mathrm{where} \quad q_i>0     calculated from L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnContactZero<escript.FunctionOnContactZero>}. For a system of PDEs
423     \f]     the contact condition takes the form
424    
425       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]}
426    
427       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
428       of the solution at side 1 and at side 0, denotes the jump of M{u} across discontinuity along the normal calcualted by
429       L{jump<util.jump>}.
430       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>}.
431       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>}.
432       In case of a single PDE and a single component solution the contact condition takes the form
433    
434       M{n[j]*J0_{j}=n[j]*J1_{j}=(y_contact+y_contact_reduced)-(d_contact+y_contact_reduced)*jump(u)}
435    
436       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>}
437    
438       @cvar DEFAULT: The default method used to solve the system of linear equations
439       @cvar DIRECT: The direct solver based on LDU factorization
440       @cvar CHOLEVSKY: The direct solver based on LDLt factorization (can only be applied for symmetric PDEs)
441       @cvar PCG: The preconditioned conjugate gradient method (can only be applied for symmetric PDEs)
442       @cvar CR: The conjugate residual method
443       @cvar CGS: The conjugate gardient square method
444       @cvar BICGSTAB: The stabilized BiConjugate Gradient method.
445       @cvar TFQMR: Transport Free Quasi Minimal Residual method.
446       @cvar MINRES: Minimum residual 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     TOL=1.e-13     DEFAULT= 0
468     # solver methods     DIRECT= 1
469     UNKNOWN=-1     CHOLEVSKY= 2
470     DEFAULT_METHOD=0     PCG= 3
471     DIRECT=1     CR= 4
472     CHOLEVSKY=2     CGS= 5
473     PCG=3     BICGSTAB= 6
474     CR=4     SSOR= 7
475     CGS=5     ILU0= 8
476     BICGSTAB=6     ILUT= 9
477     SSOR=7     JACOBI= 10
478     ILU0=8     GMRES= 11
479     ILUT=9     PRES20= 12
480     JACOBI=10     LUMPING= 13
481     GMRES=11     NO_REORDERING= 17
482     PRES20=12     MINIMUM_FILL_IN= 18
483     LUMPING=13     NESTED_DISSECTION= 19
484     # matrix reordering:     SCSL= 14
485     NO_REORDERING=0     MKL= 15
486     MINIMUM_FILL_IN=1     UMFPACK= 16
487     NESTED_DISSECTION=2     ITERATIVE= 20
488     # important keys in the dictonary used to hand over options to the solver library:     PASO= 21
489     METHOD_KEY="method"     AMG= 22
490     SYMMETRY_KEY="symmetric"     RILU = 23
491     TOLERANCE_KEY="tolerance"     TRILINOS = 24
492       NONLINEAR_GMRES = 25
493       TFQMR = 26
494       MINRES = 27
495    
496       SMALL_TOLERANCE=1.e-13
497       __PACKAGE_KEY="package"
498       __METHOD_KEY="method"
499       __SYMMETRY_KEY="symmetric"
500       __TOLERANCE_KEY="tolerance"
501       __PRECONDITIONER_KEY="preconditioner"
502    
503    
504     def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):     def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):
# Line 228  class LinearPDE: Line 506  class LinearPDE:
506       initializes a new linear PDE       initializes a new linear PDE
507    
508       @param domain: domain of the PDE       @param domain: domain of the PDE
509       @type domain: L{Domain}       @type domain: L{Domain<escript.Domain>}
510       @param numEquations: number of equations. If numEquations==None the number of equations       @param numEquations: number of equations. If numEquations==None the number of equations
511                            is exracted from the PDE coefficients.                            is exracted from the PDE coefficients.
512       @param numSolutions: number of solution components. If  numSolutions==None the number of solution components       @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
513                            is exracted from the PDE coefficients.                            is exracted from the PDE coefficients.
514       @param debug: if True debug informations are printed.       @param debug: if True debug informations are printed.
515    
   
516       """       """
517         super(LinearPDE, self).__init__()
518       #       #
519       #   the coefficients of the general PDE:       #   the coefficients of the general PDE:
520       #       #
521       self.__COEFFICIENTS_OF_GENEARL_PDE={       self.__COEFFICIENTS_OF_GENEARL_PDE={
522         "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM,PDECoefficient.SOLUTION,PDECoefficient.DIM),PDECoefficient.OPERATOR),         "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
523         "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),         "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
524         "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION,PDECoefficient.DIM),PDECoefficient.OPERATOR),         "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
525         "D"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),         "D"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
526         "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM),PDECoefficient.RIGHTHANDSIDE),         "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
527         "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),         "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
528         "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),         "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
529         "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),         "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
530         "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),         "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
531         "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),         "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
532         "r"         : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),         "A_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
533         "q"         : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.SOLUTION,),PDECoefficient.BOTH)}         "B_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
534           "C_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
535           "D_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
536           "X_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
537           "Y_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
538           "d_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
539           "y_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
540           "d_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
541           "y_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
542           "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
543           "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
544    
545       # COEFFICIENTS can be overwritten by subclasses:       # COEFFICIENTS can be overwritten by subclasses:
546       self.COEFFICIENTS=self.__COEFFICIENTS_OF_GENEARL_PDE       self.COEFFICIENTS=self.__COEFFICIENTS_OF_GENEARL_PDE
547         self.__altered_coefficients=False
548       # initialize attributes       # initialize attributes
549       self.__debug=debug       self.__debug=debug
550       self.__domain=domain       self.__domain=domain
# Line 264  class LinearPDE: Line 553  class LinearPDE:
553       self.__resetSystem()       self.__resetSystem()
554    
555       # set some default values:       # set some default values:
556       self.__homogeneous_constraint=True       self.__reduce_equation_order=False
557       self.__row_function_space=escript.Solution(self.__domain)       self.__reduce_solution_order=False
      self.__column_function_space=escript.Solution(self.__domain)  
558       self.__tolerance=1.e-8       self.__tolerance=1.e-8
559       self.__solver_method=self.DEFAULT_METHOD       self.__solver_method=self.DEFAULT
560       self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT_METHOD,False)       self.__solver_package=self.DEFAULT
561         self.__preconditioner=self.DEFAULT
562         self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT,self.DEFAULT,False)
563       self.__sym=False       self.__sym=False
564    
565       self.resetCoefficients()       self.resetCoefficients()
# Line 278  class LinearPDE: Line 568  class LinearPDE:
568     #    general stuff:     #    general stuff:
569     # =============================================================================     # =============================================================================
570     def __str__(self):     def __str__(self):
571         return "<LinearPDE %d>"%id(self)       """
572         returns string representation of the PDE
573    
574         @return: a simple representation of the PDE
575         @rtype: C{str}
576         """
577         return "<LinearPDE %d>"%id(self)
578     # =============================================================================     # =============================================================================
579     #    debug :     #    debug :
580     # =============================================================================     # =============================================================================
581     def setDebugOn(self):     def setDebugOn(self):
582       """       """
583       switches on debugging       switches on debugging
584       """       """
585       self.__debug=not None       self.__debug=not None
# Line 296  class LinearPDE: Line 592  class LinearPDE:
592    
593     def trace(self,text):     def trace(self,text):
594       """       """
595       print the text message if debugging is swiched on.       print the text message if debugging is swiched on.
596         @param text: message
597       @param name: name of the coefficient enquired.       @type text: C{string}
      @type name: C{string}  
598       """       """
599       if self.__debug: print "%s: %s"%(str(self),text)       if self.__debug: print "%s: %s"%(str(self),text)
600    
# Line 309  class LinearPDE: Line 604  class LinearPDE:
604     def getDomain(self):     def getDomain(self):
605       """       """
606       returns the domain of the PDE       returns the domain of the PDE
       
      @return : the domain of the PDE  
      @rtype : C{Domain}  
607    
608         @return: the domain of the PDE
609         @rtype: L{Domain<escript.Domain>}
610       """       """
611       return self.__domain       return self.__domain
612    
# Line 320  class LinearPDE: Line 614  class LinearPDE:
614       """       """
615       returns the spatial dimension of the PDE       returns the spatial dimension of the PDE
616    
617       @return : the spatial dimension of the PDE domain       @return: the spatial dimension of the PDE domain
618       @rtype : C{int}       @rtype: C{int}
619       """       """
620       return self.getDomain().getDim()       return self.getDomain().getDim()
621    
# Line 329  class LinearPDE: Line 623  class LinearPDE:
623       """       """
624       returns the number of equations       returns the number of equations
625    
626       @return : the number of equations       @return: the number of equations
627       @rtype : C{int}       @rtype: C{int}
628       @raise UndefinedPDEError: if the number of equations is not be specified yet.       @raise UndefinedPDEError: if the number of equations is not be specified yet.
629       """       """
630       if self.__numEquations==None:       if self.__numEquations==None:
# Line 342  class LinearPDE: Line 636  class LinearPDE:
636       """       """
637       returns the number of unknowns       returns the number of unknowns
638    
639       @return : the number of unknowns       @return: the number of unknowns
640       @rtype : C{int}       @rtype: C{int}
641       @raise UndefinedPDEError: if the number of unknowns is not be specified yet.       @raise UndefinedPDEError: if the number of unknowns is not be specified yet.
642       """       """
643       if self.__numSolutions==None:       if self.__numSolutions==None:
# Line 351  class LinearPDE: Line 645  class LinearPDE:
645       else:       else:
646          return self.__numSolutions          return self.__numSolutions
647    
648       def reduceEquationOrder(self):
649         """
650         return status for order reduction for equation
651    
652         @return: return True is reduced interpolation order is used for the represenation of the equation
653         @rtype: L{bool}
654         """
655         return self.__reduce_equation_order
656    
657       def reduceSolutionOrder(self):
658         """
659         return status for order reduction for the solution
660    
661         @return: return True is reduced interpolation order is used for the represenation of the solution
662         @rtype: L{bool}
663         """
664         return self.__reduce_solution_order
665    
666     def getFunctionSpaceForEquation(self):     def getFunctionSpaceForEquation(self):
667       """       """
668       returns the L{escript.FunctionSpace} used to discretize the equation       returns the L{FunctionSpace<escript.FunctionSpace>} used to discretize the equation
       
      @return : representation space of equation  
      @rtype : L{escript.FunctionSpace}  
669    
670         @return: representation space of equation
671         @rtype: L{FunctionSpace<escript.FunctionSpace>}
672       """       """
673       return self.__row_function_space       if self.reduceEquationOrder():
674             return escript.ReducedSolution(self.getDomain())
675         else:
676             return escript.Solution(self.getDomain())
677    
678     def getFunctionSpaceForSolution(self):     def getFunctionSpaceForSolution(self):
679       """       """
680       returns the L{escript.FunctionSpace} used to represent the solution       returns the L{FunctionSpace<escript.FunctionSpace>} used to represent the solution
       
      @return : representation space of solution  
      @rtype : L{escript.FunctionSpace}  
681    
682         @return: representation space of solution
683         @rtype: L{FunctionSpace<escript.FunctionSpace>}
684       """       """
685       return self.__column_function_space       if self.reduceSolutionOrder():
686             return escript.ReducedSolution(self.getDomain())
687         else:
688             return escript.Solution(self.getDomain())
689    
690    
691     def getOperator(self):     def getOperator(self):
692       """       """
693       provides access to the operator of the PDE       provides access to the operator of the PDE
694    
695       @return : the operator of the PDE       @return: the operator of the PDE
696       @rtype : L{Operator}       @rtype: L{Operator<escript.Operator>}
697       """       """
698       m=self.getSystem()[0]       m=self.getSystem()[0]
699       if self.isUsingLumping():       if self.isUsingLumping():
# Line 388  class LinearPDE: Line 704  class LinearPDE:
704     def getRightHandSide(self):     def getRightHandSide(self):
705       """       """
706       provides access to the right hand side of the PDE       provides access to the right hand side of the PDE
707         @return: the right hand side of the PDE
708       @return : the right hand side of the PDE       @rtype: L{Data<escript.Data>}
      @rtype : L{escript.Data}  
709       """       """
710       r=self.getSystem()[1]       r=self.getSystem()[1]
711       if self.isUsingLumping():       if self.isUsingLumping():
# Line 404  class LinearPDE: Line 719  class LinearPDE:
719    
720       @param u: argument of the operator. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}       @param u: argument of the operator. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
721                 the current solution is used.                 the current solution is used.
722       @type u: L{escript.Data} or None       @type u: L{Data<escript.Data>} or None
723       @return : image of u       @return: image of u
724       @rtype : L{escript.Data}       @rtype: L{Data<escript.Data>}
725       """       """
726       if u==None:       if u==None:
727            return self.getOperator()*self.getSolution()          return self.getOperator()*self.getSolution()
728       else:       else:
729          self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())          return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
730    
731     def getResidual(self,u=None):     def getResidual(self,u=None):
732       """       """
# Line 419  class LinearPDE: Line 734  class LinearPDE:
734    
735       @param u: argument in the residual calculation. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}       @param u: argument in the residual calculation. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
736                 the current solution is used.                 the current solution is used.
737       @type u: L{escript.Data} or None       @type u: L{Data<escript.Data>} or None
738       @return : residual of u       @return: residual of u
739       @rtype : L{escript.Data}       @rtype: L{Data<escript.Data>}
740       """       """
741       return self.applyOperator(u)-self.getRightHandSide()       return self.applyOperator(u)-self.getRightHandSide()
742    
# Line 429  class LinearPDE: Line 744  class LinearPDE:
744        """        """
745        test the PDE for symmetry.        test the PDE for symmetry.
746    
747          @param verbose: if equal to True or not present a report on coefficients which are breaking the symmetry is printed.
748       @param verbose: if equal to True or not present a report on coefficients which are breaking the symmetry is printed.        @type verbose: C{bool}
749       @type verbose: C{bool}        @return:  True if the PDE is symmetric.
750       @return:  True if the PDE is symmetric.        @rtype: L{Data<escript.Data>}
      @rtype : C{escript.Data}  
   
751        @note: This is a very expensive operation. It should be used for degugging only! The symmetry flag is not altered.        @note: This is a very expensive operation. It should be used for degugging only! The symmetry flag is not altered.
752        """        """
753        verbose=verbose or self.debug()        verbose=verbose or self.__debug
754        out=True        out=True
755        if self.getNumSolutions()!=self.getNumEquations():        if self.getNumSolutions()!=self.getNumEquations():
756           if verbose: print "non-symmetric PDE because of different number of equations and solutions"           if verbose: print "non-symmetric PDE because of different number of equations and solutions"
# Line 445  class LinearPDE: Line 758  class LinearPDE:
758        else:        else:
759           A=self.getCoefficientOfGeneralPDE("A")           A=self.getCoefficientOfGeneralPDE("A")
760           if not A.isEmpty():           if not A.isEmpty():
761              tol=util.Lsup(A)*self.TOL              tol=util.Lsup(A)*self.SMALL_TOLERANCE
762              if self.getNumSolutions()>1:              if self.getNumSolutions()>1:
763                 for i in range(self.getNumEquations()):                 for i in range(self.getNumEquations()):
764                    for j in range(self.getDim()):                    for j in range(self.getDim()):
# Line 469  class LinearPDE: Line 782  class LinearPDE:
782              if verbose: print "non-symmetric PDE because C is not present but B is"              if verbose: print "non-symmetric PDE because C is not present but B is"
783              out=False              out=False
784           elif not B.isEmpty() and not C.isEmpty():           elif not B.isEmpty() and not C.isEmpty():
785              tol=(util.Lsup(B)+util.Lsup(C))*self.TOL/2.              tol=(util.Lsup(B)+util.Lsup(C))*self.SMALL_TOLERANCE/2.
786              if self.getNumSolutions()>1:              if self.getNumSolutions()>1:
787                 for i in range(self.getNumEquations()):                 for i in range(self.getNumEquations()):
788                     for j in range(self.getDim()):                     for j in range(self.getDim()):
# Line 485  class LinearPDE: Line 798  class LinearPDE:
798           if self.getNumSolutions()>1:           if self.getNumSolutions()>1:
799             D=self.getCoefficientOfGeneralPDE("D")             D=self.getCoefficientOfGeneralPDE("D")
800             if not D.isEmpty():             if not D.isEmpty():
801               tol=util.Lsup(D)*self.TOL               tol=util.Lsup(D)*self.SMALL_TOLERANCE
802               for i in range(self.getNumEquations()):               for i in range(self.getNumEquations()):
803                  for k in range(self.getNumSolutions()):                  for k in range(self.getNumSolutions()):
804                    if util.Lsup(D[i,k]-D[k,i])>tol:                    if util.Lsup(D[i,k]-D[k,i])>tol:
805                        if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)                        if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)
806                        out=False                        out=False
807               d=self.getCoefficientOfGeneralPDE("d")
808               if not d.isEmpty():
809                 tol=util.Lsup(d)*self.SMALL_TOLERANCE
810                 for i in range(self.getNumEquations()):
811                    for k in range(self.getNumSolutions()):
812                      if util.Lsup(d[i,k]-d[k,i])>tol:
813                          if verbose: print "non-symmetric PDE because d[%d,%d]!=d[%d,%d]"%(i,k,k,i)
814                          out=False
815               d_contact=self.getCoefficientOfGeneralPDE("d_contact")
816               if not d_contact.isEmpty():
817                 tol=util.Lsup(d_contact)*self.SMALL_TOLERANCE
818                 for i in range(self.getNumEquations()):
819                    for k in range(self.getNumSolutions()):
820                      if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
821                          if verbose: print "non-symmetric PDE because d_contact[%d,%d]!=d_contact[%d,%d]"%(i,k,k,i)
822                          out=False
823             # and now the reduced coefficients
824             A_reduced=self.getCoefficientOfGeneralPDE("A_reduced")
825             if not A_reduced.isEmpty():
826                tol=util.Lsup(A_reduced)*self.SMALL_TOLERANCE
827                if self.getNumSolutions()>1:
828                   for i in range(self.getNumEquations()):
829                      for j in range(self.getDim()):
830                         for k in range(self.getNumSolutions()):
831                            for l in range(self.getDim()):
832                                if util.Lsup(A_reduced[i,j,k,l]-A_reduced[k,l,i,j])>tol:
833                                   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)
834                                   out=False
835                else:
836                   for j in range(self.getDim()):
837                      for l in range(self.getDim()):
838                         if util.Lsup(A_reduced[j,l]-A_reduced[l,j])>tol:
839                            if verbose: print "non-symmetric PDE because A_reduced[%d,%d]!=A_reduced[%d,%d]"%(j,l,l,j)
840                            out=False
841             B_reduced=self.getCoefficientOfGeneralPDE("B_reduced")
842             C_reduced=self.getCoefficientOfGeneralPDE("C_reduced")
843             if B_reduced.isEmpty() and not C_reduced.isEmpty():
844                if verbose: print "non-symmetric PDE because B_reduced is not present but C_reduced is"
845                out=False
846             elif not B_reduced.isEmpty() and C_reduced.isEmpty():
847                if verbose: print "non-symmetric PDE because C_reduced is not present but B_reduced is"
848                out=False
849             elif not B_reduced.isEmpty() and not C_reduced.isEmpty():
850                tol=(util.Lsup(B_reduced)+util.Lsup(C_reduced))*self.SMALL_TOLERANCE/2.
851                if self.getNumSolutions()>1:
852                   for i in range(self.getNumEquations()):
853                       for j in range(self.getDim()):
854                          for k in range(self.getNumSolutions()):
855                             if util.Lsup(B_reduced[i,j,k]-C_reduced[k,i,j])>tol:
856                                  if verbose: print "non-symmetric PDE because B_reduced[%d,%d,%d]!=C_reduced[%d,%d,%d]"%(i,j,k,k,i,j)
857                                  out=False
858                else:
859                   for j in range(self.getDim()):
860                      if util.Lsup(B_reduced[j]-C_reduced[j])>tol:
861                         if verbose: print "non-symmetric PDE because B_reduced[%d]!=C_reduced[%d]"%(j,j)
862                         out=False
863             if self.getNumSolutions()>1:
864               D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
865               if not D_reduced.isEmpty():
866                 tol=util.Lsup(D_reduced)*self.SMALL_TOLERANCE
867                 for i in range(self.getNumEquations()):
868                    for k in range(self.getNumSolutions()):
869                      if util.Lsup(D_reduced[i,k]-D_reduced[k,i])>tol:
870                          if verbose: print "non-symmetric PDE because D_reduced[%d,%d]!=D_reduced[%d,%d]"%(i,k,k,i)
871                          out=False
872               d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
873               if not d_reduced.isEmpty():
874                 tol=util.Lsup(d_reduced)*self.SMALL_TOLERANCE
875                 for i in range(self.getNumEquations()):
876                    for k in range(self.getNumSolutions()):
877                      if util.Lsup(d_reduced[i,k]-d_reduced[k,i])>tol:
878                          if verbose: print "non-symmetric PDE because d_reduced[%d,%d]!=d_reduced[%d,%d]"%(i,k,k,i)
879                          out=False
880               d_contact_reduced=self.getCoefficientOfGeneralPDE("d_contact_reduced")
881               if not d_contact_reduced.isEmpty():
882                 tol=util.Lsup(d_contact_reduced)*self.SMALL_TOLERANCE
883                 for i in range(self.getNumEquations()):
884                    for k in range(self.getNumSolutions()):
885                      if util.Lsup(d_contact_reduced[i,k]-d_contact_reduced[k,i])>tol:
886                          if verbose: print "non-symmetric PDE because d_contact_reduced[%d,%d]!=d_contact_reduced[%d,%d]"%(i,k,k,i)
887                          out=False
888        return out        return out
889    
890     def getSolution(self,**options):     def getSolution(self,**options):
891         """         """
892         returns the solution of the PDE. If the solution is not valid the PDE is solved.         returns the solution of the PDE. If the solution is not valid the PDE is solved.
893    
894         @return: the solution         @return: the solution
895         @rtype: L{escript.Data}         @rtype: L{Data<escript.Data>}
896         @param options: solver options         @param options: solver options
897         @keyword verbose:         @keyword verbose: True to get some information during PDE solution
898         @keyword reordering: reordering scheme to be used during elimination         @type verbose: C{bool}
899         @keyword preconditioner: preconditioner method to be used         @keyword reordering: reordering scheme to be used during elimination. Allowed values are
900                                L{NO_REORDERING}, L{MINIMUM_FILL_IN}, L{NESTED_DISSECTION}
901         @keyword iter_max: maximum number of iteration steps allowed.         @keyword iter_max: maximum number of iteration steps allowed.
902         @keyword drop_tolerance:         @keyword drop_tolerance: threshold for drupping in L{ILUT}
903         @keyword drop_storage:         @keyword drop_storage: maximum of allowed memory in L{ILUT}
904         @keyword truncation:         @keyword truncation: maximum number of residuals in L{GMRES}
905         @keyword restart:         @keyword restart: restart cycle length in L{GMRES}
906         """         """
907         if not self.__solution_isValid:         if not self.__solution_isValid:
908            mat,f=self.getSystem()            mat,f=self.getSystem()
909            if self.isUsingLumping():            if self.isUsingLumping():
910               self.__solution=self.copyConstraint(f*mat)               self.__solution=self.copyConstraint(f*mat)
911            else:            else:
912               options[self.TOLERANCE_KEY]=self.getTolerance()               options[self.__TOLERANCE_KEY]=self.getTolerance()
913               options[self.METHOD_KEY]=self.getSolverMethod()               options[self.__METHOD_KEY]=self.getSolverMethod()[0]
914               options[self.SYMMETRY_KEY]=self.isSymmetric()               options[self.__PRECONDITIONER_KEY]=self.getSolverMethod()[1]
915                 options[self.__PACKAGE_KEY]=self.getSolverPackage()
916                 options[self.__SYMMETRY_KEY]=self.isSymmetric()
917               self.trace("PDE is resolved.")               self.trace("PDE is resolved.")
918               self.trace("solver options: %s"%str(options))               self.trace("solver options: %s"%str(options))
919               self.__solution=mat.solve(f,options)               self.__solution=mat.solve(f,options)
# Line 526  class LinearPDE: Line 922  class LinearPDE:
922    
923     def getFlux(self,u=None):     def getFlux(self,u=None):
924       """       """
925       returns the flux J_ij for a given u       returns the flux M{J} for a given M{u}
926    
927         \f[       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]}
        J_ij=A_{ijkl}u_{k,l}+B_{ijk}u_k-X_{ij}  
        \f]  
928    
929       @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.       or
930       @type u: L{escript.Data} or None  
931       @return : flux       M{J[j]=(A[i,j]+A_reduced[i,j])*grad(u)[l]+(B[j]+B_reduced[j])u-X[j]-X_reduced[j]}
      @rtype : L{escript.Data}  
932    
933         @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.
934         @type u: L{Data<escript.Data>} or None
935         @return: flux
936         @rtype: L{Data<escript.Data>}
937       """       """
938       if u==None: u=self.getSolution()       if u==None: u=self.getSolution()
939       return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u))+util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u)-util.self.getCoefficientOfGeneralPDE("X")       return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u,Funtion(self.getDomain))) \
940               +util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u) \
941               -util.self.getCoefficientOfGeneralPDE("X") \
942               +util.tensormult(self.getCoefficientOfGeneralPDE("A_reduced"),util.grad(u,ReducedFuntion(self.getDomain))) \
943               +util.matrixmult(self.getCoefficientOfGeneralPDE("B_reduced"),u) \
944               -util.self.getCoefficientOfGeneralPDE("X_reduced")
945     # =============================================================================     # =============================================================================
946     #   solver settings:     #   solver settings:
947     # =============================================================================     # =============================================================================
948     def setSolverMethod(self,solver=None):     def setSolverMethod(self,solver=None,preconditioner=None):
949         """         """
950         sets a new solver         sets a new solver
951    
952         @param solver: sets a new solver method.         @param solver: sets a new solver method.
953         @type solver: C{int}         @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{TFQMR}, L{MINRES}, L{PRES20}, L{LUMPING}, L{AMG}
954           @param preconditioner: sets a new solver method.
955         """         @type preconditioner: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}, L{RILU}
956         if solver==None: solve=self.DEFAULT_METHOD         """
957         if not solver==self.getSolverMethod():         if solver==None: solver=self.__solver_method
958           if preconditioner==None: preconditioner=self.__preconditioner
959           if solver==None: solver=self.DEFAULT
960           if preconditioner==None: preconditioner=self.DEFAULT
961           if not (solver,preconditioner)==self.getSolverMethod():
962             self.__solver_method=solver             self.__solver_method=solver
963               self.__preconditioner=preconditioner
964             self.__checkMatrixType()             self.__checkMatrixType()
965             self.trace("New solver is %s"%self.getSolverMethodName())             self.trace("New solver is %s"%self.getSolverMethodName())
966    
# Line 562  class LinearPDE: Line 968  class LinearPDE:
968         """         """
969         returns the name of the solver currently used         returns the name of the solver currently used
970    
971         @return : the name of the solver currently used.         @return: the name of the solver currently used.
972         @rtype: C{string}         @rtype: C{string}
973         """         """
974    
975         m=self.getSolverMethod()         m=self.getSolverMethod()
976         if m==self.DEFAULT_METHOD: return "DEFAULT_METHOD"         p=self.getSolverPackage()
977         elif m==self.DIRECT: return "DIRECT"         method=""
978         elif m==self.CHOLEVSKY: return "CHOLEVSKY"         if m[0]==self.DEFAULT: method="DEFAULT"
979         elif m==self.PCG: return "PCG"         elif m[0]==self.DIRECT: method= "DIRECT"
980         elif m==self.CR: return "CR"         elif m[0]==self.ITERATIVE: method= "ITERATIVE"
981         elif m==self.CGS: return "CGS"         elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
982         elif m==self.BICGSTAB: return "BICGSTAB"         elif m[0]==self.PCG: method= "PCG"
983         elif m==self.SSOR: return "SSOR"         elif m[0]==self.TFQMR: method= "TFQMR"
984         elif m==self.GMRES: return "GMRES"         elif m[0]==self.MINRES: method= "MINRES"
985         elif m==self.PRES20: return "PRES20"         elif m[0]==self.CR: method= "CR"
986         elif m==self.LUMPING: return "LUMPING"         elif m[0]==self.CGS: method= "CGS"
987         return None         elif m[0]==self.BICGSTAB: method= "BICGSTAB"
988                 elif m[0]==self.SSOR: method= "SSOR"
989           elif m[0]==self.GMRES: method= "GMRES"
990           elif m[0]==self.PRES20: method= "PRES20"
991           elif m[0]==self.LUMPING: method= "LUMPING"
992           elif m[0]==self.AMG: method= "AMG"
993           if m[1]==self.DEFAULT: method+="+DEFAULT"
994           elif m[1]==self.JACOBI: method+= "+JACOBI"
995           elif m[1]==self.ILU0: method+= "+ILU0"
996           elif m[1]==self.ILUT: method+= "+ILUT"
997           elif m[1]==self.SSOR: method+= "+SSOR"
998           elif m[1]==self.AMG: method+= "+AMG"
999           elif m[1]==self.RILU: method+= "+RILU"
1000           if p==self.DEFAULT: package="DEFAULT"
1001           elif p==self.PASO: package= "PASO"
1002           elif p==self.MKL: package= "MKL"
1003           elif p==self.SCSL: package= "SCSL"
1004           elif p==self.UMFPACK: package= "UMFPACK"
1005           elif p==self.TRILINOS: package= "TRILINOS"
1006           else : method="unknown"
1007           return "%s solver of %s package"%(method,package)
1008    
1009    
1010     def getSolverMethod(self):     def getSolverMethod(self):
1011         """         """
1012         returns the solver method         returns the solver method
1013      
1014         @return : the solver method currently be used.         @return: the solver method currently be used.
1015         @rtype : C{int}         @rtype: C{int}
1016           """
1017           return self.__solver_method,self.__preconditioner
1018    
1019       def setSolverPackage(self,package=None):
1020           """
1021           sets a new solver package
1022    
1023           @param package: sets a new solver method.
1024           @type package: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMFPACK}, L{TRILINOS}
1025           """
1026           if package==None: package=self.DEFAULT
1027           if not package==self.getSolverPackage():
1028               self.__solver_package=package
1029               self.__checkMatrixType()
1030               self.trace("New solver is %s"%self.getSolverMethodName())
1031    
1032       def getSolverPackage(self):
1033           """
1034           returns the package of the solver
1035    
1036           @return: the solver package currently being used.
1037           @rtype: C{int}
1038         """         """
1039         return self.__solver_method         return self.__solver_package
1040    
1041     def isUsingLumping(self):     def isUsingLumping(self):
1042        """        """
1043        checks if matrix lumping is used a solver method        checks if matrix lumping is used a solver method
1044    
1045        @return : True is lumping is currently used a solver method.        @return: True is lumping is currently used a solver method.
1046        @rtype: C{bool}        @rtype: C{bool}
1047        """        """
1048        return self.getSolverMethod()==self.LUMPING        return self.getSolverMethod()[0]==self.LUMPING
1049    
1050     def setTolerance(self,tol=1.e-8):     def setTolerance(self,tol=1.e-8):
1051         """         """
1052         resets the tolerance for the solver method to tol where for an appropriate norm |.|         resets the tolerance for the solver method to tol where for an appropriate norm M{|.|}
1053    
1054                 |self.getResidual()|<tol*|self.getRightHandSide()|         M{|L{getResidual}()|<tol*|L{getRightHandSide}()|}
1055    
1056         defines the stopping criterion.         defines the stopping criterion.
1057    
1058         @param tol: new tolerance for the solver. If the tol is lower then the current tolerence         @param tol: new tolerance for the solver. If the tol is lower then the current tolerence
1059                     the system will be resolved.                     the system will be resolved.
1060         @type solver: C{float}         @type tol: positive C{float}
1061         @raise ValueException: if tolerance is not positive.         @raise ValueError: if tolerance is not positive.
1062         """         """
1063         if not tol>0:         if not tol>0:
1064             raise ValueException,"Tolerance as to be positive"             raise ValueError,"Tolerance as to be positive"
1065         if tol<self.getTolerance(): self.__invalidateSolution()         if tol<self.getTolerance(): self.__invalidateSolution()
1066         self.trace("New tolerance %e"%tol)         self.trace("New tolerance %e"%tol)
1067         self.__tolerance=tol         self.__tolerance=tol
# Line 634  class LinearPDE: Line 1082  class LinearPDE:
1082     def isSymmetric(self):     def isSymmetric(self):
1083        """        """
1084        checks if symmetry is indicated.        checks if symmetry is indicated.
1085        
1086        @return : True is a symmetric PDE is indicated, otherwise False is returned        @return: True is a symmetric PDE is indicated, otherwise False is returned
1087        @rtype : C{bool}        @rtype: C{bool}
1088        """        """
1089        return self.__sym        return self.__sym
1090    
# Line 661  class LinearPDE: Line 1109  class LinearPDE:
1109     def setSymmetryTo(self,flag=False):     def setSymmetryTo(self,flag=False):
1110        """        """
1111        sets the symmetry flag to flag        sets the symmetry flag to flag
1112    
1113        @param flag: If flag, the symmetry flag is set otherwise the symmetry flag is released.        @param flag: If flag, the symmetry flag is set otherwise the symmetry flag is released.
1114        @type flag: C{bool}        @type flag: C{bool}
1115        """        """
# Line 670  class LinearPDE: Line 1118  class LinearPDE:
1118        else:        else:
1119           self.setSymmetryOff()           self.setSymmetryOff()
1120    
     
1121     # =============================================================================     # =============================================================================
1122     # function space handling for the equation as well as the solution     # function space handling for the equation as well as the solution
1123     # =============================================================================     # =============================================================================
1124     def setReducedOrderOn(self):     def setReducedOrderOn(self):
1125       """       """
1126       switches on reduced order for solution and equation representation       switches on reduced order for solution and equation representation
1127    
1128         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1129       """       """
1130       self.setReducedOrderForSolutionOn()       self.setReducedOrderForSolutionOn()
1131       self.setReducedOrderForEquationOn()       self.setReducedOrderForEquationOn()
# Line 684  class LinearPDE: Line 1133  class LinearPDE:
1133     def setReducedOrderOff(self):     def setReducedOrderOff(self):
1134       """       """
1135       switches off reduced order for solution and equation representation       switches off reduced order for solution and equation representation
1136    
1137         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1138       """       """
1139       self.setReducedOrderForSolutionOff()       self.setReducedOrderForSolutionOff()
1140       self.setReducedOrderForEquationOff()       self.setReducedOrderForEquationOff()
1141    
1142     def setReducedOrderTo(self,flag=False):     def setReducedOrderTo(self,flag=False):
1143       """       """
1144       sets order reduction for both solution and equation representation according to flag.       sets order reduction for both solution and equation representation according to flag.
1145         @param flag: if flag is True, the order reduction is switched on for both  solution and equation representation, otherwise or
      @param flag: if flag is True, the order reduction is switched on for both  solution and equation representation, otherwise or  
1146                    if flag is not present order reduction is switched off                    if flag is not present order reduction is switched off
1147       @type flag: C{bool}       @type flag: C{bool}
1148         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1149       """       """
1150       self.setReducedOrderForSolutionTo(flag)       self.setReducedOrderForSolutionTo(flag)
1151       self.setReducedOrderForEquationTo(flag)       self.setReducedOrderForEquationTo(flag)
# Line 703  class LinearPDE: Line 1154  class LinearPDE:
1154     def setReducedOrderForSolutionOn(self):     def setReducedOrderForSolutionOn(self):
1155       """       """
1156       switches on reduced order for solution representation       switches on reduced order for solution representation
1157    
1158         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1159       """       """
1160       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_solution_order:
1161       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1162                  raise RuntimeError,"order cannot be altered after coefficients have been defined."
1163           self.trace("Reduced order is used to solution representation.")           self.trace("Reduced order is used to solution representation.")
1164           self.__column_function_space=new_fs           self.__reduce_solution_order=True
1165           self.__resetSystem()           self.__resetSystem()
1166    
1167     def setReducedOrderForSolutionOff(self):     def setReducedOrderForSolutionOff(self):
1168       """       """
1169       switches off reduced order for solution representation       switches off reduced order for solution representation
1170    
1171         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1172       """       """
1173       new_fs=escript.Solution(self.getDomain())       if self.__reduce_solution_order:
1174       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1175                  raise RuntimeError,"order cannot be altered after coefficients have been defined."
1176           self.trace("Full order is used to interpolate solution.")           self.trace("Full order is used to interpolate solution.")
1177           self.__column_function_space=new_fs           self.__reduce_solution_order=False
1178           self.__resetSystem()           self.__resetSystem()
1179    
1180     def setReducedOrderForSolutionTo(self,flag=False):     def setReducedOrderForSolutionTo(self,flag=False):
1181       """       """
1182       sets order for test functions according to flag       sets order for test functions according to flag
1183    
1184       @param flag: if flag is True, the order reduction is switched on for solution representation, otherwise or       @param flag: if flag is True, the order reduction is switched on for solution representation, otherwise or
1185                    if flag is not present order reduction is switched off                    if flag is not present order reduction is switched off
1186       @type flag: C{bool}       @type flag: C{bool}
1187         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1188       """       """
1189       if flag:       if flag:
1190          self.setReducedOrderForSolutionOn()          self.setReducedOrderForSolutionOn()
# Line 736  class LinearPDE: Line 1194  class LinearPDE:
1194     def setReducedOrderForEquationOn(self):     def setReducedOrderForEquationOn(self):
1195       """       """
1196       switches on reduced order for equation representation       switches on reduced order for equation representation
1197    
1198         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1199       """       """
1200       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_equation_order:
1201       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1202                  raise RuntimeError,"order cannot be altered after coefficients have been defined."
1203           self.trace("Reduced order is used for test functions.")           self.trace("Reduced order is used for test functions.")
1204           self.__row_function_space=new_fs           self.__reduce_equation_order=True
1205           self.__resetSystem()           self.__resetSystem()
1206    
1207     def setReducedOrderForEquationOff(self):     def setReducedOrderForEquationOff(self):
1208       """       """
1209       switches off reduced order for equation representation       switches off reduced order for equation representation
1210    
1211         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1212       """       """
1213       new_fs=escript.Solution(self.getDomain())       if self.__reduce_equation_order:
1214       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1215                  raise RuntimeError,"order cannot be altered after coefficients have been defined."
1216           self.trace("Full order is used for test functions.")           self.trace("Full order is used for test functions.")
1217           self.__row_function_space=new_fs           self.__reduce_equation_order=False
1218           self.__resetSystem()           self.__resetSystem()
1219    
1220     def setReducedOrderForEquationTo(self,flag=False):     def setReducedOrderForEquationTo(self,flag=False):
1221       """       """
1222       sets order for test functions according to flag       sets order for test functions according to flag
1223    
1224       @param flag: if flag is True, the order reduction is switched on for equation representation, otherwise or       @param flag: if flag is True, the order reduction is switched on for equation representation, otherwise or
1225                    if flag is not present order reduction is switched off                    if flag is not present order reduction is switched off
1226       @type flag: C{bool}       @type flag: C{bool}
1227         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1228       """       """
1229       if flag:       if flag:
1230          self.setReducedOrderForEquationOn()          self.setReducedOrderForEquationOn()
# Line 773  class LinearPDE: Line 1238  class LinearPDE:
1238       """       """
1239       reassess the matrix type and, if a new matrix is needed, resets the system.       reassess the matrix type and, if a new matrix is needed, resets the system.
1240       """       """
1241       new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod(),self.isSymmetric())       new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod()[0],self.getSolverPackage(),self.isSymmetric())
1242       if not new_matrix_type==self.__matrix_type:       if not new_matrix_type==self.__matrix_type:
1243           self.trace("Matrix type is now %d."%new_matrix_type)           self.trace("Matrix type is now %d."%new_matrix_type)
1244           self.__matrix_type=new_matrix_type           self.__matrix_type=new_matrix_type
1245           self.__resetSystem()           self.__resetSystem()
1246     #     #
1247     #   rebuild switches :     #   rebuild switches :
1248     #     #
1249     def __invalidateSolution(self):     def __invalidateSolution(self):
1250         """         """
1251         indicates the PDE has to be resolved if the solution is requested         indicates the PDE has to be resolved if the solution is requested
# Line 792  class LinearPDE: Line 1257  class LinearPDE:
1257         """         """
1258         indicates the operator has to be rebuilt next time it is used         indicates the operator has to be rebuilt next time it is used
1259         """         """
1260         if self.__operator_isValid: self.trace("Operator has to be rebuilt.")         if self.__operator_is_Valid: self.trace("Operator has to be rebuilt.")
1261         self.__invalidateSolution()         self.__invalidateSolution()
1262         self.__operator_isValid=False         self.__operator_is_Valid=False
1263    
1264     def __invalidateRightHandSide(self):     def __invalidateRightHandSide(self):
1265         """         """
# Line 819  class LinearPDE: Line 1284  class LinearPDE:
1284         """         """
1285         self.trace("New System is built from scratch.")         self.trace("New System is built from scratch.")
1286         self.__operator=escript.Operator()         self.__operator=escript.Operator()
1287         self.__operator_isValid=False         self.__operator_is_Valid=False
1288         self.__righthandside=escript.Data()         self.__righthandside=escript.Data()
1289         self.__righthandside_isValid=False         self.__righthandside_isValid=False
1290         self.__solution=escript.Data()         self.__solution=escript.Data()
1291         self.__solution_isValid=False         self.__solution_isValid=False
1292     #     #
1293     #    system initialization:     #    system initialization:
1294     #     #
1295     def __getNewOperator(self):     def __getNewOperator(self):
1296         """         """
1297         returns an instance of a new operator         returns an instance of a new operator
# Line 877  class LinearPDE: Line 1342  class LinearPDE:
1342         if self.__righthandside.isEmpty():         if self.__righthandside.isEmpty():
1343             self.__righthandside=self.__getNewRightHandSide()             self.__righthandside=self.__getNewRightHandSide()
1344         else:         else:
1345             self.__righthandside*=0             self.__righthandside.setToZero()
1346             self.trace("Right hand side is reset to zero.")             self.trace("Right hand side is reset to zero.")
1347         return self.__righthandside         return self.__righthandside
1348    
# Line 888  class LinearPDE: Line 1353  class LinearPDE:
1353         if self.__operator.isEmpty():         if self.__operator.isEmpty():
1354             self.__operator=self.__getNewOperator()             self.__operator=self.__getNewOperator()
1355         else:         else:
1356             self.__operator.setValue(0.)             self.__operator.resetValues()
1357             self.trace("Operator reset to zero")             self.trace("Operator reset to zero")
1358         return self.__operator         return self.__operator
1359    
# Line 909  class LinearPDE: Line 1374  class LinearPDE:
1374               else:               else:
1375                  r_s=escript.Data(r,self.getFunctionSpaceForSolution())                  r_s=escript.Data(r,self.getFunctionSpaceForSolution())
1376               u.copyWithMask(r_s,col_q)               u.copyWithMask(r_s,col_q)
1377               if not self.__righthandside.isEmpty():               if not self.__righthandside.isEmpty():
1378                  self.__righthandside-=self.__operator*u                  self.__righthandside-=self.__operator*u
1379                  self.__righthandside=self.copyConstraint(self.__righthandside)                  self.__righthandside=self.copyConstraint(self.__righthandside)
1380               self.__operator.nullifyRowsAndCols(row_q,col_q,1.)               self.__operator.nullifyRowsAndCols(row_q,col_q,1.)
# Line 920  class LinearPDE: Line 1385  class LinearPDE:
1385       """       """
1386       return the value of the coefficient name of the general PDE.       return the value of the coefficient name of the general PDE.
1387    
1388       @note This method is called by the assembling routine it can be overwritten       @note: This method is called by the assembling routine it can be overwritten
1389             to map coefficients of a particular PDE to the general PDE.             to map coefficients of a particular PDE to the general PDE.
1390         @param name: name of the coefficient requested.
      @param name: name of the coefficient requested.  
1391       @type name: C{string}       @type name: C{string}
1392       @return : the value of the coefficient  name       @return: the value of the coefficient  name
1393       @rtype : L{escript.Data}       @rtype: L{Data<escript.Data>}
1394       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1395                    "A", "B", "C", "D", "X", "Y", "d", "y", "d_contact", "y_contact", "r" or "q".                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1396                      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}.
1397       """       """
1398       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1399          return self.getCoefficient(name)          return self.getCoefficient(name)
# Line 938  class LinearPDE: Line 1403  class LinearPDE:
1403     def hasCoefficientOfGeneralPDE(self,name):     def hasCoefficientOfGeneralPDE(self,name):
1404       """       """
1405       checks if name is a the name of a coefficient of the general PDE.       checks if name is a the name of a coefficient of the general PDE.
1406        
1407       @param name: name of the coefficient enquired.       @param name: name of the coefficient enquired.
1408       @type name: C{string}       @type name: C{string}
1409       @return : True if name is the name of a coefficient of the general PDE. Otherwise False.       @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1410       @rtype : C{bool}       @rtype: C{bool}
1411        
1412       """       """
1413       return self.__COEFFICIENTS_OF_GENEARL_PDE.has_key(name)       return self.__COEFFICIENTS_OF_GENEARL_PDE.has_key(name)
1414    
# Line 953  class LinearPDE: Line 1418  class LinearPDE:
1418    
1419       @param name: name of the coefficient requested.       @param name: name of the coefficient requested.
1420       @type name: C{string}       @type name: C{string}
1421       @return : a coefficient name initialized to 0.       @return: a coefficient name initialized to 0.
1422       @rtype : L{escript.Data}       @rtype: L{Data<escript.Data>}
1423       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1424                    "A", "B", "C", "D", "X", "Y", "d", "y", "d_contact", "y_contact", "r" or "q".                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1425                      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}.
1426       """       """
1427       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1428          return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))          return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
# Line 965  class LinearPDE: Line 1431  class LinearPDE:
1431    
1432     def getFunctionSpaceForCoefficientOfGeneralPDE(self,name):     def getFunctionSpaceForCoefficientOfGeneralPDE(self,name):
1433       """       """
1434       return the L{escript.FunctionSpace} to be used for coefficient name of the general PDE       return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name of the general PDE
1435    
1436       @param name: name of the coefficient enquired.       @param name: name of the coefficient enquired.
1437       @type name: C{string}       @type name: C{string}
1438       @return : the function space to be used for coefficient name       @return: the function space to be used for coefficient name
1439       @rtype : L{escript.FunctionSpace}       @rtype: L{FunctionSpace<escript.FunctionSpace>}
1440       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1441                    "A", "B", "C", "D", "X", "Y", "d", "y", "d_contact", "y_contact", "r" or "q".                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1442                      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}.
1443       """       """
1444       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1445          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
# Line 985  class LinearPDE: Line 1452  class LinearPDE:
1452    
1453       @param name: name of the coefficient enquired.       @param name: name of the coefficient enquired.
1454       @type name: C{string}       @type name: C{string}
1455       @return : the shape of the coefficient name       @return: the shape of the coefficient name
1456       @rtype : C{tuple} of C{int}       @rtype: C{tuple} of C{int}
1457       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1458                    "A", "B", "C", "D", "X", "Y", "d", "y", "d_contact", "y_contact", "r" or "q".                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1459                      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}.
1460       """       """
1461       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1462          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
# Line 1003  class LinearPDE: Line 1470  class LinearPDE:
1470       """       """
1471       returns the value of the coefficient name       returns the value of the coefficient name
1472    
1473       @param name: name of the coefficient requested.       @param name: name of the coefficient requested.
1474       @type name: C{string}       @type name: C{string}
1475       @return : the value of the coefficient name       @return: the value of the coefficient name
1476       @rtype : L{escript.Data}       @rtype: L{Data<escript.Data>}
1477       @raise IllegalCoefficient: if name is not a coefficient of the PDE.       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1478       """       """
1479       if self.hasCoefficient(name):       if self.hasCoefficient(name):
# Line 1020  class LinearPDE: Line 1487  class LinearPDE:
1487    
1488       @param name: name of the coefficient enquired.       @param name: name of the coefficient enquired.
1489       @type name: C{string}       @type name: C{string}
1490       @return : True if name is the name of a coefficient of the general PDE. Otherwise False.       @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1491       @rtype : C{bool}       @rtype: C{bool}
1492       """       """
1493       return self.COEFFICIENTS.has_key(name)       return self.COEFFICIENTS.has_key(name)
1494    
1495     def createCoefficient(self, name):     def createCoefficient(self, name):
1496       """       """
1497       create a L{escript.Data} object corresponding to coefficient name       create a L{Data<escript.Data>} object corresponding to coefficient name
1498    
1499       @return : a coefficient name initialized to 0.       @return: a coefficient name initialized to 0.
1500       @rtype : L{escript.Data}       @rtype: L{Data<escript.Data>}
1501       @raise IllegalCoefficient: if name is not a coefficient of the PDE.       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1502       """       """
1503       if self.hasCoefficient(name):       if self.hasCoefficient(name):
# Line 1040  class LinearPDE: Line 1507  class LinearPDE:
1507    
1508     def getFunctionSpaceForCoefficient(self,name):     def getFunctionSpaceForCoefficient(self,name):
1509       """       """
1510       return the L{escript.FunctionSpace} to be used for coefficient name       return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name
1511    
1512       @param name: name of the coefficient enquired.       @param name: name of the coefficient enquired.
1513       @type name: C{string}       @type name: C{string}
1514       @return : the function space to be used for coefficient name       @return: the function space to be used for coefficient name
1515       @rtype : L{escript.FunctionSpace}       @rtype: L{FunctionSpace<escript.FunctionSpace>}
1516       @raise IllegalCoefficient: if name is not a coefficient of the PDE.       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1517       """       """
1518       if self.hasCoefficient(name):       if self.hasCoefficient(name):
1519          return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())          return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())
1520       else:       else:
1521          raise ValueError,"unknown coefficient %s requested"%name          raise ValueError,"unknown coefficient %s requested"%name
   
1522     def getShapeOfCoefficient(self,name):     def getShapeOfCoefficient(self,name):
1523       """       """
1524       return the shape of the coefficient name       return the shape of the coefficient name
1525    
1526       @param name: name of the coefficient enquired.       @param name: name of the coefficient enquired.
1527       @type name: C{string}       @type name: C{string}
1528       @return : the shape of the coefficient name       @return: the shape of the coefficient name
1529       @rtype : C{tuple} of C{int}       @rtype: C{tuple} of C{int}
1530       @raise IllegalCoefficient: if name is not a coefficient of the PDE.       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1531       """       """
1532       if self.hasCoefficient(name):       if self.hasCoefficient(name):
# Line 1082  class LinearPDE: Line 1548  class LinearPDE:
1548       @param name: name of the coefficient enquired.       @param name: name of the coefficient enquired.
1549       @type name: C{string}       @type name: C{string}
1550       @raise IllegalCoefficient: if name is not a coefficient of the PDE.       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1551         @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.
1552       """       """
1553       if self.hasCoefficient(name):       if self.hasCoefficient(name):
1554          self.trace("Coefficient %s has been altered."%name)          self.trace("Coefficient %s has been altered."%name)
1555          if self.COEFFICIENTS[name].isAlteringOperator(): self.__invalidateOperator()          if not ((name=="q" or name=="r") and self.isUsingLumping()):
1556          if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__invalidateRightHandSide()             if self.COEFFICIENTS[name].isAlteringOperator(): self.__invalidateOperator()
1557               if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__invalidateRightHandSide()
1558       else:       else:
1559          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1560    
1561     def copyConstraint(self,u):     def copyConstraint(self,u):
1562        """        """
1563        copies the constraint into u and returns u.        copies the constraint into u and returns u.
   
       @param u: a function of rank 0 is a single PDE is solved and of shape (numSolution,) for a system of PDEs  
       @type u: L{escript.Data}  
       @return : the input u modified by the constraints.  
       @rtype : L{escript.Data}  
       @warning: u is altered if it has the appropriate L{escript.FunctionSpace}  
1564    
1565          @param u: a function of rank 0 is a single PDE is solved and of shape (numSolution,) for a system of PDEs
1566          @type u: L{Data<escript.Data>}
1567          @return: the input u modified by the constraints.
1568          @rtype: L{Data<escript.Data>}
1569          @warning: u is altered if it has the appropriate L{FunctionSpace<escript.FunctionSpace>}
1570        """        """
1571        q=self.getCoefficientOfGeneralPDE("q")        q=self.getCoefficientOfGeneralPDE("q")
1572        r=self.getCoefficientOfGeneralPDE("r")        r=self.getCoefficientOfGeneralPDE("r")
# Line 1116  class LinearPDE: Line 1583  class LinearPDE:
1583        """        """
1584        sets new values to coefficients        sets new values to coefficients
1585    
1586        @note This method is called by the assembling routine it can be overwritten        @param coefficients: new values assigned to coefficients
1587             to map coefficients of a particular PDE to the general PDE.        @keyword A: value for coefficient A.
1588          @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1589        @param name: name of the coefficient requested.        @keyword A_reduced: value for coefficient A_reduced.
1590        @type name: C{string}        @type A_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
       @keyword A: value for coefficient A.  
       @type A: any type that can be interpreted as L{escript.Data} object on L{escript.Function}.  
1591        @keyword B: value for coefficient B        @keyword B: value for coefficient B
1592        @type B: any type that can be interpreted as L{escript.Data} object on L{escript.Function}.        @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1593          @keyword B_reduced: value for coefficient B_reduced
1594          @type B_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1595        @keyword C: value for coefficient C        @keyword C: value for coefficient C
1596        @type C: any type that can be interpreted as L{escript.Data} object on L{escript.Function}.        @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1597          @keyword C_reduced: value for coefficient C_reduced
1598          @type C_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1599        @keyword D: value for coefficient D        @keyword D: value for coefficient D
1600        @type D: any type that can be interpreted as L{escript.Data} object on L{escript.Function}.        @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1601          @keyword D_reduced: value for coefficient D_reduced
1602          @type D_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1603        @keyword X: value for coefficient X        @keyword X: value for coefficient X
1604        @type X: any type that can be interpreted as L{escript.Data} object on L{escript.Function}.        @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1605          @keyword X_reduced: value for coefficient X_reduced
1606          @type X_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1607        @keyword Y: value for coefficient Y        @keyword Y: value for coefficient Y
1608        @type Y: any type that can be interpreted as L{escript.Data} object on L{escript.Function}.        @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1609          @keyword Y_reduced: value for coefficient Y_reduced
1610          @type Y_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.Function>}.
1611        @keyword d: value for coefficient d        @keyword d: value for coefficient d
1612        @type d: any type that can be interpreted as L{escript.Data} object on L{escript.FunctionOnBoundary}.        @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1613          @keyword d_reduced: value for coefficient d_reduced
1614          @type d_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
1615        @keyword y: value for coefficient y        @keyword y: value for coefficient y
1616        @type y: any type that can be interpreted as L{escript.Data} object on L{escript.FunctionOnBoundary}.        @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1617        @keyword d_contact: value for coefficient d_contact        @keyword d_contact: value for coefficient d_contact
1618        @type d_contact: any type that can be interpreted as L{escript.Data} object on L{escript.FunctionOnContactOne}.        @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>}.
1619                         or  L{escript.FunctionOnContactZero}.        @keyword d_contact_reduced: value for coefficient d_contact_reduced
1620          @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>}.
1621        @keyword y_contact: value for coefficient y_contact        @keyword y_contact: value for coefficient y_contact
1622        @type y_contact: any type that can be interpreted as L{escript.Data} object on L{escript.FunctionOnContactOne}.        @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>}.
1623                         or  L{escript.FunctionOnContactZero}.        @keyword y_contact_reduced: value for coefficient y_contact_reduced
1624          @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>}.
1625        @keyword r: values prescribed to the solution at the locations of constraints        @keyword r: values prescribed to the solution at the locations of constraints
1626        @type r: any type that can be interpreted as L{escript.Data} object on L{escript.Solution} or L{escript.ReducedSolution}        @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1627                 depending of reduced order is used for the solution.                 depending of reduced order is used for the solution.
1628        @keyword q: mask for location of constraints        @keyword q: mask for location of constraints
1629        @type q: any type that can be interpreted as L{escript.Data} object on L{escript.Solution} or L{escript.ReducedSolution}        @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1630                 depending of reduced order is used for the representation of the equation.                 depending of reduced order is used for the representation of the equation.
1631        @raise IllegalCoefficient: if an unknown coefficient keyword is used.        @raise IllegalCoefficient: if an unknown coefficient keyword is used.
   
1632        """        """
1633        # check if the coefficients are  legal:        # check if the coefficients are  legal:
1634        for i in coefficients.iterkeys():        for i in coefficients.iterkeys():
# Line 1178  class LinearPDE: Line 1656  class LinearPDE:
1656        # now we check the shape of the coefficient if numEquations and numSolutions are set:        # now we check the shape of the coefficient if numEquations and numSolutions are set:
1657        for i,d in coefficients.iteritems():        for i,d in coefficients.iteritems():
1658          try:          try:
1659             self.COEFFICIENTS[i].setValue(self.getDomain(),self.getNumEquations(),self.getNumSolutions(),d)             self.COEFFICIENTS[i].setValue(self.getDomain(),
1660                                             self.getNumEquations(),self.getNumSolutions(),
1661                                             self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1662               self.alteredCoefficient(i)
1663            except IllegalCoefficientFunctionSpace,m:
1664                # if the function space is wrong then we try the reduced version:
1665                i_red=i+"_reduced"
1666                if (not i_red in coefficients.keys()) and i_red in self.COEFFICIENTS.keys():
1667                    try:
1668                        self.COEFFICIENTS[i_red].setValue(self.getDomain(),
1669                                                          self.getNumEquations(),self.getNumSolutions(),
1670                                                          self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1671                        self.alteredCoefficient(i_red)
1672                    except IllegalCoefficientValue,m:
1673                        raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1674                    except IllegalCoefficientFunctionSpace,m:
1675                        raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1676                else:
1677                    raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1678          except IllegalCoefficientValue,m:          except IllegalCoefficientValue,m:
1679             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1680          self.alteredCoefficient(i)        self.__altered_coefficients=True
   
1681        # check if the systrem is inhomogeneous:        # check if the systrem is inhomogeneous:
1682        if len(coefficients)>0 and not self.isUsingLumping():        if len(coefficients)>0 and not self.isUsingLumping():
1683           q=self.getCoefficientOfGeneralPDE("q")           q=self.getCoefficientOfGeneralPDE("q")
1684           r=self.getCoefficientOfGeneralPDE("r")           r=self.getCoefficientOfGeneralPDE("r")
1685           homogeneous_constraint=True           homogeneous_constraint=True
1686           if not q.isEmpty() and not r.isEmpty():           if not q.isEmpty() and not r.isEmpty():
1687               if util.Lsup(q*r)>=1.e-13*util.Lsup(r):               if util.Lsup(q*r)>0.:
1688                 self.trace("Inhomogeneous constraint detected.")                 self.trace("Inhomogeneous constraint detected.")
1689                 self.__invalidateSystem()                 self.__invalidateSystem()
1690    
   
1691     def getSystem(self):     def getSystem(self):
1692         """         """
1693         return the operator and right hand side of the PDE         return the operator and right hand side of the PDE
1694    
1695           @return: the discrete version of the PDE
1696           @rtype: C{tuple} of L{Operator,<escript.Operator>} and L{Data<escript.Data>}.
1697         """         """
1698         if not self.__operator_isValid or not self.__righthandside_isValid:         if not self.__operator_is_Valid or not self.__righthandside_isValid:
1699            if self.isUsingLumping():            if self.isUsingLumping():
1700                if not self.__operator_isValid:                if not self.__operator_is_Valid:
1701                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution(): raise TypeError,"Lumped matrix requires same order for equations and unknowns"                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():
1702                   if not self.getCoefficientOfGeneralPDE("A").isEmpty(): raise Warning,"Lumped matrix does not allow coefficient A"                        raise TypeError,"Lumped matrix requires same order for equations and unknowns"
1703                   if not self.getCoefficientOfGeneralPDE("B").isEmpty(): raise Warning,"Lumped matrix does not allow coefficient B"                   if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1704                   if not self.getCoefficientOfGeneralPDE("C").isEmpty(): raise Warning,"Lumped matrix does not allow coefficient C"                        raise ValueError,"coefficient A in lumped matrix may not be present."
1705                   mat=self.__getNewOperator()                   if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1706                   self.getDomain().addPDEToSystem(mat,escript.Data(), \                        raise ValueError,"coefficient B in lumped matrix may not be present."
1707                             self.getCoefficientOfGeneralPDE("A"), \                   if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1708                             self.getCoefficientOfGeneralPDE("B"), \                        raise ValueError,"coefficient C in lumped matrix may not be present."
1709                             self.getCoefficientOfGeneralPDE("C"), \                   if not self.getCoefficientOfGeneralPDE("d_contact").isEmpty():
1710                             self.getCoefficientOfGeneralPDE("D"), \                        raise ValueError,"coefficient d_contact in lumped matrix may not be present."
1711                             escript.Data(), \                   if not self.getCoefficientOfGeneralPDE("A_reduced").isEmpty():
1712                             escript.Data(), \                        raise ValueError,"coefficient A_reduced in lumped matrix may not be present."
1713                             self.getCoefficientOfGeneralPDE("d"), \                   if not self.getCoefficientOfGeneralPDE("B_reduced").isEmpty():
1714                             escript.Data(),\                        raise ValueError,"coefficient B_reduced in lumped matrix may not be present."
1715                             self.getCoefficientOfGeneralPDE("d_contact"), \                   if not self.getCoefficientOfGeneralPDE("C_reduced").isEmpty():
1716                             escript.Data())                        raise ValueError,"coefficient C_reduced in lumped matrix may not be present."
1717                   self.__operator=1./(mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True))                   if not self.getCoefficientOfGeneralPDE("d_contact_reduced").isEmpty():
1718                   del mat                        raise ValueError,"coefficient d_contact_reduced in lumped matrix may not be present."
1719                     D=self.getCoefficientOfGeneralPDE("D")
1720                     d=self.getCoefficientOfGeneralPDE("d")
1721                     D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
1722                     d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
1723                     if not D.isEmpty():
1724                         if self.getNumSolutions()>1:
1725                            D_times_e=util.matrix_mult(D,numarray.ones((self.getNumSolutions(),)))
1726                         else:
1727                            D_times_e=D
1728                     else:
1729                        D_times_e=escript.Data()
1730                     if not d.isEmpty():
1731                         if self.getNumSolutions()>1:
1732                            d_times_e=util.matrix_mult(d,numarray.ones((self.getNumSolutions(),)))
1733                         else:
1734                            d_times_e=d
1735                     else:
1736                        d_times_e=escript.Data()
1737          
1738                     if not D_reduced.isEmpty():
1739                         if self.getNumSolutions()>1:
1740                            D_reduced_times_e=util.matrix_mult(D_reduced,numarray.ones((self.getNumSolutions(),)))
1741                         else:
1742                            D_reduced_times_e=D_reduced
1743                     else:
1744                        D_reduced_times_e=escript.Data()
1745                     if not d_reduced.isEmpty():
1746                         if self.getNumSolutions()>1:
1747                            d_reduced_times_e=util.matrix_mult(d_reduced,numarray.ones((self.getNumSolutions(),)))
1748                         else:
1749                            d_reduced_times_e=d_reduced
1750                     else:
1751                        d_reduced_times_e=escript.Data()
1752    
1753                     self.__operator=self.__getNewRightHandSide()
1754                     if False and hasattr(self.getDomain(), "addPDEToLumpedSystem") :
1755                        self.getDomain().addPDEToLumpedSystem(self.__operator, D_times_e, d_times_e)
1756                        self.getDomain().addPDEToLumpedSystem(self.__operator, D_reduced_times_e, d_reduced_times_e)
1757                     else:
1758                        self.getDomain().addPDEToRHS(self.__operator, \
1759                                                     escript.Data(), \
1760                                                     D_times_e, \
1761                                                     d_times_e,\
1762                                                     escript.Data())
1763                        self.getDomain().addPDEToRHS(self.__operator, \
1764                                                     escript.Data(), \
1765                                                     D_reduced_times_e, \
1766                                                     d_reduced_times_e,\
1767                                                     escript.Data())
1768                     self.__operator=1./self.__operator
1769                   self.trace("New lumped operator has been built.")                   self.trace("New lumped operator has been built.")
1770                   self.__operator_isValid=True                   self.__operator_is_Valid=True
1771                if not self.__righthandside_isValid:                if not self.__righthandside_isValid:
1772                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1773                                 self.getCoefficientOfGeneralPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1774                                 self.getCoefficientOfGeneralPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1775                                 self.getCoefficientOfGeneralPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1776                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1777                     self.getDomain().addPDEToRHS(self.__righthandside, \
1778                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1779                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1780                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1781                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1782                   self.trace("New right hand side as been built.")                   self.trace("New right hand side as been built.")
1783                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1784            else:            else:
1785               if not self.__operator_isValid and not self.__righthandside_isValid:               if not self.__operator_is_Valid and not self.__righthandside_isValid:
1786                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \
1787                                 self.getCoefficientOfGeneralPDE("A"), \                                 self.getCoefficientOfGeneralPDE("A"), \
1788                                 self.getCoefficientOfGeneralPDE("B"), \                                 self.getCoefficientOfGeneralPDE("B"), \
# Line 1242  class LinearPDE: Line 1794  class LinearPDE:
1794                                 self.getCoefficientOfGeneralPDE("y"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1795                                 self.getCoefficientOfGeneralPDE("d_contact"), \                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1796                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1797                     self.getDomain().addPDEToSystem(self.__operator,self.__righthandside, \
1798                                   self.getCoefficientOfGeneralPDE("A_reduced"), \
1799                                   self.getCoefficientOfGeneralPDE("B_reduced"), \
1800                                   self.getCoefficientOfGeneralPDE("C_reduced"), \
1801                                   self.getCoefficientOfGeneralPDE("D_reduced"), \
1802                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1803                                   self.getCoefficientOfGeneralPDE("Y_reduced"), \
1804                                   self.getCoefficientOfGeneralPDE("d_reduced"), \
1805                                   self.getCoefficientOfGeneralPDE("y_reduced"), \
1806                                   self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1807                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1808                   self.__applyConstraint()                   self.__applyConstraint()
1809                   self.__righthandside=self.copyConstraint(self.__righthandside)                   self.__righthandside=self.copyConstraint(self.__righthandside)
1810                   self.trace("New system has been built.")                   self.trace("New system has been built.")
1811                   self.__operator_isValid=True                   self.__operator_is_Valid=True
1812                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1813               elif not self.__righthandside_isValid:               elif not self.__righthandside_isValid:
1814                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
# Line 1253  class LinearPDE: Line 1816  class LinearPDE:
1816                                 self.getCoefficientOfGeneralPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1817                                 self.getCoefficientOfGeneralPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1818                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1819                     self.getDomain().addPDEToRHS(self.__righthandside, \
1820                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1821                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1822                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1823                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1824                   self.__righthandside=self.copyConstraint(self.__righthandside)                   self.__righthandside=self.copyConstraint(self.__righthandside)
1825                   self.trace("New right hand side has been built.")                   self.trace("New right hand side has been built.")
1826                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1827               elif not self.__operator_isValid:               elif not self.__operator_is_Valid:
1828                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \
1829                              self.getCoefficientOfGeneralPDE("A"), \                              self.getCoefficientOfGeneralPDE("A"), \
1830                              self.getCoefficientOfGeneralPDE("B"), \                              self.getCoefficientOfGeneralPDE("B"), \
# Line 1268  class LinearPDE: Line 1836  class LinearPDE:
1836                              escript.Data(),\                              escript.Data(),\
1837                              self.getCoefficientOfGeneralPDE("d_contact"), \                              self.getCoefficientOfGeneralPDE("d_contact"), \
1838                              escript.Data())                              escript.Data())
1839                     self.getDomain().addPDEToSystem(self.__operator,escript.Data(), \
1840                                self.getCoefficientOfGeneralPDE("A_reduced"), \
1841                                self.getCoefficientOfGeneralPDE("B_reduced"), \
1842                                self.getCoefficientOfGeneralPDE("C_reduced"), \
1843                                self.getCoefficientOfGeneralPDE("D_reduced"), \
1844                                escript.Data(), \
1845                                escript.Data(), \
1846                                self.getCoefficientOfGeneralPDE("d_reduced"), \
1847                                escript.Data(),\
1848                                self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1849                                escript.Data())
1850                   self.__applyConstraint()                   self.__applyConstraint()
1851                   self.trace("New operator has been built.")                   self.trace("New operator has been built.")
1852                   self.__operator_isValid=True                   self.__operator_is_Valid=True
1853         return (self.__operator,self.__righthandside)         return (self.__operator,self.__righthandside)
1854    
1855    
1856    class Poisson(LinearPDE):
   
 class AdvectivePDE(LinearPDE):  
1857     """     """
1858     Class to handle a linear PDE dominated by advective terms:     Class to define a Poisson equation problem, which is genear L{LinearPDE} of the form
   
    class to define a linear PDE of the form  
   
    \f[  
    -(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  
    \f]  
   
    with boundary conditons:  
1859    
1860     \f[     M{-grad(grad(u)[j])[j] = f}
    n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i  
    \f]  
1861    
1862     and contact conditions     with natural boundary conditons
1863    
1864     \f[     M{n[j]*grad(u)[j] = 0 }
    n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d^{contact}_{ik}[u_k] = - n_j*X_{ij} + y^{contact}_{i}  
    \f]  
1865    
1866     and constraints:     and constraints:
1867    
1868     \f[     M{u=0} where M{q>0}
1869     u_i=r_i \quad \mathrm{where} \quad q_i>0  
    \f]  
1870     """     """
    def __init__(self,domain,numEquations=0,numSolutions=0,xi=None,debug=False):  
       LinearPDE.__init__(self,domain,numEquations,numSolutions,debug)  
       if xi==None:  
          self.__xi=AdvectivePDE.ELMAN_RAMAGE  
       else:  
          self.__xi=xi  
       self.__Xi=escript.Data()  
1871    
1872     def __calculateXi(self,peclet_factor,Z,h):     def __init__(self,domain,debug=False):
1873         Z_max=util.Lsup(Z)       """
1874         if Z_max>0.:       initializes a new Poisson equation
           return h*self.__xi(Z*peclet_factor)/(Z+Z_max*self.TOL)  
        else:  
           return 0.  
1875    
1876     def setValue(self,**args):       @param domain: domain of the PDE
1877         if "A" in args.keys()   or "B" in args.keys() or "C" in args.keys(): self.__Xi=escript.Data()       @type domain: L{Domain<escript.Domain>}
1878         LinearPDE.setValue(**args)       @param debug: if True debug informations are printed.
   
    def ELMAN_RAMAGE(P):  
      """   """  
      return (P-1.).wherePositive()*0.5*(1.-1./(P+1.e-15))  
    def SIMPLIFIED_BROOK_HUGHES(P):  
      """   """  
      c=(P-3.).whereNegative()  
      return P/6.*c+1./2.*(1.-c)  
   
    def HALF(P):  
     """ """  
     return escript.Scalar(0.5,P.getFunctionSpace())  
   
    def getXi(self):  
       if self.__Xi.isEmpty():  
          B=self.getCoefficient("B")  
          C=self.getCoefficient("C")  
          A=self.getCoefficient("A")  
          h=self.getDomain().getSize()  
          self.__Xi=escript.Scalar(0.,self.getFunctionSpaceForCoefficient("A"))  
          if not C.isEmpty() or not B.isEmpty():  
             if not C.isEmpty() and not B.isEmpty():  
                 Z2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))  
                 if self.getNumEquations()>1:  
                    if self.getNumSolutions()>1:  
                       for i in range(self.getNumEquations()):  
                          for k in range(self.getNumSolutions()):  
                             for l in range(self.getDim()): Z2+=(C[i,k,l]-B[i,l,k])**2  
                    else:  
                       for i in range(self.getNumEquations()):  
                          for l in range(self.getDim()): Z2+=(C[i,l]-B[i,l])**2  
                 else:  
                    if self.getNumSolutions()>1:  
                       for k in range(self.getNumSolutions()):  
                          for l in range(self.getDim()): Z2+=(C[k,l]-B[l,k])**2  
                    else:  
                       for l in range(self.getDim()): Z2+=(C[l]-B[l])**2  
                 length_of_Z=util.sqrt(Z2)  
             elif C.isEmpty():  
               length_of_Z=util.length(B)  
             else:  
               length_of_Z=util.length(C)  
1879    
1880              Z_max=util.Lsup(length_of_Z)       """
1881              if Z_max>0.:       super(Poisson, self).__init__(domain,1,1,debug)
1882                 length_of_A=util.length(A)       self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1883                 A_max=util.Lsup(length_of_A)                          "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1884                 if A_max>0:                          "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1885                      inv_A=1./(length_of_A+A_max*self.TOL)       self.setSymmetryOn()
1886                 else:  
1887                      inv_A=1./self.TOL     def setValue(self,**coefficients):
1888                 peclet_number=length_of_Z*h/2*inv_A       """
1889                 xi=self.__xi(peclet_number)       sets new values to coefficients
                self.__Xi=h*xi/(length_of_Z+Z_max*self.TOL)  
                print "@ preclet number = %e"%util.Lsup(peclet_number),util.Lsup(xi),util.Lsup(length_of_Z)  
       return self.__Xi  
1890    
1891         @param coefficients: new values assigned to coefficients
1892         @keyword f: value for right hand side M{f}
1893         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1894         @keyword q: mask for location of constraints
1895         @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>}
1896                   depending of reduced order is used for the representation of the equation.
1897         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1898         """
1899         super(Poisson, self).setValue(**coefficients)
1900    
1901     def getCoefficientOfGeneralPDE(self,name):     def getCoefficientOfGeneralPDE(self,name):
1902       """       """
1903       return the value of the coefficient name of the general PDE       return the value of the coefficient name of the general PDE
1904         @param name: name of the coefficient requested.
1905       @param name:       @type name: C{string}
1906         @return: the value of the coefficient  name
1907         @rtype: L{Data<escript.Data>}
1908         @raise IllegalCoefficient: if name is not one of coefficients
1909                      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}.
1910         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1911       """       """
      if not self.getNumEquations() == self.getNumSolutions():  
           raise ValueError,"AdvectivePDE expects the number of solution componets and the number of equations to be equal."  
   
1912       if name == "A" :       if name == "A" :
1913           A=self.getCoefficient("A")           return escript.Data(util.kronecker(self.getDim()),escript.Function(self.getDomain()))
          B=self.getCoefficient("B")  
          C=self.getCoefficient("C")  
          if B.isEmpty() and C.isEmpty():  
             Aout=A  
          else:  
             if A.isEmpty():  
                Aout=self.createNewCoefficient("A")  
             else:  
                Aout=A[:]  
             Xi=self.getXi()  
             if self.getNumEquations()>1:  
                 for i in range(self.getNumEquations()):  
                    for j in range(self.getDim()):  
                       for k in range(self.getNumSolutions()):  
                          for l in range(self.getDim()):  
                             if not C.isEmpty() and not B.isEmpty():  
                                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])  
                             elif C.isEmpty():  
                                for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*B[p,j,i]*B[p,l,k]  
                             else:  
                                for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*C[p,i,j]*C[p,k,l]  
             else:  
                 for j in range(self.getDim()):  
                    for l in range(self.getDim()):  
                       if not C.isEmpty() and not B.isEmpty():  
                           Aout[j,l]+=Xi*(C[j]-B[j])*(C[l]-B[l])  
                       elif C.isEmpty():  
                           Aout[j,l]+=Xi*B[j]*B[l]  
                       else:  
                           Aout[j,l]+=Xi*C[j]*C[l]  
          return Aout  
1914       elif name == "B" :       elif name == "B" :
1915           B=self.getCoefficient("B")           return escript.Data()
          C=self.getCoefficient("C")  
          D=self.getCoefficient("D")  
          if C.isEmpty() or D.isEmpty():  
             Bout=B  
          else:  
             Xi=self.getXi()  
             if B.isEmpty():  
                 Bout=self.createNewCoefficient("B")  
             else:  
                 Bout=B[:]  
             if self.getNumEquations()>1:  
                for k in range(self.getNumSolutions()):  
                   for p in range(self.getNumEquations()):  
                      tmp=Xi*D[p,k]  
                      for i in range(self.getNumEquations()):  
                         for j in range(self.getDim()):  
                            Bout[i,j,k]+=tmp*C[p,i,j]  
             else:  
                tmp=Xi*D  
                for j in range(self.getDim()): Bout[j]+=tmp*C[j]  
          return Bout  
1916       elif name == "C" :       elif name == "C" :
1917           B=self.getCoefficient("B")           return escript.Data()
          C=self.getCoefficient("C")  
          D=self.getCoefficient("D")  
          if B.isEmpty() or D.isEmpty():  
             Cout=C  
          else:  
             Xi=self.getXi()  
             if C.isEmpty():  
                 Cout=self.createNewCoefficient("C")  
             else:  
                 Cout=C[:]  
             if self.getNumEquations()>1:  
                for k in range(self.getNumSolutions()):  
                    for p in range(self.getNumEquations()):  
                       tmp=Xi*D[p,k]  
                       for i in range(self.getNumEquations()):  
                         for l in range(self.getDim()):  
                                  Cout[i,k,l]+=tmp*B[p,l,i]  
             else:  
                tmp=Xi*D  
                for j in range(self.getDim()): Cout[j]+=tmp*B[j]  
          return Cout  
1918       elif name == "D" :       elif name == "D" :
1919           return self.getCoefficient("D")           return escript.Data()
1920       elif name == "X" :       elif name == "X" :
1921           X=self.getCoefficient("X")           return escript.Data()
          Y=self.getCoefficient("Y")  
          B=self.getCoefficient("B")  
          C=self.getCoefficient("C")  
          if Y.isEmpty() or (B.isEmpty() and C.isEmpty()):  
             Xout=X  
          else:  
             if X.isEmpty():  
                 Xout=self.createNewCoefficient("X")  
             else:  
                 Xout=X[:]  
             Xi=self.getXi()  
             if self.getNumEquations()>1:  
                  for p in range(self.getNumEquations()):  
                     tmp=Xi*Y[p]  
                     for i in range(self.getNumEquations()):  
                        for j in range(self.getDim()):  
                           if not C.isEmpty() and not B.isEmpty():  
                              Xout[i,j]+=tmp*(C[p,i,j]-B[p,j,i])  
                           elif C.isEmpty():  
                              Xout[i,j]-=tmp*B[p,j,i]  
                           else:  
                              Xout[i,j]+=tmp*C[p,i,j]  
             else:  
                  tmp=Xi*Y  
                  for j in range(self.getDim()):  
                     if not C.isEmpty() and not B.isEmpty():  
                        Xout[j]+=tmp*(C[j]-B[j])  
                     elif C.isEmpty():  
                        Xout[j]-=tmp*B[j]  
                     else:  
                        Xout[j]+=tmp*C[j]  
          return Xout  
1922       elif name == "Y" :       elif name == "Y" :
1923           return self.getCoefficient("Y")           return self.getCoefficient("f")
1924       elif name == "d" :       elif name == "d" :
1925           return self.getCoefficient("d")           return escript.Data()
1926       elif name == "y" :       elif name == "y" :
1927           return self.getCoefficient("y")           return escript.Data()
1928       elif name == "d_contact" :       elif name == "d_contact" :
1929           return self.getCoefficient("d_contact")           return escript.Data()
1930       elif name == "y_contact" :       elif name == "y_contact" :
1931           return self.getCoefficient("y_contact")           return escript.Data()
1932         elif name == "A_reduced" :
1933             return escript.Data()
1934         elif name == "B_reduced" :
1935             return escript.Data()
1936         elif name == "C_reduced" :
1937             return escript.Data()
1938         elif name == "D_reduced" :
1939             return escript.Data()
1940         elif name == "X_reduced" :
1941             return escript.Data()
1942         elif name == "Y_reduced" :
1943             return self.getCoefficient("f_reduced")
1944         elif name == "d_reduced" :
1945             return escript.Data()
1946         elif name == "y_reduced" :
1947             return escript.Data()
1948         elif name == "d_contact_reduced" :
1949             return escript.Data()
1950         elif name == "y_contact_reduced" :
1951             return escript.Data()
1952       elif name == "r" :       elif name == "r" :
1953           return self.getCoefficient("r")           return escript.Data()
1954       elif name == "q" :       elif name == "q" :
1955           return self.getCoefficient("q")           return self.getCoefficient("q")
1956       else:       else:
1957           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
   
1958    
1959  class Poisson(LinearPDE):  class Helmholtz(LinearPDE):
1960     """     """
1961     Class to define a Poisson equation problem:     Class to define a Helmhotz equation problem, which is genear L{LinearPDE} of the form
1962    
1963       M{S{omega}*u - grad(k*grad(u)[j])[j] = f}
1964    
1965     class to define a linear PDE of the form     with natural boundary conditons
1966     \f[  
1967     -u_{,jj} = f     M{k*n[j]*grad(u)[j] = g- S{alpha}u }
    \f]  
   
    with boundary conditons:  
   
    \f[  
    n_j*u_{,j} = 0  
    \f]  
1968    
1969     and constraints:     and constraints:
1970    
1971     \f[     M{u=r} where M{q>0}
1972     u=0 \quad \mathrm{where} \quad q>0  
    \f]  
1973     """     """
1974    
1975     def __init__(self,domain,f=escript.Data(),q=escript.Data(),debug=False):     def __init__(self,domain,debug=False):
1976         LinearPDE.__init__(self,domain,1,1,debug)       """
1977         self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),       initializes a new Poisson equation
1978                            "q": PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.BOTH)}  
1979         self.setSymmetryOn()       @param domain: domain of the PDE
1980         self.setValue(f,q)       @type domain: L{Domain<escript.Domain>}
1981         @param debug: if True debug informations are printed.
1982     def setValue(self,f=escript.Data(),q=escript.Data()):  
1983         """set value of PDE parameters f and q"""       """
1984         self._LinearPDE__setValue(f=f,q=q)       super(Helmholtz, self).__init__(domain,1,1,debug)
1985         self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1986                            "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1987                            "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1988                            "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1989                            "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1990                            "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1991                            "g_reduced": PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1992                            "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1993                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1994         self.setSymmetryOn()
1995    
1996       def setValue(self,**coefficients):
1997         """
1998         sets new values to coefficients
1999    
2000         @param coefficients: new values assigned to coefficients
2001         @keyword omega: value for coefficient M{S{omega}}
2002         @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2003         @keyword k: value for coefficeint M{k}
2004         @type k: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2005         @keyword f: value for right hand side M{f}
2006         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2007         @keyword alpha: value for right hand side M{S{alpha}}
2008         @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2009         @keyword g: value for right hand side M{g}
2010         @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2011         @keyword r: prescribed values M{r} for the solution in constraints.
2012         @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2013                   depending of reduced order is used for the representation of the equation.
2014         @keyword q: mask for location of constraints
2015         @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2016                   depending of reduced order is used for the representation of the equation.
2017         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2018         """
2019         super(Helmholtz, self).setValue(**coefficients)
2020    
2021     def getCoefficientOfGeneralPDE(self,name):     def getCoefficientOfGeneralPDE(self,name):
2022       """       """
2023       return the value of the coefficient name of the general PDE       return the value of the coefficient name of the general PDE
2024    
2025       @param name:       @param name: name of the coefficient requested.
2026         @type name: C{string}
2027         @return: the value of the coefficient  name
2028         @rtype: L{Data<escript.Data>}
2029         @raise IllegalCoefficient: if name is not one of coefficients
2030                      "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}.
2031         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2032       """       """
2033       if name == "A" :       if name == "A" :
2034           return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))           return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))*self.getCoefficient("k")
2035       elif name == "B" :       elif name == "B" :
2036           return escript.Data()           return escript.Data()
2037       elif name == "C" :       elif name == "C" :
2038           return escript.Data()           return escript.Data()
2039       elif name == "D" :       elif name == "D" :
2040           return escript.Data()           return self.getCoefficient("omega")
2041       elif name == "X" :       elif name == "X" :
2042           return escript.Data()           return escript.Data()
2043       elif name == "Y" :       elif name == "Y" :
2044           return self.getCoefficient("f")           return self.getCoefficient("f")
2045       elif name == "d" :       elif name == "d" :
2046           return escript.Data()           return self.getCoefficient("alpha")
2047       elif name == "y" :       elif name == "y" :
2048           return escript.Data()           return self.getCoefficient("g")
2049       elif name == "d_contact" :       elif name == "d_contact" :
2050           return escript.Data()           return escript.Data()
2051       elif name == "y_contact" :       elif name == "y_contact" :
2052           return escript.Data()           return escript.Data()
2053       elif name == "r" :       elif name == "A_reduced" :
2054             return escript.Data()
2055         elif name == "B_reduced" :
2056             return escript.Data()
2057         elif name == "C_reduced" :
2058             return escript.Data()
2059         elif name == "D_reduced" :
2060             return escript.Data()
2061         elif name == "X_reduced" :
2062             return escript.Data()
2063         elif name == "Y_reduced" :
2064             return self.getCoefficient("f_reduced")
2065         elif name == "d_reduced" :
2066             return escript.Data()
2067         elif name == "y_reduced" :
2068            return self.getCoefficient("g_reduced")
2069         elif name == "d_contact_reduced" :
2070             return escript.Data()
2071         elif name == "y_contact_reduced" :
2072           return escript.Data()           return escript.Data()
2073         elif name == "r" :
2074             return self.getCoefficient("r")
2075       elif name == "q" :       elif name == "q" :
2076           return self.getCoefficient("q")           return self.getCoefficient("q")
2077       else:       else:
2078           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2079    
2080  class LameEquation(LinearPDE):  class LameEquation(LinearPDE):
2081     """     """
2082     Class to define a Lame equation problem:     Class to define a Lame equation problem:
2083    
2084     class to define a linear PDE of the form     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] }
2085     \f[  
2086     -(\mu (u_{i,j}+u_{j,i}))_{,j} - \lambda u_{j,ji}} = F_i -\sigma_{ij,j}     with natural boundary conditons:
2087     \f]  
2088       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] }
    with boundary conditons:  
   
    \f[  
    n_j(\mu (u_{i,j}+u_{j,i})-sigma_{ij}) + n_i\lambda u_{j,j} = f_i  
    \f]  
2089    
2090     and constraints:     and constraints:
2091    
2092     \f[     M{u[i]=r[i]} where M{q[i]>0}
2093     u_i=r_i \quad \mathrm{where} \quad q_i>0  
    \f]  
2094     """     """
2095    
2096     def __init__(self,domain,f=escript.Data(),q=escript.Data(),debug=False):     def __init__(self,domain,debug=False):
2097         LinearPDE.__init__(self,domain,domain.getDim(),domain.getDim(),debug)        super(LameEquation, self).__init__(domain,\
2098         self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),                                           domain.getDim(),domain.getDim(),debug)
2099          self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2100                            "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),                            "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2101                            "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),                            "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2102                            "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM),PDECoefficient.RIGHTHANDSIDE),                            "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
2103                            "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),                            "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2104                            "r"            : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.BOTH),                            "r"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
2105                            "q"            : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.BOTH)}                            "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
2106         self.setSymmetryOn()        self.setSymmetryOn()
2107    
2108     def setValue(self,lame_lambda=escript.Data(),lame_mu=escript.Data(),F=escript.Data(),sigma=escript.Data(),f=escript.Data(),r=escript.Data(),q=escript.Data()):     def setValues(self,**coefficients):
2109         """set value of PDE parameters"""       """
2110         self._LinearPDE__setValue(lame_lambda=lame_lambda, \       sets new values to coefficients
2111                                   lame_mu=lame_mu, \  
2112                                   F=F, \       @param coefficients: new values assigned to coefficients
2113                                   sigma=sigma, \       @keyword lame_mu: value for coefficient M{S{mu}}
2114                                   f=f, \       @type lame_mu: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2115                                   r=r, \       @keyword lame_lambda: value for coefficient M{S{lambda}}
2116                                   q=q)       @type lame_lambda: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2117         @keyword F: value for internal force M{F}
2118         @type F: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}
2119         @keyword sigma: value for initial stress M{S{sigma}}
2120         @type sigma: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}
2121         @keyword f: value for extrenal force M{f}
2122         @type f: any type that can be casted to L{Vector<escript.Vector>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}
2123         @keyword r: prescribed values M{r} for the solution in constraints.
2124         @type r: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2125                   depending of reduced order is used for the representation of the equation.
2126         @keyword q: mask for location of constraints
2127         @type q: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2128                   depending of reduced order is used for the representation of the equation.
2129         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2130         """
2131         super(LameEquation, self).setValues(**coefficients)
2132    
2133     def getCoefficientOfGeneralPDE(self,name):     def getCoefficientOfGeneralPDE(self,name):
2134       """       """
2135       return the value of the coefficient name of the general PDE       return the value of the coefficient name of the general PDE
2136    
2137       @param name:       @param name: name of the coefficient requested.
2138         @type name: C{string}
2139         @return: the value of the coefficient  name
2140         @rtype: L{Data<escript.Data>}
2141         @raise IllegalCoefficient: if name is not one of coefficients
2142                      "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}.
2143         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2144       """       """
2145       if name == "A" :       if name == "A" :
2146           out =self.createCoefficientOfGeneralPDE("A")           out =self.createCoefficientOfGeneralPDE("A")
# Line 1662  class LameEquation(LinearPDE): Line 2168  class LameEquation(LinearPDE):
2168           return escript.Data()           return escript.Data()
2169       elif name == "y_contact" :       elif name == "y_contact" :
2170           return escript.Data()           return escript.Data()
2171         elif name == "A_reduced" :
2172             return escript.Data()
2173         elif name == "B_reduced" :
2174             return escript.Data()
2175         elif name == "C_reduced" :
2176             return escript.Data()
2177         elif name == "D_reduced" :
2178             return escript.Data()
2179         elif name == "X_reduced" :
2180             return escript.Data()
2181         elif name == "Y_reduced" :
2182             return escript.Data()
2183         elif name == "d_reduced" :
2184             return escript.Data()
2185         elif name == "y_reduced" :
2186             return escript.Data()
2187         elif name == "d_contact_reduced" :
2188             return escript.Data()
2189         elif name == "y_contact_reduced" :
2190             return escript.Data()
2191       elif name == "r" :       elif name == "r" :
2192           return self.getCoefficient("r")           return self.getCoefficient("r")
2193       elif name == "q" :       elif name == "q" :
2194           return self.getCoefficient("q")           return self.getCoefficient("q")
2195       else:       else:
2196           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2197    
2198  # $Log$  def LinearSinglePDE(domain,debug=False):
2199  # Revision 1.11  2005/08/23 01:24:28  jgs     """
2200  # Merge of development branch dev-02 back to main trunk on 2005-08-23     defines a single linear PDEs
2201  #  
2202  # Revision 1.10  2005/08/12 01:45:36  jgs     @param domain: domain of the PDE
2203  # erge of development branch dev-02 back to main trunk on 2005-08-12     @type domain: L{Domain<escript.Domain>}
2204  #     @param debug: if True debug informations are printed.
2205  # Revision 1.9.2.4  2005/08/22 07:11:09  gross     @rtype: L{LinearPDE}
2206  # some problems with LinearPDEs fixed.     """
2207  #     return LinearPDE(domain,numEquations=1,numSolutions=1,debug=debug)
2208  # Revision 1.9.2.3  2005/08/18 04:48:48  gross  
2209  # the methods SetLumping*() are removed. Lumping is set trough setSolverMethod(LinearPDE.LUMPING)  def LinearPDESystem(domain,debug=False):
2210  #     """
2211  # Revision 1.9.2.2  2005/08/18 04:39:32  gross     defines a system of linear PDEs
2212  # the constants have been removed from util.py as they not needed anymore. PDE related constants are accessed through LinearPDE attributes now  
2213  #     @param domain: domain of the PDE
2214  # Revision 1.9.2.1  2005/07/29 07:10:27  gross     @type domain: L{Domain<escript.Domain>}
2215  # new functions in util and a new pde type in linearPDEs     @param debug: if True debug informations are printed.
2216  #     @rtype: L{LinearPDE}
2217  # Revision 1.1.2.25  2005/07/28 04:21:09  gross     """
2218  # Lame equation: (linear elastic, isotropic) added     return LinearPDE(domain,numEquations=domain.getDim(),numSolutions=domain.getDim(),debug=debug)
2219  #  
2220  # Revision 1.1.2.24  2005/07/22 06:37:11  gross  class TransportPDE(object):
2221  # some extensions to modellib and linearPDEs       """
2222  #       Warning: This is still a very experimental. The class is still changing!
2223  # Revision 1.1.2.23  2005/05/13 00:55:20  cochrane  
2224  # Fixed up some docstrings.  Moved module-level functions to top of file so       Mu_{,t} =-(A_{ij}u_{,j})_j-(B_{j}u)_{,j} + C_{j} u_{,j} + Y_i + X_{i,i}
2225  # that epydoc and doxygen can pick them up properly.      
2226  #       u=r where q>0
2227  # Revision 1.1.2.22  2005/05/12 11:41:30  gross      
2228  # some basic Models have been added       all coefficients are constant over time.
2229  #  
2230  # Revision 1.1.2.21  2005/05/12 07:16:12  cochrane       typical usage:
2231  # Moved ELMAN_RAMAGE, SIMPLIFIED_BROOK_HUGHES, and HALF functions to bottom of  
2232  # file so that the AdvectivePDE class is picked up by doxygen.  Some           p=TransportPDE(dom)
2233  # reformatting of docstrings.  Addition of code to make equations come out           p.setValue(M=Scalar(1.,Function(dom),C=Scalar(1.,Function(dom)*[-1.,0.])
2234  # as proper LaTeX.           p.setInitialSolution(u=exp(-length(dom.getX()-[0.1,0.1])**2)
2235  #           t=0
2236  # Revision 1.1.2.20  2005/04/15 07:09:08  gross           dt=0.1
2237  # some problems with functionspace and linearPDEs fixed.           while (t<1.):
2238  #                u=p.solve(dt)
2239  # Revision 1.1.2.19  2005/03/04 05:27:07  gross  
2240  # bug in SystemPattern fixed.       """
2241  #       def __init__(self,domain,num_equations=1,theta=0.5,useSUPG=False,trace=True):
2242  # Revision 1.1.2.18  2005/02/08 06:16:45  gross          self.__domain=domain
2243  # Bugs in AdvectivePDE fixed, AdvectiveTest is stable but more testing is needed          self.__num_equations=num_equations
2244  #          self.__useSUPG=useSUPG
2245  # Revision 1.1.2.17  2005/02/08 05:56:19  gross          self.__trace=trace
2246  # Reference Number handling added          self.__theta=theta
2247  #          self.__matrix_type=0
2248  # Revision 1.1.2.16  2005/02/07 04:41:28  gross          self.__reduced=True
2249  # some function exposed to python to make mesh merging running          self.__reassemble=True
2250  #          if self.__useSUPG:
2251  # Revision 1.1.2.15  2005/02/03 00:14:44  gross             self.__pde=LinearPDE(domain,numEquations=num_equations,numSolutions=num_equations,debug=trace)
2252  # timeseries add and ESySParameter.py renames esysXML.py for consistence             self.__pde.setSymmetryOn()
2253  #             self.__pde.setReducedOrderOn()
2254  # Revision 1.1.2.14  2005/02/01 06:44:10  gross          else:
2255  # new implementation of AdvectivePDE which now also updates right hand side. systems of PDEs are still not working             self.__transport_problem=self.__getNewTransportProblem()
2256  #          self.setTolerance()
2257  # Revision 1.1.2.13  2005/01/25 00:47:07  gross          self.__M=escript.Data()
2258  # updates in the documentation          self.__A=escript.Data()
2259  #          self.__B=escript.Data()
2260  # Revision 1.1.2.12  2005/01/12 01:28:04  matt          self.__C=escript.Data()
2261  # Added createCoefficient method for linearPDEs.          self.__D=escript.Data()
2262  #          self.__X=escript.Data()
2263  # Revision 1.1.2.11  2005/01/11 01:55:34  gross          self.__Y=escript.Data()
2264  # a problem in linearPDE class fixed          self.__d=escript.Data()
2265  #          self.__y=escript.Data()
2266  # Revision 1.1.2.10  2005/01/07 01:13:29  gross          self.__d_contact=escript.Data()
2267  # some bugs in linearPDE fixed          self.__y_contact=escript.Data()
2268  #          self.__r=escript.Data()
2269  # Revision 1.1.2.9  2005/01/06 06:24:58  gross          self.__q=escript.Data()
2270  # some bugs in slicing fixed  
2271  #       def trace(self,text):
2272  # Revision 1.1.2.8  2005/01/05 04:21:40  gross               if self.__trace: print text
2273  # FunctionSpace checking/matchig in slicing added       def getSafeTimeStepSize(self):
2274  #          if self.__useSUPG:
2275  # Revision 1.1.2.7  2004/12/29 10:03:41  gross              if self.__reassemble:
2276  # bug in setValue fixed                 h=self.__domain.getSize()
2277  #                 dt=None
2278  # Revision 1.1.2.6  2004/12/29 05:29:59  gross                 if not self.__A.isEmpty():
2279  # AdvectivePDE successfully tested for Peclet number 1000000. there is still a problem with setValue and Data()                    dt2=util.inf(h**2*self.__M/util.length(self.__A))
2280  #                    if dt == None:
2281  # Revision 1.1.2.5  2004/12/29 00:18:41  gross                       dt = dt2
2282  # AdvectivePDE added                    else:
2283  #                       dt=1./(1./dt+1./dt2)
2284  # Revision 1.1.2.4  2004/12/24 06:05:41  gross                 if not self.__B.isEmpty():
2285  # some changes in linearPDEs to add AdevectivePDE                    dt2=util.inf(h*self.__M/util.length(self.__B))
2286  #                    if dt == None:
2287  # Revision 1.1.2.3  2004/12/16 00:12:34  gross                       dt = dt2
2288  # __init__ of LinearPDE does not accept any coefficient anymore                    else:
2289  #                       dt=1./(1./dt+1./dt2)
2290  # Revision 1.1.2.2  2004/12/14 03:55:01  jgs                 if not  self.__C.isEmpty():
2291  # *** empty log message ***                    dt2=util.inf(h*self.__M/util.length(self.__C))
2292  #                    if dt == None:
2293  # Revision 1.1.2.1  2004/12/12 22:53:47  gross                       dt = dt2
2294  # linearPDE has been renamed LinearPDE                    else:
2295  #                       dt=1./(1./dt+1./dt2)
2296  # Revision 1.1.1.1.2.7  2004/12/07 10:13:08  gross                 if not self.__D.isEmpty():
2297  # GMRES added                    dt2=util.inf(self.__M/util.length(self.__D))
2298  #                    if dt == None:
2299  # Revision 1.1.1.1.2.6  2004/12/07 03:19:50  gross                       dt = dt2
2300  # options for GMRES and PRES20 added                    else:
2301  #                       dt=1./(1./dt+1./dt2)
2302  # Revision 1.1.1.1.2.5  2004/12/01 06:25:15  gross                 self.__dt = dt/2
2303  # some small changes              return self.__dt
2304  #          else:
2305  # Revision 1.1.1.1.2.4  2004/11/24 01:50:21  gross              return self.__getTransportProblem().getSafeTimeStepSize()
2306  # Finley solves 4M unknowns now       def getDomain(self):
2307  #          return self.__domain
2308  # Revision 1.1.1.1.2.3  2004/11/15 06:05:26  gross       def getTheta(self):
2309  # poisson solver added          return self.__theta
2310  #       def getNumEquations(self):
2311  # Revision 1.1.1.1.2.2  2004/11/12 06:58:15  gross          return self.__num_equations
2312  # a lot of changes to get the linearPDE class running: most important change is that there is no matrix format exposed to the user anymore. the format is chosen by the Domain according to the solver and symmetry       def setReducedOn(self):
2313  #            if not self.reduced():
2314  # Revision 1.1.1.1.2.1  2004/10/28 22:59:22  gross                if self.__useSUPG:
2315  # finley's RecTest.py is running now: problem in SystemMatrixAdapater fixed                   self.__pde.setReducedOrderOn()
2316  #                else:
2317  # Revision 1.1.1.1  2004/10/26 06:53:56  jgs                   self.__transport_problem=self.__getNewTransportProblem()
2318  # initial import of project esys2            self.__reduced=True
2319  #       def setReducedOff(self):
2320  # Revision 1.3.2.3  2004/10/26 06:43:48  jgs            if self.reduced():
2321  # committing Lutz's and Paul's changes to brach jgs                if self.__useSUPG:
2322  #                   self.__pde.setReducedOrderOff()
2323  # Revision 1.3.4.1  2004/10/20 05:32:51  cochrane                else:
2324  # Added incomplete Doxygen comments to files, or merely put the docstrings that already exist into Doxygen form.                   self.__transport_problem=self.__getNewTransportProblem()
2325  #            self.__reduced=False
2326  # Revision 1.3  2004/09/23 00:53:23  jgs       def reduced(self):
2327  # minor fixes           return self.__reduced
2328  #       def getFunctionSpace(self):
2329  # Revision 1.1  2004/08/28 12:58:06  gross          if self.reduced():
2330  # SimpleSolve is not running yet: problem with == of functionsspace             return escript.ReducedSolution(self.getDomain())
2331  #          else:
2332  #             return escript.Solution(self.getDomain())
2333    
2334         def setTolerance(self,tol=1.e-8):
2335            self.__tolerance=tol
2336            if self.__useSUPG:
2337                  self.__pde.setTolerance(self.__tolerance)
2338    
2339         def __getNewTransportProblem(self):
2340           """
2341           returns an instance of a new operator
2342           """
2343           self.trace("New Transport problem is allocated.")
2344           return self.getDomain().newTransportProblem( \
2345                                   self.getTheta(),
2346                                   self.getNumEquations(), \
2347                                   self.getFunctionSpace(), \
2348                                   self.__matrix_type)
2349              
2350         def __getNewSolutionVector(self):
2351             if self.getNumEquations() ==1 :
2352                    out=escript.Data(0.0,(),self.getFunctionSpace())
2353             else:
2354                    out=escript.Data(0.0,(self.getNumEquations(),),self.getFunctionSpace())
2355             return out
2356    
2357         def __getTransportProblem(self):
2358           if self.__reassemble:
2359                 self.__source=self.__getNewSolutionVector()
2360                 self.__transport_problem.reset()
2361                 self.getDomain().addPDEToTransportProblem(
2362                             self.__transport_problem,
2363                             self.__source,
2364                             self.__M,
2365                             self.__A,
2366                             self.__B,
2367                             self.__C,
2368                             self.__D,
2369                             self.__X,
2370                             self.__Y,
2371                             self.__d,
2372                             self.__y,
2373                             self.__d_contact,
2374                             self.__y_contact)
2375                 self.__transport_problem.insertConstraint(self.__source,self.__q,self.__r)
2376                 self.__reassemble=False
2377           return self.__transport_problem
2378         def setValue(self,M=None, A=None, B=None, C=None, D=None, X=None, Y=None,
2379                      d=None, y=None, d_contact=None, y_contact=None, q=None, r=None):
2380                 if not M==None:
2381                      self.__reassemble=True
2382                      self.__M=M
2383                 if not A==None:
2384                      self.__reassemble=True
2385                      self.__A=A
2386                 if not B==None:
2387                      self.__reassemble=True
2388                      self.__B=B
2389                 if not C==None:
2390                      self.__reassemble=True
2391                      self.__C=C
2392                 if not D==None:
2393                      self.__reassemble=True
2394                      self.__D=D
2395                 if not X==None:
2396                      self.__reassemble=True
2397                      self.__X=X
2398                 if not Y==None:
2399                      self.__reassemble=True
2400                      self.__Y=Y
2401                 if not d==None:
2402                      self.__reassemble=True
2403                      self.__d=d
2404                 if not y==None:
2405                      self.__reassemble=True
2406                      self.__y=y
2407                 if not d_contact==None:
2408                      self.__reassemble=True
2409                      self.__d_contact=d_contact
2410                 if not y_contact==None:
2411                      self.__reassemble=True
2412                      self.__y_contact=y_contact
2413                 if not q==None:
2414                      self.__reassemble=True
2415                      self.__q=q
2416                 if not r==None:
2417                      self.__reassemble=True
2418                      self.__r=r
2419    
2420         def setInitialSolution(self,u):
2421                 if self.__useSUPG:
2422                     self.__u=util.interpolate(u,self.getFunctionSpace())
2423                 else:
2424                     self.__transport_problem.setInitialValue(util.interpolate(u,self.getFunctionSpace()))
2425    
2426         def solve(self,dt,**kwarg):
2427               if self.__useSUPG:
2428                    if self.__reassemble:
2429                        self.__pde.setValue(D=self.__M,d=self.__d,d_contact=self.__d_contact,q=self.__q) # ,r=self.__r)
2430                        self.__reassemble=False
2431                    dt2=self.getSafeTimeStepSize()
2432                    nn=max(math.ceil(dt/self.getSafeTimeStepSize()),1.)
2433                    dt2=dt/nn
2434                    nnn=0
2435                    u=self.__u
2436                    self.trace("number of substeps is %d."%nn)
2437                    while nnn<nn :
2438                        self.__setSUPG(u,u,dt2/2)
2439                        u_half=self.__pde.getSolution(verbose=True)
2440                        self.__setSUPG(u,u_half,dt2)
2441                        u=self.__pde.getSolution(verbose=True)
2442                        nnn+=1
2443                    self.__u=u
2444                    return self.__u
2445               else:
2446                   kwarg["tolerance"]=self.__tolerance
2447                   tp=self.__getTransportProblem()
2448                   return tp.solve(self.__source,dt,kwarg)
2449         def __setSUPG(self,u0,u,dt):
2450                g=util.grad(u)
2451                X=0
2452                Y=self.__M*u0
2453                X=0
2454                self.__pde.setValue(r=u0)
2455                if not self.__A.isEmpty():
2456                   X=X+dt*util.matrixmult(self.__A,g)
2457                if not self.__B.isEmpty():
2458                   X=X+dt*self.__B*u
2459                if not  self.__C.isEmpty():
2460                   Y=Y+dt*util.inner(self.__C,g)
2461                if not self.__D.isEmpty():
2462                   Y=Y+dt*self.__D*u
2463                if not self.__X.isEmpty():
2464                   X=X+dt*self.__X
2465                if not self.__Y.isEmpty():
2466                   Y=Y+dt*self.__Y
2467                self.__pde.setValue(X=X,Y=Y)
2468                if not self.__y.isEmpty():
2469                   self.__pde.setValue(y=dt*self.__y)
2470                if not self.__y_contact.isEmpty():
2471                   self.__pde.setValue(y=dt*self.__y_contact)
2472                self.__pde.setValue(r=u0)

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