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trunk/esys2/escript/py_src/linearPDEs.py revision 104 by jgs, Fri Dec 17 07:43:12 2004 UTC trunk/escript/py_src/linearPDEs.py revision 609 by elspeth, Tue Mar 21 09:46:39 2006 UTC
# Line 1  Line 1 
1  # $Id$  # $Id$
   
 ## @file linearPDEs.py  
   
2  """  """
3  @brief Functions and classes for linear PDEs  The module provides an interface to define and solve linear partial
4    differential equations (PDEs) within L{escript}. L{linearPDEs} does not provide any
5    solver capabilities in itself but hands the PDE over to
6    the PDE solver library defined through the L{Domain<escript.Domain>} of the PDE.
7    The general interface is provided through the L{LinearPDE} class. The
8    L{AdvectivePDE} which is derived from the L{LinearPDE} class
9    provides an interface to PDE dominated by its advective terms. The L{Poisson},
10    L{Helmholtz}, L{LameEquation}, L{AdvectionDiffusion}
11    classs which are also derived form the L{LinearPDE} class should be used
12    to define of solve these sepecial PDEs.
13    
14    @var __author__: name of author
15    @var __licence__: licence agreement
16    @var __url__: url entry point on documentation
17    @var __version__: version
18    @var __date__: date of the version
19  """  """
20    
21  import escript  import escript
22  import util  import util
23  import numarray  import numarray
24    
25  def identifyDomain(domain=None,data={}):  __author__="Lutz Gross, l.gross@uq.edu.au"
26       """  __copyright__="""  Copyright (c) 2006 by ACcESS MNRF
27       @brief Return the Domain which is equal to the input domain (if not None)                      http://www.access.edu.au
28       and is the domain of all Data objects in the dictionary data.                  Primary Business: Queensland, Australia"""
29       An exception is raised if this is not possible  __licence__="""Licensed under the Open Software License version 3.0
30                 http://www.opensource.org/licences/osl-3.0.php"""
31       @param domain  __url__="http://www.iservo.edu.au/esys/escript"
32       @param data  __version__="$Revision$"
33       """  __date__="$Date$"
34       # get the domain used by any Data object in the list data:  
35       data_domain=None  
36       for d in data.itervalues():  class IllegalCoefficient(ValueError):
37            if isinstance(d,escript.Data):     """
38               if not d.isEmpty(): data_domain=d.getDomain()     raised if an illegal coefficient of the general ar particular PDE is requested.
39       # check if domain and data_domain are identical?     """
40       if domain == None:  
41           if data_domain == None:  class IllegalCoefficientValue(ValueError):
42                raise ValueError,"Undefined PDE domain. Specify a domain or use a Data class object as coefficient"     """
43       else:     raised if an incorrect value for a coefficient is used.
44           if data_domain == None:     """
               data_domain=domain  
          else:  
            if not data_domain == domain:  
                  raise ValueError,"Domain of coefficients doesnot match specified domain"  
      # now we check if all Data class object coefficients are defined on data_domain:  
      for i,d in data.iteritems():  
          if isinstance(d,escript.Data):  
             if not d.isEmpty():  
                if not data_domain==d.getDomain():  
                  raise ValueError,"Illegal domain for coefficient %s."%i  
      # done:  
      return data_domain  
   
 def identifyNumEquationsAndSolutions(dim,coef={}):  
      # get number of equations and number of unknowns:  
      numEquations=0  
      numSolutions=0  
      for i in coef.iterkeys():  
         if not coef[i].isEmpty():  
            res=_PDECoefficientTypes[i].estimateNumEquationsAndNumSolutions(coef[i].getShape(),dim)  
            if res==None:  
                raise ValueError,"Illegal shape %s of coefficient %s"%(coef[i].getShape().__str__(),i)  
            else:  
                numEquations=max(numEquations,res[0])  
                numSolutions=max(numSolutions,res[1])  
      return numEquations,numSolutions  
   
   
 def _CompTuple2(t1,t2):  
    """  
    @brief  
   
    @param t1  
    @param t2  
    """  
    dif=t1[0]+t1[1]-(t2[0]+t2[1])  
    if dif<0: return 1  
    elif dif>0: return -1  
    else: return 0  
45    
46  class PDECoefficientType:  class UndefinedPDEError(ValueError):
47       """
48       raised if a PDE is not fully defined yet.
49       """
50    
51    class PDECoefficient(object):
52      """      """
53      @brief      A class for describing a PDE coefficient
54    
55        @cvar INTERIOR: indicator that coefficient is defined on the interior of the PDE domain
56        @cvar BOUNDARY: indicator that coefficient is defined on the boundary of the PDE domain
57        @cvar CONTACT: indicator that coefficient is defined on the contact region within the PDE domain
58        @cvar SOLUTION: indicator that coefficient is defined trough a solution of the PDE
59        @cvar REDUCED: indicator that coefficient is defined trough a reduced solution of the PDE
60        @cvar BY_EQUATION: indicator that the dimension of the coefficient shape is defined by the number PDE equations
61        @cvar BY_SOLUTION: indicator that the dimension of the coefficient shape is defined by the number PDE solutions
62        @cvar BY_DIM: indicator that the dimension of the coefficient shape is defined by the spatial dimension
63        @cvar OPERATOR: indicator that the the coefficient alters the operator of the PDE
64        @cvar RIGHTHANDSIDE: indicator that the the coefficient alters the right hand side of the PDE
65        @cvar BOTH: indicator that the the coefficient alters the operator as well as the right hand side of the PDE
66    
67      """      """
     # identifier for location of Data objects defining coefficients  
68      INTERIOR=0      INTERIOR=0
69      BOUNDARY=1      BOUNDARY=1
70      CONTACT=2      CONTACT=2
71      CONTINUOUS=3      SOLUTION=3
72      # identifier in the pattern of coefficients:      REDUCED=4
73      # 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
74      # number of unknowns.      BY_SOLUTION=6
75      EQUATION=3      BY_DIM=7
76      SOLUTION=4      OPERATOR=10
77      DIM=5      RIGHTHANDSIDE=11
78      # indicator for what is altered if the coefficient is altered:      BOTH=12
79      OPERATOR=5  
     RIGHTHANDSIDE=6  
     BOTH=7  
80      def __init__(self,where,pattern,altering):      def __init__(self,where,pattern,altering):
81         """         """
82         @brief Initialise a PDE Coefficient type         Initialise a PDE Coefficient type
83    
84           @param where: describes where the coefficient lives
85           @type where: one of L{INTERIOR}, L{BOUNDARY}, L{CONTACT}, L{SOLUTION}, L{REDUCED}
86           @param pattern: describes the shape of the coefficient and how the shape is build for a given
87                  spatial dimension and numbers of equation and solution in then PDE. For instance,
88                  (L{BY_EQUATION},L{BY_SOLUTION},L{BY_DIM}) descrbes a rank 3 coefficient which
89                  is instanciated as shape (3,2,2) in case of a three equations and two solution components
90                  on a 2-dimensional domain. In the case of single equation and a single solution component
91                  the shape compoments marked by L{BY_EQUATION} or L{BY_SOLUTION} are dropped. In this case
92                  the example would be read as (2,).
93           @type pattern: C{tuple} of L{BY_EQUATION}, L{BY_SOLUTION}, L{BY_DIM}
94           @param altering: indicates what part of the PDE is altered if the coefficiennt is altered
95           @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}
96    
97         """         """
98           super(PDECoefficient, self).__init__()
99         self.what=where         self.what=where
100         self.pattern=pattern         self.pattern=pattern
101         self.altering=altering         self.altering=altering
102           self.resetValue()
103    
104      def getFunctionSpace(self,domain):      def resetValue(self):
105         """         """
106         @brief defines the FunctionSpace of the coefficient on the domain         resets coefficient value to default
   
        @param domain  
107         """         """
108         if self.what==self.INTERIOR: return escript.Function(domain)         self.value=escript.Data()
109         elif self.what==self.BOUNDARY: return escript.FunctionOnBoundary(domain)  
110         elif self.what==self.CONTACT: return escript.FunctionOnContactZero(domain)      def getFunctionSpace(self,domain,reducedEquationOrder=False,reducedSolutionOrder=False):
111         elif self.what==self.CONTINUOUS: return escript.ContinuousFunction(domain)         """
112           defines the L{FunctionSpace<escript.FunctionSpace>} of the coefficient
113    
114           @param domain: domain on which the PDE uses the coefficient
115           @type domain: L{Domain<escript.Domain>}
116           @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
117           @type domain: C{bool}
118           @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
119           @type domain: C{bool}
120           @return:  L{FunctionSpace<escript.FunctionSpace>} of the coefficient
121           @rtype:  L{FunctionSpace<escript.FunctionSpace>}
122           """
123           if self.what==self.INTERIOR:
124                return escript.Function(domain)
125           elif self.what==self.BOUNDARY:
126                return escript.FunctionOnBoundary(domain)
127           elif self.what==self.CONTACT:
128                return escript.FunctionOnContactZero(domain)
129           elif self.what==self.SOLUTION:
130                if reducedEquationOrder and reducedSolutionOrder:
131                    return escript.ReducedSolution(domain)
132                else:
133                    return escript.Solution(domain)
134           elif self.what==self.REDUCED:
135                return escript.ReducedSolution(domain)
136    
137        def getValue(self):
138           """
139           returns the value of the coefficient
140    
141           @return:  value of the coefficient
142           @rtype:  L{Data<escript.Data>}
143           """
144           return self.value
145    
146        def setValue(self,domain,numEquations=1,numSolutions=1,reducedEquationOrder=False,reducedSolutionOrder=False,newValue=None):
147           """
148           set the value of the coefficient to a new value
149    
150           @param domain: domain on which the PDE uses the coefficient
151           @type domain: L{Domain<escript.Domain>}
152           @param numEquations: number of equations of the PDE
153           @type numEquations: C{int}
154           @param numSolutions: number of components of the PDE solution
155           @type numSolutions: C{int}
156           @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
157           @type domain: C{bool}
158           @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
159           @type domain: C{bool}
160           @param newValue: number of components of the PDE solution
161           @type newValue: any object that can be converted into a L{Data<escript.Data>} object with the appropriate shape and L{FunctionSpace<escript.FunctionSpace>}
162           @raise IllegalCoefficientValue: if the shape of the assigned value does not match the shape of the coefficient
163           """
164           if newValue==None:
165               newValue=escript.Data()
166           elif isinstance(newValue,escript.Data):
167               if not newValue.isEmpty():
168                  try:
169                     newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
170                  except:
171                     raise IllegalCoefficientValue,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)
172           else:
173               newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
174           if not newValue.isEmpty():
175               if not self.getShape(domain,numEquations,numSolutions)==newValue.getShape():
176                   raise IllegalCoefficientValue,"Expected shape of coefficient is %s but actual shape is %s."%(self.getShape(domain,numEquations,numSolutions),newValue.getShape())
177           self.value=newValue
178    
179      def isAlteringOperator(self):      def isAlteringOperator(self):
180          """          """
181      @brief 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
182    
183            @return:  True if the operator of the PDE is changed when the coefficient is changed
184            @rtype:  C{bool}
185      """      """
186          if self.altering==self.OPERATOR or self.altering==self.BOTH:          if self.altering==self.OPERATOR or self.altering==self.BOTH:
187              return not None              return not None
# Line 119  class PDECoefficientType: Line 190  class PDECoefficientType:
190    
191      def isAlteringRightHandSide(self):      def isAlteringRightHandSide(self):
192          """          """
193      @brief 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
194    
195        @rtype:  C{bool}
196            @return:  True if the right hand side of the PDE is changed when the coefficient is changed
197      """      """
198          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:
199              return not None              return not None
200          else:          else:
201              return None              return None
202    
203      def estimateNumEquationsAndNumSolutions(self,shape=(),dim=3):      def estimateNumEquationsAndNumSolutions(self,domain,shape=()):
204         """         """
205         @brief 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
206    
207         @param shape         @param domain: domain on which the PDE uses the coefficient
208         @param dim         @type domain: L{Domain<escript.Domain>}
209           @param shape: suggested shape of the coefficient
210           @type shape: C{tuple} of C{int} values
211           @return: the number of equations and number of solutions of the PDE is the coefficient has shape s.
212                     If no appropriate numbers could be identified, C{None} is returned
213           @rtype: C{tuple} of two C{int} values or C{None}
214         """         """
215           dim=domain.getDim()
216         if len(shape)>0:         if len(shape)>0:
217             num=max(shape)+1             num=max(shape)+1
218         else:         else:
219             num=1             num=1
220         search=[]         search=[]
221         for u in range(num):         if self.definesNumEquation() and self.definesNumSolutions():
222            for e in range(num):            for u in range(num):
223               search.append((e,u))               for e in range(num):
224         search.sort(_CompTuple2)                  search.append((e,u))
225         for item in search:            search.sort(self.__CompTuple2)
226               s=self.buildShape(item[0],item[1],dim)            for item in search:
227                 s=self.getShape(domain,item[0],item[1])
228               if len(s)==0 and len(shape)==0:               if len(s)==0 and len(shape)==0:
229                   return (1,1)                   return (1,1)
230               else:               else:
231                   if s==shape: return item                   if s==shape: return item
232           elif self.definesNumEquation():
233              for e in range(num,0,-1):
234                 s=self.getShape(domain,e,0)
235                 if len(s)==0 and len(shape)==0:
236                     return (1,None)
237                 else:
238                     if s==shape: return (e,None)
239    
240           elif self.definesNumSolutions():
241              for u in range(num,0,-1):
242                 s=self.getShape(domain,0,u)
243                 if len(s)==0 and len(shape)==0:
244                     return (None,1)
245                 else:
246                     if s==shape: return (None,u)
247         return None         return None
248        def definesNumSolutions(self):
249           """
250           checks if the coefficient allows to estimate the number of solution components
251    
252      def buildShape(self,e=1,u=1,dim=3):         @return: True if the coefficient allows an estimate of the number of solution components
253          """         @rtype: C{bool}
254      @brief builds the required shape for a given number of equations e, number of unknowns u and spatial dimension dim         """
255           for i in self.pattern:
256                 if i==self.BY_SOLUTION: return True
257           return False
258    
259      @param e      def definesNumEquation(self):
260      @param u         """
261      @param dim         checks if the coefficient allows to estimate the number of equations
262      """  
263          s=()         @return: True if the coefficient allows an estimate of the number of equations
264          for i in self.pattern:         @rtype: C{bool}
265               if i==self.EQUATION:         """
266                  if e>1: s=s+(e,)         for i in self.pattern:
267               elif i==self.SOLUTION:               if i==self.BY_EQUATION: return True
268                  if u>1: s=s+(u,)         return False
269    
270        def __CompTuple2(self,t1,t2):
271          """
272          Compare two tuples of possible number of equations and number of solutions
273    
274          @param t1: The first tuple
275          @param t2: The second tuple
276    
277          """
278    
279          dif=t1[0]+t1[1]-(t2[0]+t2[1])
280          if dif<0: return 1
281          elif dif>0: return -1
282          else: return 0
283    
284        def getShape(self,domain,numEquations=1,numSolutions=1):
285           """
286           builds the required shape of the coefficient
287    
288           @param domain: domain on which the PDE uses the coefficient
289           @type domain: L{Domain<escript.Domain>}
290           @param numEquations: number of equations of the PDE
291           @type numEquations: C{int}
292           @param numSolutions: number of components of the PDE solution
293           @type numSolutions: C{int}
294           @return: shape of the coefficient
295           @rtype: C{tuple} of C{int} values
296           """
297           dim=domain.getDim()
298           s=()
299           for i in self.pattern:
300                 if i==self.BY_EQUATION:
301                    if numEquations>1: s=s+(numEquations,)
302                 elif i==self.BY_SOLUTION:
303                    if numSolutions>1: s=s+(numSolutions,)
304               else:               else:
305                  s=s+(dim,)                  s=s+(dim,)
306          return s         return s
307    
308  _PDECoefficientTypes={  class LinearPDE(object):
 "A"         : PDECoefficientType(PDECoefficientType.INTERIOR,(PDECoefficientType.EQUATION,PDECoefficientType.DIM,PDECoefficientType.SOLUTION,PDECoefficientType.DIM),PDECoefficientType.OPERATOR),  
 "B"         : PDECoefficientType(PDECoefficientType.INTERIOR,(PDECoefficientType.EQUATION,PDECoefficientType.DIM,PDECoefficientType.SOLUTION),PDECoefficientType.OPERATOR),  
 "C"         : PDECoefficientType(PDECoefficientType.INTERIOR,(PDECoefficientType.EQUATION,PDECoefficientType.SOLUTION,PDECoefficientType.DIM),PDECoefficientType.OPERATOR),  
 "D"         : PDECoefficientType(PDECoefficientType.INTERIOR,(PDECoefficientType.EQUATION,PDECoefficientType.SOLUTION),PDECoefficientType.OPERATOR),  
 "X"         : PDECoefficientType(PDECoefficientType.INTERIOR,(PDECoefficientType.EQUATION,PDECoefficientType.DIM),PDECoefficientType.RIGHTHANDSIDE),  
 "Y"         : PDECoefficientType(PDECoefficientType.INTERIOR,(PDECoefficientType.EQUATION,),PDECoefficientType.RIGHTHANDSIDE),  
 "d"         : PDECoefficientType(PDECoefficientType.BOUNDARY,(PDECoefficientType.EQUATION,PDECoefficientType.SOLUTION),PDECoefficientType.OPERATOR),  
 "y"         : PDECoefficientType(PDECoefficientType.BOUNDARY,(PDECoefficientType.EQUATION,),PDECoefficientType.RIGHTHANDSIDE),  
 "d_contact" : PDECoefficientType(PDECoefficientType.CONTACT,(PDECoefficientType.EQUATION,PDECoefficientType.SOLUTION),PDECoefficientType.OPERATOR),  
 "y_contact" : PDECoefficientType(PDECoefficientType.CONTACT,(PDECoefficientType.EQUATION,),PDECoefficientType.RIGHTHANDSIDE),  
 "r"         : PDECoefficientType(PDECoefficientType.CONTINUOUS,(PDECoefficientType.EQUATION,),PDECoefficientType.RIGHTHANDSIDE),  
 "q"         : PDECoefficientType(PDECoefficientType.CONTINUOUS,(PDECoefficientType.SOLUTION,),PDECoefficientType.BOTH),  
 }  
   
 class LinearPDE:  
309     """     """
310     @brief Class to define a linear PDE     This class is used to define a general linear, steady, second order PDE
311         for an unknown function M{u} on a given domain defined through a L{Domain<escript.Domain>} object.
    class to define a linear PDE of the form  
312    
313       -(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     For a single PDE with a solution with a single component the linear PDE is defined in the following form:
314    
315       with boundary conditons:     M{-grad(A[j,l]*grad(u)[l]+B[j]u)[j]+C[l]*grad(u)[l]+D*u =-grad(X)[j,j]+Y}
316    
317          n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i     where M{grad(F)} denotes the spatial derivative of M{F}. Einstein's summation convention,
318       ie. summation over indexes appearing twice in a term of a sum is performed, is used.
319       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
320       L{Function<escript.Function>} on the PDE or objects that can be converted into such L{Data<escript.Data>} objects.
321       M{A} is a rank two, M{B}, M{C} and M{X} are rank one and M{D} and M{Y} are scalar.
322    
323      and contact conditions     The following natural boundary conditions are considered:
324    
325          n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_contact_{ik}[u_k] = - n_j*X_{ij} + y_contact_i     M{n[j]*(A[i,j]*grad(u)[l]+B[j]*u)+d*u=n[j]*X[j]+y}
326    
327      and constraints:     where M{n} is the outer normal field calculated by L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
328       Notice that the coefficients M{A}, M{B} and M{X} are defined in the PDE. The coefficients M{d} and M{y} are
329       each a scalar in the L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
330    
          u_i=r_i where q_i>0  
331    
332     """     Constraints for the solution prescribing the value of the solution at certain locations in the domain. They have the form
    DEFAULT_METHOD=util.DEFAULT_METHOD  
    DIRECT=util.DIRECT  
    CHOLEVSKY=util.CHOLEVSKY  
    PCG=util.PCG  
    CR=util.CR  
    CGS=util.CGS  
    BICGSTAB=util.BICGSTAB  
    SSOR=util.SSOR  
    GMRES=util.GMRES  
    PRES20=util.PRES20  
333    
334     def __init__(self,domain,numEquations=0,numSolutions=0):     M{u=r}  where M{q>0}
335       """  
336       @brief initializes a new linear PDE.     M{r} and M{q} are each scalar where M{q} is the characteristic function defining where the constraint is applied.
337       The constraints override any other condition set by the PDE or the boundary condition.
338    
339       The PDE is symmetrical if
340    
341       M{A[i,j]=A[j,i]}  and M{B[j]=C[j]}
342    
343       For a system of PDEs and a solution with several components the PDE has the form
344    
345       M{-grad(A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]*u[k])[j]+C[i,k,l]*grad(u[k])[l]+D[i,k]*u[k] =-grad(X[i,j])[j]+Y[i] }
346    
347       M{A} is a ramk four, M{B} and M{C} are each a rank three, M{D} and M{X} are each a rank two and M{Y} is a rank one.
348       The natural boundary conditions take the form:
349    
350       M{n[j]*(A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]*u[k])+d[i,k]*u[k]=n[j]*X[i,j]+y[i]}
351    
352    
353       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
354    
      @param args  
      """  
355    
356       M{u[i]=r[i]}  where  M{q[i]>0}
357    
358       M{r} and M{q} are each rank one. Notice that at some locations not necessarily all components must have a constraint.
359    
360       The system of PDEs is symmetrical if
361    
362            - M{A[i,j,k,l]=A[k,l,i,j]}
363            - M{B[i,j,k]=C[k,i,j]}
364            - M{D[i,k]=D[i,k]}
365            - M{d[i,k]=d[k,i]}
366    
367       L{LinearPDE} also supports solution discontinuities over a contact region in the domain. To specify the conditions across the
368       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
369       defined as
370    
371       M{J[i,j]=A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]*u[k]-X[i,j]}
372    
373       For the case of single solution component and single PDE M{J} is defined
374    
375       M{J_{j}=A[i,j]*grad(u)[j]+B[i]*u-X[i]}
376    
377       In the context of discontinuities M{n} denotes the normal on the discontinuity pointing from side 0 towards side 1
378       calculated from L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnContactZero<escript.FunctionOnContactZero>}. For a system of PDEs
379       the contact condition takes the form
380    
381       M{n[j]*J0[i,j]=n[j]*J1[i,j]=y_contact[i]- d_contact[i,k]*jump(u)[k]}
382    
383       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
384       of the solution at side 1 and at side 0, denotes the jump of M{u} across discontinuity along the normal calcualted by
385       L{jump<util.jump>}.
386       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>}.
387       In case of a single PDE and a single component solution the contact condition takes the form
388    
389       M{n[j]*J0_{j}=n[j]*J1_{j}=y_contact-d_contact*jump(u)}
390    
391       In this case the the coefficient M{d_contact} and M{y_contact} are eaach scalar
392       both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
393    
394       @cvar DEFAULT: The default method used to solve the system of linear equations
395       @cvar DIRECT: The direct solver based on LDU factorization
396       @cvar CHOLEVSKY: The direct solver based on LDLt factorization (can only be applied for symmetric PDEs)
397       @cvar PCG: The preconditioned conjugate gradient method (can only be applied for symmetric PDEs)
398       @cvar CR: The conjugate residual method
399       @cvar CGS: The conjugate gardient square method
400       @cvar BICGSTAB: The stabilized BiConjugate Gradient method.
401       @cvar SSOR: The symmetric overrealaxtion method
402       @cvar ILU0: The incomplete LU factorization preconditioner  with no fill in
403       @cvar ILUT: The incomplete LU factorization preconditioner with will in
404       @cvar JACOBI: The Jacobi preconditioner
405       @cvar GMRES: The Gram-Schmidt minimum residual method
406       @cvar PRES20: Special GMRES with restart after 20 steps and truncation after 5 residuals
407       @cvar LUMPING: Matrix lumping.
408       @cvar NO_REORDERING: No matrix reordering allowed
409       @cvar MINIMUM_FILL_IN: Reorder matrix to reduce fill-in during factorization
410       @cvar NESTED_DISSECTION: Reorder matrix to improve load balancing during factorization
411       @cvar PASO: PASO solver package
412       @cvar SCSL: SGI SCSL solver library
413       @cvar MKL: Intel's MKL solver library
414       @cvar UMFPACK: the UMFPACK library
415       @cvar ITERATIVE: The default iterative solver
416       @cvar AMG: algebraic multi grid
417       @cvar RILU: recursive ILU
418    
419       """
420       DEFAULT= 0
421       DIRECT= 1
422       CHOLEVSKY= 2
423       PCG= 3
424       CR= 4
425       CGS= 5
426       BICGSTAB= 6
427       SSOR= 7
428       ILU0= 8
429       ILUT= 9
430       JACOBI= 10
431       GMRES= 11
432       PRES20= 12
433       LUMPING= 13
434       NO_REORDERING= 17
435       MINIMUM_FILL_IN= 18
436       NESTED_DISSECTION= 19
437       SCSL= 14
438       MKL= 15
439       UMFPACK= 16
440       ITERATIVE= 20
441       PASO= 21
442       AMG= 22
443       RILU = 23
444    
445       SMALL_TOLERANCE=1.e-13
446       __PACKAGE_KEY="package"
447       __METHOD_KEY="method"
448       __SYMMETRY_KEY="symmetric"
449       __TOLERANCE_KEY="tolerance"
450       __PRECONDITIONER_KEY="preconditioner"
451    
452    
453       def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):
454         """
455         initializes a new linear PDE
456    
457         @param domain: domain of the PDE
458         @type domain: L{Domain<escript.Domain>}
459         @param numEquations: number of equations. If numEquations==None the number of equations
460                              is exracted from the PDE coefficients.
461         @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
462                              is exracted from the PDE coefficients.
463         @param debug: if True debug informations are printed.
464    
465         """
466         super(LinearPDE, self).__init__()
467         #
468         #   the coefficients of the general PDE:
469         #
470         self.__COEFFICIENTS_OF_GENEARL_PDE={
471           "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
472           "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
473           "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
474           "D"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
475           "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
476           "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
477           "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
478           "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
479           "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
480           "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
481           "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
482           "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
483    
484         # COEFFICIENTS can be overwritten by subclasses:
485         self.COEFFICIENTS=self.__COEFFICIENTS_OF_GENEARL_PDE
486         self.__altered_coefficients=False
487       # initialize attributes       # initialize attributes
488       self.__debug=None       self.__debug=debug
489       self.__domain=domain       self.__domain=domain
490       self.__numEquations=numEquations       self.__numEquations=numEquations
491       self.__numSolutions=numSolutions       self.__numSolutions=numSolutions
492       self.cleanCoefficients()       self.__resetSystem()
   
      self.__operator=escript.Operator()  
      self.__operator_isValid=False  
      self.__righthandside=escript.Data()  
      self.__righthandside_isValid=False  
      self.__solution=escript.Data()  
      self.__solution_isValid=False  
493    
494       # set some default values:       # set some default values:
495       self.__homogeneous_constraint=True       self.__reduce_equation_order=False
496       self.__row_function_space=escript.Solution(self.__domain)       self.__reduce_solution_order=False
      self.__column_function_space=escript.Solution(self.__domain)  
497       self.__tolerance=1.e-8       self.__tolerance=1.e-8
498       self.__solver_method=util.DEFAULT_METHOD       self.__solver_method=self.DEFAULT
499       self.__matrix_type=self.__domain.getSystemMatrixTypeId(util.DEFAULT_METHOD,False)       self.__solver_package=self.DEFAULT
500         self.__preconditioner=self.DEFAULT
501         self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT,self.DEFAULT,False)
502       self.__sym=False       self.__sym=False
      self.__lumping=False  
503    
504     def getCoefficient(self,name):       self.resetCoefficients()
505         self.trace("PDE Coeffients are %s"%str(self.COEFFICIENTS.keys()))
506       # =============================================================================
507       #    general stuff:
508       # =============================================================================
509       def __str__(self):
510         """
511         returns string representation of the PDE
512    
513         @return: a simple representation of the PDE
514         @rtype: C{str}
515         """
516         return "<LinearPDE %d>"%id(self)
517       # =============================================================================
518       #    debug :
519       # =============================================================================
520       def setDebugOn(self):
521       """       """
522       @brief return the value of the coefficient name       switches on debugging
523         """
524         self.__debug=not None
525    
526       @param name     def setDebugOff(self):
527       """       """
528       return self.__coefficient[name]       switches off debugging
529         """
530         self.__debug=None
531    
532     def setValue(self,**coefficients):     def trace(self,text):
533        """       """
534        @brief sets new values to coefficients       print the text message if debugging is swiched on.
535         @param text: message
536         @type text: C{string}
537         """
538         if self.__debug: print "%s: %s"%(str(self),text)
539    
540        @param coefficients     # =============================================================================
541        """     # some service functions:
542        self._setValue(**coefficients)     # =============================================================================
543             def getDomain(self):
544         """
545         returns the domain of the PDE
546    
547     def _setValue(self,**coefficients):       @return: the domain of the PDE
548        """       @rtype: L{Domain<escript.Domain>}
549        @brief sets new values to coefficients       """
550         return self.__domain
551    
552        @param coefficients     def getDim(self):
553        """       """
554               returns the spatial dimension of the PDE
       # get the dictionary of the coefficinets been altered:  
       alteredCoefficients={}  
       for i,d in coefficients.iteritems():  
          if self.hasCoefficient(i):  
             if d == None:  
                 alteredCoefficients[i]=escript.Data()  
             elif isinstance(d,escript.Data):  
                 if d.isEmpty():  
                   alteredCoefficients[i]=escript.Data()  
                 else:  
                   alteredCoefficients[i]=escript.Data(d,self.getFunctionSpaceOfCoefficient(i))  
             else:  
                 alteredCoefficients[i]=escript.Data(d,self.getFunctionSpaceOfCoefficient(i))  
          else:  
             raise ValueError,"Attempt to set undefined coefficient %s"%i  
       # if numEquations and numSolutions is undefined we try identify their values based on the coefficients:  
       if self.__numEquations<1 or self.__numSolutions<1:  
             numEquations,numSolutions=identifyNumEquationsAndSolutions(self.getDomain().getDim(),alteredCoefficients)  
             if self.__numEquations<1 and numEquations>0: self.__numEquations=numEquations  
             if self.__numSolutions<1 and numSolutions>0: self.__numSolutions=numSolutions  
             if self.debug() and self.__numEquations>0: print "PDE Debug: identified number of equations is ",self.__numEquations  
             if self.debug() and self.__numSolutions>0: print "PDE Debug: identified number of solutions is ",self.__numSolutions  
555    
556        # now we check the shape of the coefficient if numEquations and numSolutions are set:       @return: the spatial dimension of the PDE domain
557        if  self.__numEquations>0 and  self.__numSolutions>0:       @rtype: C{int}
558           for i in self.__coefficient.iterkeys():       """
559               if alteredCoefficients.has_key(i) and not alteredCoefficients[i].isEmpty():       return self.getDomain().getDim()
                  if not self.getShapeOfCoefficient(i)==alteredCoefficients[i].getShape():  
                     raise ValueError,"Expected shape for coefficient %s is %s but actual shape is %s."%(i,self.getShapeOfCoefficient(i),alteredCoefficients[i].getShape())  
              else:  
                  if not self.__coefficient[i].isEmpty():  
                     if not self.getShapeOfCoefficient(i)==self.__coefficient[i].getShape():  
                        raise ValueError,"Expected shape for coefficient %s is %s but actual shape is %s."%(i,self.getShapeOfCoefficient(i),self.__coefficient[i].getShape())  
       # overwrite new values:  
       for i,d in alteredCoefficients.iteritems():  
          if self.debug(): print "PDE Debug: Coefficient %s has been altered."%i  
          self.__coefficient[i]=d  
          self.alteredCoefficient(i)  
   
       # reset the HomogeneousConstraintFlag:  
       self.__setHomogeneousConstraintFlag()  
       if not "q" in alteredCoefficients and not self.__homogeneous_constraint: self.__rebuildSystem()  
   
    def cleanCoefficients(self):  
      """  
      @brief resets all coefficients to default values.  
      """  
      self.__coefficient={}  
      for i in _PDECoefficientTypes.iterkeys():  
          self.__coefficient[i]=escript.Data()  
560    
561     def getShapeOfCoefficient(self,name):     def getNumEquations(self):
562       """       """
563       @brief return the shape of the coefficient name       returns the number of equations
564    
565       @param name       @return: the number of equations
566         @rtype: C{int}
567         @raise UndefinedPDEError: if the number of equations is not be specified yet.
568       """       """
569       if self.hasCoefficient(name):       if self.__numEquations==None:
570          return _PDECoefficientTypes[name].buildShape(self.getNumEquations(),self.getNumSolutions(),self.getDomain().getDim())           raise UndefinedPDEError,"Number of equations is undefined. Please specify argument numEquations."
571       else:       else:
572          raise ValueError,"Solution coefficient %s requested"%name           return self.__numEquations
573    
574     def getFunctionSpaceOfCoefficient(self,name):     def getNumSolutions(self):
575       """       """
576       @brief return the atoms of the coefficient name       returns the number of unknowns
577    
578       @param name       @return: the number of unknowns
579         @rtype: C{int}
580         @raise UndefinedPDEError: if the number of unknowns is not be specified yet.
581       """       """
582       if self.hasCoefficient(name):       if self.__numSolutions==None:
583          return _PDECoefficientTypes[name].getFunctionSpace(self.getDomain())          raise UndefinedPDEError,"Number of solution is undefined. Please specify argument numSolutions."
584       else:       else:
585          raise ValueError,"Solution coefficient %s requested"%name          return self.__numSolutions
586    
587     def alteredCoefficient(self,name):     def reduceEquationOrder(self):
588       """       """
589       @brief annonced that coefficient name has been changed       return status for order reduction for equation
590    
591       @param name       @return: return True is reduced interpolation order is used for the represenation of the equation
592         @rtype: L{bool}
593       """       """
594       if self.hasCoefficient(name):       return self.__reduce_equation_order
         if _PDECoefficientTypes[name].isAlteringOperator(): self.__rebuildOperator()  
         if _PDECoefficientTypes[name].isAlteringRightHandSide(): self.__rebuildRightHandSide()  
      else:  
         raise ValueError,"Solution coefficient %s requested"%name  
   
    def __setHomogeneousConstraintFlag(self):  
       """  
       @brief checks if the constraints are homogeneous and sets self.__homogeneous_constraint accordingly.  
       """  
       self.__homogeneous_constraint=True  
       q=self.getCoefficient("q")  
       r=self.getCoefficient("r")  
       if not q.isEmpty() and not r.isEmpty():  
          print (q*r).Lsup(), 1.e-13*r.Lsup()  
          if (q*r).Lsup()>=1.e-13*r.Lsup(): self.__homogeneous_constraint=False  
       if self.debug():  
            if self.__homogeneous_constraint:  
                print "PDE Debug: Constraints are homogeneous."  
            else:  
                print "PDE Debug: Constraints are inhomogeneous."  
   
595    
596     def hasCoefficient(self,name):     def reduceSolutionOrder(self):
597        """       """
598        @brief return true if name is the name of a coefficient       return status for order reduction for the solution
599    
600        @param name       @return: return True is reduced interpolation order is used for the represenation of the solution
601        """       @rtype: L{bool}
602        return self.__coefficient.has_key(name)       """
603         return self.__reduce_solution_order
604    
605     def getFunctionSpaceForEquation(self):     def getFunctionSpaceForEquation(self):
606       """       """
607       @brief return true if the test functions should use reduced order       returns the L{FunctionSpace<escript.FunctionSpace>} used to discretize the equation
608    
609         @return: representation space of equation
610         @rtype: L{FunctionSpace<escript.FunctionSpace>}
611       """       """
612       return self.__row_function_space       if self.reduceEquationOrder():
613             return escript.ReducedSolution(self.getDomain())
614         else:
615             return escript.Solution(self.getDomain())
616    
617     def getFunctionSpaceForSolution(self):     def getFunctionSpaceForSolution(self):
618       """       """
619       @brief return true if the interpolation of the solution should use reduced order       returns the L{FunctionSpace<escript.FunctionSpace>} used to represent the solution
620    
621         @return: representation space of solution
622         @rtype: L{FunctionSpace<escript.FunctionSpace>}
623       """       """
624       return self.__column_function_space       if self.reduceSolutionOrder():
625             return escript.ReducedSolution(self.getDomain())
626         else:
627             return escript.Solution(self.getDomain())
628    
629     # ===== debug ==============================================================  
630     def setDebugOn(self):     def getOperator(self):
631         """
632         provides access to the operator of the PDE
633    
634         @return: the operator of the PDE
635         @rtype: L{Operator<escript.Operator>}
636         """
637         m=self.getSystem()[0]
638         if self.isUsingLumping():
639             return self.copyConstraint(1./m)
640         else:
641             return m
642    
643       def getRightHandSide(self):
644         """
645         provides access to the right hand side of the PDE
646         @return: the right hand side of the PDE
647         @rtype: L{Data<escript.Data>}
648         """
649         r=self.getSystem()[1]
650         if self.isUsingLumping():
651             return self.copyConstraint(r)
652         else:
653             return r
654    
655       def applyOperator(self,u=None):
656         """
657         applies the operator of the PDE to a given u or the solution of PDE if u is not present.
658    
659         @param u: argument of the operator. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
660                   the current solution is used.
661         @type u: L{Data<escript.Data>} or None
662         @return: image of u
663         @rtype: L{Data<escript.Data>}
664         """
665         if u==None:
666              return self.getOperator()*self.getSolution()
667         else:
668            self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
669    
670       def getResidual(self,u=None):
671         """
672         return the residual of u or the current solution if u is not present.
673    
674         @param u: argument in the residual calculation. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
675                   the current solution is used.
676         @type u: L{Data<escript.Data>} or None
677         @return: residual of u
678         @rtype: L{Data<escript.Data>}
679         """
680         return self.applyOperator(u)-self.getRightHandSide()
681    
682       def checkSymmetry(self,verbose=True):
683          """
684          test the PDE for symmetry.
685    
686          @param verbose: if equal to True or not present a report on coefficients which are breaking the symmetry is printed.
687          @type verbose: C{bool}
688          @return:  True if the PDE is symmetric.
689          @rtype: L{Data<escript.Data>}
690          @note: This is a very expensive operation. It should be used for degugging only! The symmetry flag is not altered.
691          """
692          verbose=verbose or self.__debug
693          out=True
694          if self.getNumSolutions()!=self.getNumEquations():
695             if verbose: print "non-symmetric PDE because of different number of equations and solutions"
696             out=False
697          else:
698             A=self.getCoefficientOfGeneralPDE("A")
699             if not A.isEmpty():
700                tol=util.Lsup(A)*self.SMALL_TOLERANCE
701                if self.getNumSolutions()>1:
702                   for i in range(self.getNumEquations()):
703                      for j in range(self.getDim()):
704                         for k in range(self.getNumSolutions()):
705                            for l in range(self.getDim()):
706                                if util.Lsup(A[i,j,k,l]-A[k,l,i,j])>tol:
707                                   if verbose: print "non-symmetric PDE because A[%d,%d,%d,%d]!=A[%d,%d,%d,%d]"%(i,j,k,l,k,l,i,j)
708                                   out=False
709                else:
710                   for j in range(self.getDim()):
711                      for l in range(self.getDim()):
712                         if util.Lsup(A[j,l]-A[l,j])>tol:
713                            if verbose: print "non-symmetric PDE because A[%d,%d]!=A[%d,%d]"%(j,l,l,j)
714                            out=False
715             B=self.getCoefficientOfGeneralPDE("B")
716             C=self.getCoefficientOfGeneralPDE("C")
717             if B.isEmpty() and not C.isEmpty():
718                if verbose: print "non-symmetric PDE because B is not present but C is"
719                out=False
720             elif not B.isEmpty() and C.isEmpty():
721                if verbose: print "non-symmetric PDE because C is not present but B is"
722                out=False
723             elif not B.isEmpty() and not C.isEmpty():
724                tol=(util.Lsup(B)+util.Lsup(C))*self.SMALL_TOLERANCE/2.
725                if self.getNumSolutions()>1:
726                   for i in range(self.getNumEquations()):
727                       for j in range(self.getDim()):
728                          for k in range(self.getNumSolutions()):
729                             if util.Lsup(B[i,j,k]-C[k,i,j])>tol:
730                                  if verbose: print "non-symmetric PDE because B[%d,%d,%d]!=C[%d,%d,%d]"%(i,j,k,k,i,j)
731                                  out=False
732                else:
733                   for j in range(self.getDim()):
734                      if util.Lsup(B[j]-C[j])>tol:
735                         if verbose: print "non-symmetric PDE because B[%d]!=C[%d]"%(j,j)
736                         out=False
737             if self.getNumSolutions()>1:
738               D=self.getCoefficientOfGeneralPDE("D")
739               if not D.isEmpty():
740                 tol=util.Lsup(D)*self.SMALL_TOLERANCE
741                 for i in range(self.getNumEquations()):
742                    for k in range(self.getNumSolutions()):
743                      if util.Lsup(D[i,k]-D[k,i])>tol:
744                          if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)
745                          out=False
746               d=self.getCoefficientOfGeneralPDE("d")
747               if not d.isEmpty():
748                 tol=util.Lsup(d)*self.SMALL_TOLERANCE
749                 for i in range(self.getNumEquations()):
750                    for k in range(self.getNumSolutions()):
751                      if util.Lsup(d[i,k]-d[k,i])>tol:
752                          if verbose: print "non-symmetric PDE because d[%d,%d]!=d[%d,%d]"%(i,k,k,i)
753                          out=False
754               d_contact=self.getCoefficientOfGeneralPDE("d_contact")
755               if not d_contact.isEmpty():
756                 tol=util.Lsup(d_contact)*self.SMALL_TOLERANCE
757                 for i in range(self.getNumEquations()):
758                    for k in range(self.getNumSolutions()):
759                      if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
760                          if verbose: print "non-symmetric PDE because d_contact[%d,%d]!=d_contact[%d,%d]"%(i,k,k,i)
761                          out=False
762          return out
763    
764       def getSolution(self,**options):
765         """         """
766         @brief         returns the solution of the PDE. If the solution is not valid the PDE is solved.
767    
768           @return: the solution
769           @rtype: L{Data<escript.Data>}
770           @param options: solver options
771           @keyword verbose: True to get some information during PDE solution
772           @type verbose: C{bool}
773           @keyword reordering: reordering scheme to be used during elimination. Allowed values are
774                                L{NO_REORDERING}, L{MINIMUM_FILL_IN}, L{NESTED_DISSECTION}
775           @keyword iter_max: maximum number of iteration steps allowed.
776           @keyword drop_tolerance: threshold for drupping in L{ILUT}
777           @keyword drop_storage: maximum of allowed memory in L{ILUT}
778           @keyword truncation: maximum number of residuals in L{GMRES}
779           @keyword restart: restart cycle length in L{GMRES}
780         """         """
781         self.__debug=not None         if not self.__solution_isValid:
782              mat,f=self.getSystem()
783              if self.isUsingLumping():
784                 self.__solution=self.copyConstraint(f*mat)
785              else:
786                 options[self.__TOLERANCE_KEY]=self.getTolerance()
787                 options[self.__METHOD_KEY]=self.getSolverMethod()[0]
788                 options[self.__PRECONDITIONER_KEY]=self.getSolverMethod()[1]
789                 options[self.__PACKAGE_KEY]=self.getSolverPackage()
790                 options[self.__SYMMETRY_KEY]=self.isSymmetric()
791                 self.trace("PDE is resolved.")
792                 self.trace("solver options: %s"%str(options))
793                 self.__solution=mat.solve(f,options)
794              self.__solution_isValid=True
795           return self.__solution
796    
797     def setDebugOff(self):     def getFlux(self,u=None):
798         """
799         returns the flux M{J} for a given M{u}
800    
801         M{J[i,j]=A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]u[k]-X[i,j]}
802    
803         or
804    
805         M{J[j]=A[i,j]*grad(u)[l]+B[j]u-X[j]}
806    
807         @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.
808         @type u: L{Data<escript.Data>} or None
809         @return: flux
810         @rtype: L{Data<escript.Data>}
811         """
812         if u==None: u=self.getSolution()
813         return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u))+util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u)-util.self.getCoefficientOfGeneralPDE("X")
814       # =============================================================================
815       #   solver settings:
816       # =============================================================================
817       def setSolverMethod(self,solver=None,preconditioner=None):
818         """         """
819         @brief         sets a new solver
820    
821           @param solver: sets a new solver method.
822           @type solver: one of L{DEFAULT}, L{ITERATIVE} L{DIRECT}, L{CHOLEVSKY}, L{PCG}, L{CR}, L{CGS}, L{BICGSTAB}, L{SSOR}, L{GMRES}, L{PRES20}, L{LUMPING}, L{AMG}
823           @param preconditioner: sets a new solver method.
824           @type preconditioner: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}, L{RILU}
825         """         """
826         self.__debug=None         if solver==None: solve=self.DEFAULT
827           if preconditioner==None: preconditioner=self.DEFAULT
828           if not (solver,preconditioner)==self.getSolverMethod():
829               self.__solver_method=solver
830               self.__preconditioner=preconditioner
831               self.__checkMatrixType()
832               self.trace("New solver is %s"%self.getSolverMethodName())
833    
834     def debug(self):     def getSolverMethodName(self):
835         """         """
836         @brief returns true if the PDE is in the debug mode         returns the name of the solver currently used
837    
838           @return: the name of the solver currently used.
839           @rtype: C{string}
840         """         """
        return self.__debug  
841    
842     #===== Lumping ===========================         m=self.getSolverMethod()
843     def setLumpingOn(self):         p=self.getSolverPackage()
844        """         method=""
845        @brief indicates to use matrix lumping         if m[0]==self.DEFAULT: method="DEFAULT"
846        """         elif m[0]==self.DIRECT: method= "DIRECT"
847        if not self.isUsingLumping():         elif m[0]==self.ITERATIVE: method= "ITERATIVE"
848           raise SystemError,"Lumping is not working yet! Talk to the experts"         elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
849           if self.debug() : print "PDE Debug: lumping is set on"         elif m[0]==self.PCG: method= "PCG"
850           self.__rebuildOperator()         elif m[0]==self.CR: method= "CR"
851           self.__lumping=True         elif m[0]==self.CGS: method= "CGS"
852           elif m[0]==self.BICGSTAB: method= "BICGSTAB"
853           elif m[0]==self.SSOR: method= "SSOR"
854           elif m[0]==self.GMRES: method= "GMRES"
855           elif m[0]==self.PRES20: method= "PRES20"
856           elif m[0]==self.LUMPING: method= "LUMPING"
857           elif m[0]==self.AMG: method= "AMG"
858           if m[1]==self.DEFAULT: method+="+DEFAULT"
859           elif m[1]==self.JACOBI: method+= "+JACOBI"
860           elif m[1]==self.ILU0: method+= "+ILU0"
861           elif m[1]==self.ILUT: method+= "+ILUT"
862           elif m[1]==self.SSOR: method+= "+SSOR"
863           elif m[1]==self.AMG: method+= "+AMG"
864           elif m[1]==self.RILU: method+= "+RILU"
865           if p==self.DEFAULT: package="DEFAULT"
866           elif p==self.PASO: package= "PASO"
867           elif p==self.MKL: package= "MKL"
868           elif p==self.SCSL: package= "SCSL"
869           elif p==self.UMFPACK: package= "UMFPACK"
870           else : method="unknown"
871           return "%s solver of %s package"%(method,package)
872    
    def setLumpingOff(self):  
       """  
       @brief switches off matrix lumping  
       """  
       if self.isUsingLumping():  
          if self.debug() : print "PDE Debug: lumping is set off"  
          self.__rebuildOperator()  
          self.__lumping=False  
873    
874     def setLumping(self,flag=False):     def getSolverMethod(self):
875        """         """
876        @brief set the matrix lumping flag to flag         returns the solver method
       """  
       if flag:  
          self.setLumpingOn()  
       else:  
          self.setLumpingOff()  
877    
878     def isUsingLumping(self):         @return: the solver method currently be used.
879        """         @rtype: C{int}
880        @brief         """
881        """         return self.__solver_method,self.__preconditioner
       return self.__lumping  
882    
883     #============ method business =========================================================     def setSolverPackage(self,package=None):
    def setSolverMethod(self,solver=util.DEFAULT_METHOD):  
884         """         """
885         @brief sets a new solver         sets a new solver package
886    
887           @param solver: sets a new solver method.
888           @type solver: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMLPACK}
889         """         """
890         if not solver==self.getSolverMethod():         if package==None: package=self.DEFAULT
891           if not package==self.getSolverPackage():
892             self.__solver_method=solver             self.__solver_method=solver
            if self.debug() : print "PDE Debug: New solver is %s"%solver  
893             self.__checkMatrixType()             self.__checkMatrixType()
894               self.trace("New solver is %s"%self.getSolverMethodName())
895    
896     def getSolverMethod(self):     def getSolverPackage(self):
897         """         """
898         @brief returns the solver method         returns the package of the solver
899    
900           @return: the solver package currently being used.
901           @rtype: C{int}
902         """         """
903         return self.__solver_method         return self.__solver_package
904    
905       def isUsingLumping(self):
906          """
907          checks if matrix lumping is used a solver method
908    
909          @return: True is lumping is currently used a solver method.
910          @rtype: C{bool}
911          """
912          return self.getSolverMethod()[0]==self.LUMPING
913    
    #============ tolerance business =========================================================  
914     def setTolerance(self,tol=1.e-8):     def setTolerance(self,tol=1.e-8):
915         """         """
916         @brief resets the tolerance to tol.         resets the tolerance for the solver method to tol where for an appropriate norm M{|.|}
917    
918           M{|L{getResidual}()|<tol*|L{getRightHandSide}()|}
919    
920           defines the stopping criterion.
921    
922           @param tol: new tolerance for the solver. If the tol is lower then the current tolerence
923                       the system will be resolved.
924           @type tol: positive C{float}
925           @raise ValueException: if tolerance is not positive.
926         """         """
927         if not tol>0:         if not tol>0:
928             raise ValueException,"Tolerance as to be positive"             raise ValueException,"Tolerance as to be positive"
929         if tol<self.getTolerance(): self.__rebuildSolution()         if tol<self.getTolerance(): self.__invalidateSolution()
930         if self.debug() : print "PDE Debug: New tolerance %e",tol         self.trace("New tolerance %e"%tol)
931         self.__tolerance=tol         self.__tolerance=tol
932         return         return
933    
934     def getTolerance(self):     def getTolerance(self):
935         """         """
936         @brief returns the tolerance set for the solution         returns the tolerance set for the solution
937    
938           @return: tolerance currently used.
939           @rtype: C{float}
940         """         """
941         return self.__tolerance         return self.__tolerance
942    
943     #===== symmetry  flag ==========================     # =============================================================================
944       #    symmetry  flag:
945       # =============================================================================
946     def isSymmetric(self):     def isSymmetric(self):
947        """        """
948        @brief returns true is the operator is considered to be symmetric        checks if symmetry is indicated.
949    
950          @return: True is a symmetric PDE is indicated, otherwise False is returned
951          @rtype: C{bool}
952        """        """
953        return self.__sym        return self.__sym
954    
955     def setSymmetryOn(self):     def setSymmetryOn(self):
956        """        """
957        @brief sets the symmetry flag to true        sets the symmetry flag.
958        """        """
959        if not self.isSymmetric():        if not self.isSymmetric():
960           if self.debug() : print "PDE Debug: Operator is set to be symmetric"           self.trace("PDE is set to be symmetric")
961           self.__sym=True           self.__sym=True
962           self.__checkMatrixType()           self.__checkMatrixType()
963    
964     def setSymmetryOff(self):     def setSymmetryOff(self):
965        """        """
966        @brief sets the symmetry flag to false        removes the symmetry flag.
967        """        """
968        if self.isSymmetric():        if self.isSymmetric():
969           if self.debug() : print "PDE Debug: Operator is set to be unsymmetric"           self.trace("PDE is set to be unsymmetric")
970           self.__sym=False           self.__sym=False
971           self.__checkMatrixType()           self.__checkMatrixType()
972    
973     def setSymmetryTo(self,flag=False):     def setSymmetryTo(self,flag=False):
974       """        """
975       @brief sets the symmetry flag to flag        sets the symmetry flag to flag
976    
977       @param flag        @param flag: If flag, the symmetry flag is set otherwise the symmetry flag is released.
978       """        @type flag: C{bool}
979       if flag:        """
980          self.setSymmetryOn()        if flag:
981       else:           self.setSymmetryOn()
982          self.setSymmetryOff()        else:
983             self.setSymmetryOff()
984    
985     #===== order reduction ==========================     # =============================================================================
986       # function space handling for the equation as well as the solution
987       # =============================================================================
988     def setReducedOrderOn(self):     def setReducedOrderOn(self):
989       """       """
990       @brief switches to on reduced order       switches on reduced order for solution and equation representation
991    
992         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
993       """       """
994       self.setReducedOrderForSolutionOn()       self.setReducedOrderForSolutionOn()
995       self.setReducedOrderForEquationOn()       self.setReducedOrderForEquationOn()
996    
997     def setReducedOrderOff(self):     def setReducedOrderOff(self):
998       """       """
999       @brief switches to full order       switches off reduced order for solution and equation representation
1000    
1001         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1002       """       """
1003       self.setReducedOrderForSolutionOff()       self.setReducedOrderForSolutionOff()
1004       self.setReducedOrderForEquationOff()       self.setReducedOrderForEquationOff()
1005    
1006     def setReducedOrderTo(self,flag=False):     def setReducedOrderTo(self,flag=False):
1007       """       """
1008       @brief sets order according to flag       sets order reduction for both solution and equation representation according to flag.
1009         @param flag: if flag is True, the order reduction is switched on for both  solution and equation representation, otherwise or
1010       @param flag                    if flag is not present order reduction is switched off
1011         @type flag: C{bool}
1012         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1013       """       """
1014       self.setReducedOrderForSolutionTo(flag)       self.setReducedOrderForSolutionTo(flag)
1015       self.setReducedOrderForEquationTo(flag)       self.setReducedOrderForEquationTo(flag)
                                                                                                                                                             
1016    
1017     #===== order reduction solution ==========================  
1018     def setReducedOrderForSolutionOn(self):     def setReducedOrderForSolutionOn(self):
1019       """       """
1020       @brief switches to reduced order to interpolate solution       switches on reduced order for solution representation
1021    
1022         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1023       """       """
1024       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_solution_order:
1025       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1026           if self.debug() : print "PDE Debug: Reduced order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1027           self.__column_function_space=new_fs           self.trace("Reduced order is used to solution representation.")
1028           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=True
1029             self.__resetSystem()
1030    
1031     def setReducedOrderForSolutionOff(self):     def setReducedOrderForSolutionOff(self):
1032       """       """
1033       @brief switches to full order to interpolate solution       switches off reduced order for solution representation
1034    
1035         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1036       """       """
1037       new_fs=escript.Solution(self.getDomain())       if self.__reduce_solution_order:
1038       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1039           if self.debug() : print "PDE Debug: Full order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1040           self.__column_function_space=new_fs           self.trace("Full order is used to interpolate solution.")
1041           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=False
1042             self.__resetSystem()
1043    
1044     def setReducedOrderForSolutionTo(self,flag=False):     def setReducedOrderForSolutionTo(self,flag=False):
1045       """       """
1046       @brief sets order for test functions according to flag       sets order for test functions according to flag
1047    
1048       @param flag       @param flag: if flag is True, the order reduction is switched on for solution representation, otherwise or
1049                      if flag is not present order reduction is switched off
1050         @type flag: C{bool}
1051         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1052       """       """
1053       if flag:       if flag:
1054          self.setReducedOrderForSolutionOn()          self.setReducedOrderForSolutionOn()
1055       else:       else:
1056          self.setReducedOrderForSolutionOff()          self.setReducedOrderForSolutionOff()
1057                                                                                                                                                              
    #===== order reduction equation ==========================  
1058     def setReducedOrderForEquationOn(self):     def setReducedOrderForEquationOn(self):
1059       """       """
1060       @brief switches to reduced order for test functions       switches on reduced order for equation representation
1061    
1062         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1063       """       """
1064       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_equation_order:
1065       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1066           if self.debug() : print "PDE Debug: Reduced order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1067           self.__row_function_space=new_fs           self.trace("Reduced order is used for test functions.")
1068           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=True
1069             self.__resetSystem()
1070    
1071     def setReducedOrderForEquationOff(self):     def setReducedOrderForEquationOff(self):
1072       """       """
1073       @brief switches to full order for test functions       switches off reduced order for equation representation
1074    
1075         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1076       """       """
1077       new_fs=escript.Solution(self.getDomain())       if self.__reduce_equation_order:
1078       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1079           if self.debug() : print "PDE Debug: Full order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1080           self.__row_function_space=new_fs           self.trace("Full order is used for test functions.")
1081           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=False
1082             self.__resetSystem()
1083    
1084     def setReducedOrderForEquationTo(self,flag=False):     def setReducedOrderForEquationTo(self,flag=False):
1085       """       """
1086       @brief sets order for test functions according to flag       sets order for test functions according to flag
1087    
1088       @param flag       @param flag: if flag is True, the order reduction is switched on for equation representation, otherwise or
1089                      if flag is not present order reduction is switched off
1090         @type flag: C{bool}
1091         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1092       """       """
1093       if flag:       if flag:
1094          self.setReducedOrderForEquationOn()          self.setReducedOrderForEquationOn()
1095       else:       else:
1096          self.setReducedOrderForEquationOff()          self.setReducedOrderForEquationOff()
                                                                                                                                                             
1097    
1098     # ==== initialization =====================================================================     # =============================================================================
1099     def __makeNewOperator(self):     # private method:
1100       # =============================================================================
1101       def __checkMatrixType(self):
1102         """
1103         reassess the matrix type and, if a new matrix is needed, resets the system.
1104         """
1105         new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod()[0],self.getSolverPackage(),self.isSymmetric())
1106         if not new_matrix_type==self.__matrix_type:
1107             self.trace("Matrix type is now %d."%new_matrix_type)
1108             self.__matrix_type=new_matrix_type
1109             self.__resetSystem()
1110       #
1111       #   rebuild switches :
1112       #
1113       def __invalidateSolution(self):
1114           """
1115           indicates the PDE has to be resolved if the solution is requested
1116           """
1117           if self.__solution_isValid: self.trace("PDE has to be resolved.")
1118           self.__solution_isValid=False
1119    
1120       def __invalidateOperator(self):
1121         """         """
1122         @brief         indicates the operator has to be rebuilt next time it is used
1123         """         """
1124           if self.__operator_is_Valid: self.trace("Operator has to be rebuilt.")
1125           self.__invalidateSolution()
1126           self.__operator_is_Valid=False
1127    
1128       def __invalidateRightHandSide(self):
1129           """
1130           indicates the right hand side has to be rebuild next time it is used
1131           """
1132           if self.__righthandside_isValid: self.trace("Right hand side has to be rebuilt.")
1133           self.__invalidateSolution()
1134           self.__righthandside_isValid=False
1135    
1136       def __invalidateSystem(self):
1137           """
1138           annonced that everthing has to be rebuild:
1139           """
1140           if self.__righthandside_isValid: self.trace("System has to be rebuilt.")
1141           self.__invalidateSolution()
1142           self.__invalidateOperator()
1143           self.__invalidateRightHandSide()
1144    
1145       def __resetSystem(self):
1146           """
1147           annonced that everthing has to be rebuild:
1148           """
1149           self.trace("New System is built from scratch.")
1150           self.__operator=escript.Operator()
1151           self.__operator_is_Valid=False
1152           self.__righthandside=escript.Data()
1153           self.__righthandside_isValid=False
1154           self.__solution=escript.Data()
1155           self.__solution_isValid=False
1156       #
1157       #    system initialization:
1158       #
1159       def __getNewOperator(self):
1160           """
1161           returns an instance of a new operator
1162           """
1163           self.trace("New operator is allocated.")
1164         return self.getDomain().newOperator( \         return self.getDomain().newOperator( \
1165                             self.getNumEquations(), \                             self.getNumEquations(), \
1166                             self.getFunctionSpaceForEquation(), \                             self.getFunctionSpaceForEquation(), \
# Line 617  class LinearPDE: Line 1168  class LinearPDE:
1168                             self.getFunctionSpaceForSolution(), \                             self.getFunctionSpaceForSolution(), \
1169                             self.__matrix_type)                             self.__matrix_type)
1170    
1171     def __makeNewRightHandSide(self):     def __getNewRightHandSide(self):
1172         """         """
1173         @brief         returns an instance of a new right hand side
1174         """         """
1175         return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)         self.trace("New right hand side is allocated.")
1176           if self.getNumEquations()>1:
1177               return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)
1178           else:
1179               return escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)
1180    
1181     def __makeNewSolution(self):     def __getNewSolution(self):
1182         """         """
1183         @brief         returns an instance of a new solution
1184         """         """
1185         return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)         self.trace("New solution is allocated.")
1186           if self.getNumSolutions()>1:
1187               return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)
1188           else:
1189               return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)
1190    
1191     def __getFreshOperator(self):     def __makeFreshSolution(self):
1192         """         """
1193         @brief         makes sure that the solution is instantiated and returns it initialized by zeros
1194         """         """
1195         if self.__operator.isEmpty():         if self.__solution.isEmpty():
1196             self.__operator=self.__makeNewOperator()             self.__solution=self.__getNewSolution()
            if self.debug() : print "PDE Debug: New operator allocated"  
1197         else:         else:
1198             self.__operator.setValue(0.)             self.__solution*=0
1199             if self.debug() : print "PDE Debug: Operator reset to zero"             self.trace("Solution is reset to zero.")
1200         return self.__operator         return self.__solution
1201    
1202     def __getFreshRightHandSide(self):     def __makeFreshRightHandSide(self):
1203         """         """
1204         @brief         makes sure that the right hand side is instantiated and returns it initialized by zeros
1205         """         """
1206         if self.__righthandside.isEmpty():         if self.__righthandside.isEmpty():
1207             self.__righthandside=self.__makeNewRightHandSide()             self.__righthandside=self.__getNewRightHandSide()
            if self.debug() : print "PDE Debug: New right hand side allocated"  
1208         else:         else:
1209             print "fix self.__righthandside*=0"             self.__righthandside*=0
1210             self.__righthandside*=0.             self.trace("Right hand side is reset to zero.")
1211             if self.debug() : print "PDE Debug: Right hand side reset to zero"         return self.__righthandside
        return  self.__righthandside  
1212    
1213     # ==== rebuild switches =====================================================================     def __makeFreshOperator(self):
    def __rebuildSolution(self,deep=False):  
1214         """         """
1215         @brief indicates the PDE has to be reolved if the solution is requested         makes sure that the operator is instantiated and returns it initialized by zeros
1216         """         """
1217         if self.__solution_isValid and self.debug() : print "PDE Debug: PDE has to be resolved."         if self.__operator.isEmpty():
1218         self.__solution_isValid=False             self.__operator=self.__getNewOperator()
1219         if deep: self.__solution=escript.Data(deep)         else:
1220               self.__operator.resetValues()
1221               self.trace("Operator reset to zero")
1222           return self.__operator
1223    
1224     def __rebuildOperator(self,deep=False):     def __applyConstraint(self):
1225         """         """
1226         @brief indicates the operator has to be rebuilt next time it is used         applies the constraints defined by q and r to the system
1227         """         """
1228         if self.__operator_isValid and self.debug() : print "PDE Debug: Operator has to be rebuilt."         if not self.isUsingLumping():
1229         self.__rebuildSolution(deep)            q=self.getCoefficientOfGeneralPDE("q")
1230         self.__operator_isValid=False            r=self.getCoefficientOfGeneralPDE("r")
1231         if deep: self.__operator=escript.Operator()            if not q.isEmpty() and not self.__operator.isEmpty():
1232                 # q is the row and column mask to indicate where constraints are set:
1233                 row_q=escript.Data(q,self.getFunctionSpaceForEquation())
1234                 col_q=escript.Data(q,self.getFunctionSpaceForSolution())
1235                 u=self.__getNewSolution()
1236                 if r.isEmpty():
1237                    r_s=self.__getNewSolution()
1238                 else:
1239                    r_s=escript.Data(r,self.getFunctionSpaceForSolution())
1240                 u.copyWithMask(r_s,col_q)
1241                 if not self.__righthandside.isEmpty():
1242                    self.__righthandside-=self.__operator*u
1243                    self.__righthandside=self.copyConstraint(self.__righthandside)
1244                 self.__operator.nullifyRowsAndCols(row_q,col_q,1.)
1245       # =============================================================================
1246       # function giving access to coefficients of the general PDE:
1247       # =============================================================================
1248       def getCoefficientOfGeneralPDE(self,name):
1249         """
1250         return the value of the coefficient name of the general PDE.
1251    
1252         @note: This method is called by the assembling routine it can be overwritten
1253               to map coefficients of a particular PDE to the general PDE.
1254         @param name: name of the coefficient requested.
1255         @type name: C{string}
1256         @return: the value of the coefficient  name
1257         @rtype: L{Data<escript.Data>}
1258         @raise IllegalCoefficient: if name is not one of coefficients
1259                      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}.
1260         """
1261         if self.hasCoefficientOfGeneralPDE(name):
1262            return self.getCoefficient(name)
1263         else:
1264            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1265    
1266     def __rebuildRightHandSide(self,deep=False):     def hasCoefficientOfGeneralPDE(self,name):
1267         """       """
1268         @brief indicates the right hand side has to be rebuild next time it is used       checks if name is a the name of a coefficient of the general PDE.
1269         """  
1270         if self.__righthandside_isValid and self.debug() : print "PDE Debug: Right hand side has to be rebuilt."       @param name: name of the coefficient enquired.
1271         self.__rebuildSolution(deep)       @type name: C{string}
1272         self.__righthandside_isValid=False       @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1273         if not self.__homogeneous_constraint: self.__rebuildOperator()       @rtype: C{bool}
        if deep: self.__righthandside=escript.Data()  
1274    
    def __rebuildSystem(self,deep=False):  
        """  
        @brief annonced that all coefficient name has been changed  
        """  
        self.__rebuildSolution(deep)  
        self.__rebuildOperator(deep)  
        self.__rebuildRightHandSide(deep)  
     
    def __checkMatrixType(self):  
1275       """       """
1276       @brief reassess the matrix type and, if needed, initiates an operator rebuild       return self.__COEFFICIENTS_OF_GENEARL_PDE.has_key(name)
1277    
1278       def createCoefficientOfGeneralPDE(self,name):
1279       """       """
1280       new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod(),self.isSymmetric())       returns a new instance of a coefficient for coefficient name of the general PDE
      if not new_matrix_type==self.__matrix_type:  
          if self.debug() : print "PDE Debug: Matrix type is now %d."%new_matrix_type  
          self.__matrix_type=new_matrix_type  
          self.__rebuildOperator(deep=True)  
1281    
1282     #============ assembling =======================================================       @param name: name of the coefficient requested.
1283     def __copyConstraint(self,u):       @type name: C{string}
1284         @return: a coefficient name initialized to 0.
1285         @rtype: L{Data<escript.Data>}
1286         @raise IllegalCoefficient: if name is not one of coefficients
1287                      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}.
1288         """
1289         if self.hasCoefficientOfGeneralPDE(name):
1290            return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
1291         else:
1292            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1293    
1294       def getFunctionSpaceForCoefficientOfGeneralPDE(self,name):
1295         """
1296         return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name of the general PDE
1297    
1298         @param name: name of the coefficient enquired.
1299         @type name: C{string}
1300         @return: the function space to be used for coefficient name
1301         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1302         @raise IllegalCoefficient: if name is not one of coefficients
1303                      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}.
1304         """
1305         if self.hasCoefficientOfGeneralPDE(name):
1306            return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
1307         else:
1308            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1309    
1310       def getShapeOfCoefficientOfGeneralPDE(self,name):
1311         """
1312         return the shape of the coefficient name of the general PDE
1313    
1314         @param name: name of the coefficient enquired.
1315         @type name: C{string}
1316         @return: the shape of the coefficient name
1317         @rtype: C{tuple} of C{int}
1318         @raise IllegalCoefficient: if name is not one of coefficients
1319                      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}.
1320         """
1321         if self.hasCoefficientOfGeneralPDE(name):
1322            return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1323         else:
1324            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1325    
1326       # =============================================================================
1327       # functions giving access to coefficients of a particular PDE implementation:
1328       # =============================================================================
1329       def getCoefficient(self,name):
1330         """
1331         returns the value of the coefficient name
1332    
1333         @param name: name of the coefficient requested.
1334         @type name: C{string}
1335         @return: the value of the coefficient name
1336         @rtype: L{Data<escript.Data>}
1337         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1338         """
1339         if self.hasCoefficient(name):
1340             return self.COEFFICIENTS[name].getValue()
1341         else:
1342            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1343    
1344       def hasCoefficient(self,name):
1345         """
1346         return True if name is the name of a coefficient
1347    
1348         @param name: name of the coefficient enquired.
1349         @type name: C{string}
1350         @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1351         @rtype: C{bool}
1352         """
1353         return self.COEFFICIENTS.has_key(name)
1354    
1355       def createCoefficient(self, name):
1356         """
1357         create a L{Data<escript.Data>} object corresponding to coefficient name
1358    
1359         @return: a coefficient name initialized to 0.
1360         @rtype: L{Data<escript.Data>}
1361         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1362         """
1363         if self.hasCoefficient(name):
1364            return escript.Data(0.,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))
1365         else:
1366            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1367    
1368       def getFunctionSpaceForCoefficient(self,name):
1369         """
1370         return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name
1371    
1372         @param name: name of the coefficient enquired.
1373         @type name: C{string}
1374         @return: the function space to be used for coefficient name
1375         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1376         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1377         """
1378         if self.hasCoefficient(name):
1379            return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())
1380         else:
1381            raise ValueError,"unknown coefficient %s requested"%name
1382       def getShapeOfCoefficient(self,name):
1383         """
1384         return the shape of the coefficient name
1385    
1386         @param name: name of the coefficient enquired.
1387         @type name: C{string}
1388         @return: the shape of the coefficient name
1389         @rtype: C{tuple} of C{int}
1390         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1391         """
1392         if self.hasCoefficient(name):
1393            return self.COEFFICIENTS[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1394         else:
1395            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1396    
1397       def resetCoefficients(self):
1398         """
1399         resets all coefficients to there default values.
1400         """
1401         for i in self.COEFFICIENTS.iterkeys():
1402             self.COEFFICIENTS[i].resetValue()
1403    
1404       def alteredCoefficient(self,name):
1405         """
1406         announce that coefficient name has been changed
1407    
1408         @param name: name of the coefficient enquired.
1409         @type name: C{string}
1410         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1411         @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.
1412         """
1413         if self.hasCoefficient(name):
1414            self.trace("Coefficient %s has been altered."%name)
1415            if not ((name=="q" or name=="r") and self.isUsingLumping()):
1416               if self.COEFFICIENTS[name].isAlteringOperator(): self.__invalidateOperator()
1417               if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__invalidateRightHandSide()
1418         else:
1419            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1420    
1421       def copyConstraint(self,u):
1422        """        """
1423        @brief copies the constrint condition into u        copies the constraint into u and returns u.
1424    
1425          @param u: a function of rank 0 is a single PDE is solved and of shape (numSolution,) for a system of PDEs
1426          @type u: L{Data<escript.Data>}
1427          @return: the input u modified by the constraints.
1428          @rtype: L{Data<escript.Data>}
1429          @warning: u is altered if it has the appropriate L{FunctionSpace<escript.FunctionSpace>}
1430        """        """
1431        q=self.getCoefficient("q")        q=self.getCoefficientOfGeneralPDE("q")
1432        r=self.getCoefficient("r")        r=self.getCoefficientOfGeneralPDE("r")
1433        if not q.isEmpty():        if not q.isEmpty():
1434            if r.isEmpty():           if u.isEmpty(): u=escript.Data(0.,q.getShape(),q.getFunctionSpace())
1435               r2=escript.Data(0,u.getShape(),u.getFunctionSpace())           if r.isEmpty():
1436            else:               r=escript.Data(0,u.getShape(),u.getFunctionSpace())
1437               r2=escript.Data(r,u.getFunctionSpace())           else:
1438            u.copyWithMask(r2,escript.Data(q,u.getFunctionSpace()))               r=escript.Data(r,u.getFunctionSpace())
1439             u.copyWithMask(r,escript.Data(q,u.getFunctionSpace()))
1440     def __applyConstraint(self,rhs_update=True):        return u
        """  
        @brief applies the constraints  defined by q and r to the system  
        """  
        q=self.getCoefficient("q")  
        r=self.getCoefficient("r")  
        if not q.isEmpty() and not self.__operator.isEmpty():  
           # q is the row and column mask to indicate where constraints are set:  
           row_q=escript.Data(q,self.getFunctionSpaceForEquation())  
           col_q=escript.Data(q,self.getFunctionSpaceForSolution())  
           u=self.__makeNewSolution()  
           if r.isEmpty():  
              r_s=self.__makeNewSolution()  
           else:  
              r_s=escript.Data(r,self.getFunctionSpaceForSolution())  
           u.copyWithMask(r_s,col_q)  
           if not self.__righthandside.isEmpty() and rhs_update: self.__righthandside-=self.__operator*u  
           self.__operator.nullifyRowsAndCols(row_q,col_q,1.)  
   
    def getOperator(self):  
        """  
        @brief returns the operator of the PDE  
        """  
        if not self.__operator_isValid:  
            # some Constraints are applying for a lumpled stifness matrix:  
            if self.isUsingLumping():  
               if self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():  
                        raise TypeError,"Lumped matrix requires same order for equations and unknowns"  
               if not self.getCoefficient("A").isEmpty():  
                        raise Warning,"Lumped matrix does not allow coefficient A"  
               if not self.getCoefficient("B").isEmpty():  
                        raise Warning,"Lumped matrix does not allow coefficient B"  
               if not self.getCoefficient("C").isEmpty():  
                        raise Warning,"Lumped matrix does not allow coefficient C"  
               if not self.getCoefficient("D").isEmpty():  
                        raise Warning,"Lumped matrix does not allow coefficient D"  
               if self.debug() : print "PDE Debug: New lumped operator is built."  
               mat=self.__makeNewOperator(self)  
            else:  
               if self.debug() : print "PDE Debug: New operator is built."  
               mat=self.__getFreshOperator()  
   
            self.getDomain().addPDEToSystem(mat,escript.Data(), \  
                         self.getCoefficient("A"), \  
                         self.getCoefficient("B"), \  
                         self.getCoefficient("C"), \  
                         self.getCoefficient("D"), \  
                         escript.Data(), \  
                         escript.Data(), \  
                         self.getCoefficient("d"), \  
                         escript.Data(),\  
                         self.getCoefficient("d_contact"), \  
                         escript.Data())  
            if self.isUsingLumping():  
               self.__operator=mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceOfSolution(),True)  
            else:  
               self.__applyConstraint(rhs_update=False)  
            self.__operator_isValid=True  
        return self.__operator  
1441    
1442     def getRightHandSide(self,ignoreConstraint=False):     def setValue(self,**coefficients):
1443         """        """
1444         @brief returns the right hand side of the PDE        sets new values to coefficients
1445    
1446         @param ignoreConstraint        @param coefficients: new values assigned to coefficients
1447         """        @keyword A: value for coefficient A.
1448         if not self.__righthandside_isValid:        @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1449             if self.debug() : print "PDE Debug: New right hand side is built."        @keyword B: value for coefficient B
1450             self.getDomain().addPDEToRHS(self.__getFreshRightHandSide(), \        @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1451                           self.getCoefficient("X"), \        @keyword C: value for coefficient C
1452                           self.getCoefficient("Y"),\        @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1453                           self.getCoefficient("y"),\        @keyword D: value for coefficient D
1454                           self.getCoefficient("y_contact"))        @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1455             self.__righthandside_isValid=True        @keyword X: value for coefficient X
1456             if ignoreConstraint: self.__copyConstraint(self.__righthandside)        @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1457         return self.__righthandside        @keyword Y: value for coefficient Y
1458          @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1459          @keyword d: value for coefficient d
1460          @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1461          @keyword y: value for coefficient y
1462          @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1463          @keyword d_contact: value for coefficient d_contact
1464          @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1465                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1466          @keyword y_contact: value for coefficient y_contact
1467          @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1468                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1469          @keyword r: values prescribed to the solution at the locations of constraints
1470          @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1471                   depending of reduced order is used for the solution.
1472          @keyword q: mask for location of constraints
1473          @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1474                   depending of reduced order is used for the representation of the equation.
1475          @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1476          """
1477          # check if the coefficients are  legal:
1478          for i in coefficients.iterkeys():
1479             if not self.hasCoefficient(i):
1480                raise IllegalCoefficient,"Attempt to set unknown coefficient %s"%i
1481          # if the number of unknowns or equations is still unknown we try to estimate them:
1482          if self.__numEquations==None or self.__numSolutions==None:
1483             for i,d in coefficients.iteritems():
1484                if hasattr(d,"shape"):
1485                    s=d.shape
1486                elif hasattr(d,"getShape"):
1487                    s=d.getShape()
1488                else:
1489                    s=numarray.array(d).shape
1490                if s!=None:
1491                    # get number of equations and number of unknowns:
1492                    res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(self.getDomain(),s)
1493                    if res==None:
1494                        raise IllegalCoefficientValue,"Illegal shape %s of coefficient %s"%(s,i)
1495                    else:
1496                        if self.__numEquations==None: self.__numEquations=res[0]
1497                        if self.__numSolutions==None: self.__numSolutions=res[1]
1498          if self.__numEquations==None: raise UndefinedPDEError,"unidententified number of equations"
1499          if self.__numSolutions==None: raise UndefinedPDEError,"unidententified number of solutions"
1500          # now we check the shape of the coefficient if numEquations and numSolutions are set:
1501          for i,d in coefficients.iteritems():
1502            try:
1503               self.COEFFICIENTS[i].setValue(self.getDomain(),self.getNumEquations(),self.getNumSolutions(),self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1504            except IllegalCoefficientValue,m:
1505               raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1506            self.alteredCoefficient(i)
1507    
1508          self.__altered_coefficients=True
1509          # check if the systrem is inhomogeneous:
1510          if len(coefficients)>0 and not self.isUsingLumping():
1511             q=self.getCoefficientOfGeneralPDE("q")
1512             r=self.getCoefficientOfGeneralPDE("r")
1513             homogeneous_constraint=True
1514             if not q.isEmpty() and not r.isEmpty():
1515                 if util.Lsup(q*r)>=1.e-13*util.Lsup(r):
1516                   self.trace("Inhomogeneous constraint detected.")
1517                   self.__invalidateSystem()
1518    
1519     def getSystem(self):     def getSystem(self):
1520         """         """
1521         @brief         return the operator and right hand side of the PDE
1522    
1523           @return: the discrete version of the PDE
1524           @rtype: C{tuple} of L{Operator,<escript.Operator>} and L{Data<escript.Data>}.
1525         """         """
1526         if not self.__operator_isValid and not self.__righthandside_isValid:         if not self.__operator_is_Valid or not self.__righthandside_isValid:
           if self.debug() : print "PDE Debug: New PDE is built."  
1527            if self.isUsingLumping():            if self.isUsingLumping():
1528                self.getRightHandSide(ignoreConstraint=True)                if not self.__operator_is_Valid:
1529                self.getOperator()                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():
1530                          raise TypeError,"Lumped matrix requires same order for equations and unknowns"
1531                     if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1532                          raise ValueError,"coefficient A in lumped matrix may not be present."
1533                     if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1534                          raise ValueError,"coefficient A in lumped matrix may not be present."
1535                     if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1536                          raise ValueError,"coefficient A in lumped matrix may not be present."
1537                     D=self.getCoefficientOfGeneralPDE("D")
1538                     if not D.isEmpty():
1539                         if self.getNumSolutions()>1:
1540                            D_times_e=util.matrixmult(D,numarray.ones((self.getNumSolutions(),)))
1541                         else:
1542                            D_times_e=D
1543                     else:
1544                        D_times_e=escript.Data()
1545                     d=self.getCoefficientOfGeneralPDE("d")
1546                     if not d.isEmpty():
1547                         if self.getNumSolutions()>1:
1548                            d_times_e=util.matrixmult(d,numarray.ones((self.getNumSolutions(),)))
1549                         else:
1550                            d_times_e=d
1551                     else:
1552                        d_times_e=escript.Data()
1553                     d_contact=self.getCoefficientOfGeneralPDE("d_contact")
1554                     if not d_contact.isEmpty():
1555                         if self.getNumSolutions()>1:
1556                            d_contact_times_e=util.matrixmult(d_contact,numarray.ones((self.getNumSolutions(),)))
1557                         else:
1558                            d_contact_times_e=d_contact
1559                     else:
1560                        d_contact_times_e=escript.Data()
1561        
1562                     self.__operator=self.__getNewRightHandSide()
1563                     self.getDomain().addPDEToRHS(self.__operator, \
1564                                                  escript.Data(), \
1565                                                  D_times_e, \
1566                                                  d_times_e,\
1567                                                  d_contact_times_e)
1568                     self.__operator=1./self.__operator
1569                     self.trace("New lumped operator has been built.")
1570                     self.__operator_is_Valid=True
1571                  if not self.__righthandside_isValid:
1572                     self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1573                                   self.getCoefficientOfGeneralPDE("X"), \
1574                                   self.getCoefficientOfGeneralPDE("Y"),\
1575                                   self.getCoefficientOfGeneralPDE("y"),\
1576                                   self.getCoefficientOfGeneralPDE("y_contact"))
1577                     self.trace("New right hand side as been built.")
1578                     self.__righthandside_isValid=True
1579            else:            else:
1580                self.getDomain().addPDEToSystem(self.__getFreshOperator(),self.__getFreshRightHandSide(), \               if not self.__operator_is_Valid and not self.__righthandside_isValid:
1581                              self.getCoefficient("A"), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \
1582                              self.getCoefficient("B"), \                                 self.getCoefficientOfGeneralPDE("A"), \
1583                              self.getCoefficient("C"), \                                 self.getCoefficientOfGeneralPDE("B"), \
1584                              self.getCoefficient("D"), \                                 self.getCoefficientOfGeneralPDE("C"), \
1585                              self.getCoefficient("X"), \                                 self.getCoefficientOfGeneralPDE("D"), \
1586                              self.getCoefficient("Y"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1587                              self.getCoefficient("d"), \                                 self.getCoefficientOfGeneralPDE("Y"), \
1588                              self.getCoefficient("y"), \                                 self.getCoefficientOfGeneralPDE("d"), \
1589                              self.getCoefficient("d_contact"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1590                              self.getCoefficient("y_contact"))                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1591            self.__operator_isValid=True                                 self.getCoefficientOfGeneralPDE("y_contact"))
1592            self.__righthandside_isValid=True                   self.__applyConstraint()
1593            self.__applyConstraint()                   self.__righthandside=self.copyConstraint(self.__righthandside)
1594            self.__copyConstraint(self.__righthandside)                   self.trace("New system has been built.")
1595         elif not self.__operator_isValid:                   self.__operator_is_Valid=True
1596            self.getOperator()                   self.__righthandside_isValid=True
1597         elif not self.__righthandside_isValid:               elif not self.__righthandside_isValid:
1598            self.getRightHandSide()                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1599                                   self.getCoefficientOfGeneralPDE("X"), \
1600                                   self.getCoefficientOfGeneralPDE("Y"),\
1601                                   self.getCoefficientOfGeneralPDE("y"),\
1602                                   self.getCoefficientOfGeneralPDE("y_contact"))
1603                     self.__righthandside=self.copyConstraint(self.__righthandside)
1604                     self.trace("New right hand side has been built.")
1605                     self.__righthandside_isValid=True
1606                 elif not self.__operator_is_Valid:
1607                     self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \
1608                                self.getCoefficientOfGeneralPDE("A"), \
1609                                self.getCoefficientOfGeneralPDE("B"), \
1610                                self.getCoefficientOfGeneralPDE("C"), \
1611                                self.getCoefficientOfGeneralPDE("D"), \
1612                                escript.Data(), \
1613                                escript.Data(), \
1614                                self.getCoefficientOfGeneralPDE("d"), \
1615                                escript.Data(),\
1616                                self.getCoefficientOfGeneralPDE("d_contact"), \
1617                                escript.Data())
1618                     self.__applyConstraint()
1619                     self.trace("New operator has been built.")
1620                     self.__operator_is_Valid=True
1621         return (self.__operator,self.__righthandside)         return (self.__operator,self.__righthandside)
1622    
    def solve(self,**options):  
       """  
       @brief solve the PDE  
1623    
1624        @param options  class Poisson(LinearPDE):
1625        """     """
1626        mat,f=self.getSystem()     Class to define a Poisson equation problem, which is genear L{LinearPDE} of the form
       if self.isUsingLumping():  
          out=f/mat  
          self.__copyConstraint(out)  
       else:  
          options[util.TOLERANCE_KEY]=self.getTolerance()  
          options[util.METHOD_KEY]=self.getSolverMethod()  
          options[util.SYMMETRY_KEY]=self.isSymmetric()  
          if self.debug() : print "PDE Debug: solver options: ",options  
          out=mat.solve(f,options)  
       return out  
1627    
1628     def getSolution(self,**options):     M{-grad(grad(u)[j])[j] = f}
        """  
        @brief returns the solution of the PDE  
1629    
1630         @param options     with natural boundary conditons
        """  
        if not self.__solution_isValid:  
            if self.debug() : print "PDE Debug: PDE is resolved."  
            self.__solution=self.solve(**options)  
            self.__solution_isValid=True  
        return self.__solution  
    #============ some serivice functions  =====================================================  
    def getDomain(self):  
      """  
      @brief returns the domain of the PDE  
      """  
      return self.__domain  
1631    
1632     def getDim(self):     M{n[j]*grad(u)[j] = 0 }
1633       """  
1634       @brief returns the spatial dimension of the PDE     and constraints:
1635    
1636       M{u=0} where M{q>0}
1637    
1638       """
1639    
1640       def __init__(self,domain,debug=False):
1641       """       """
1642       return self.getDomain().getDim()       initializes a new Poisson equation
1643    
1644         @param domain: domain of the PDE
1645         @type domain: L{Domain<escript.Domain>}
1646         @param debug: if True debug informations are printed.
1647    
    def getNumEquations(self):  
1648       """       """
1649       @brief returns the number of equations       super(Poisson, self).__init__(domain,1,1,debug)
1650         self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1651                              "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1652         self.setSymmetryOn()
1653    
1654       def setValue(self,**coefficients):
1655       """       """
1656       if self.__numEquations>0:       sets new values to coefficients
1657           return self.__numEquations  
1658         @param coefficients: new values assigned to coefficients
1659         @keyword f: value for right hand side M{f}
1660         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1661         @keyword q: mask for location of constraints
1662         @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>}
1663                   depending of reduced order is used for the representation of the equation.
1664         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1665         """
1666         super(Poisson, self).setValue(**coefficients)
1667    
1668       def getCoefficientOfGeneralPDE(self,name):
1669         """
1670         return the value of the coefficient name of the general PDE
1671         @param name: name of the coefficient requested.
1672         @type name: C{string}
1673         @return: the value of the coefficient  name
1674         @rtype: L{Data<escript.Data>}
1675         @raise IllegalCoefficient: if name is not one of coefficients
1676                      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}.
1677         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1678         """
1679         if name == "A" :
1680             return escript.Data(util.kronecker(self.getDim()),escript.Function(self.getDomain()))
1681         elif name == "B" :
1682             return escript.Data()
1683         elif name == "C" :
1684             return escript.Data()
1685         elif name == "D" :
1686             return escript.Data()
1687         elif name == "X" :
1688             return escript.Data()
1689         elif name == "Y" :
1690             return self.getCoefficient("f")
1691         elif name == "d" :
1692             return escript.Data()
1693         elif name == "y" :
1694             return escript.Data()
1695         elif name == "d_contact" :
1696             return escript.Data()
1697         elif name == "y_contact" :
1698             return escript.Data()
1699         elif name == "r" :
1700             return escript.Data()
1701         elif name == "q" :
1702             return self.getCoefficient("q")
1703       else:       else:
1704           raise ValueError,"Number of equations is undefined. Please specify argument numEquations."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1705    
1706     def getNumSolutions(self):  class Helmholtz(LinearPDE):
1707       """
1708       Class to define a Helmhotz equation problem, which is genear L{LinearPDE} of the form
1709    
1710       M{S{omega}*u - grad(k*grad(u)[j])[j] = f}
1711    
1712       with natural boundary conditons
1713    
1714       M{k*n[j]*grad(u)[j] = g- S{alpha}u }
1715    
1716       and constraints:
1717    
1718       M{u=r} where M{q>0}
1719    
1720       """
1721    
1722       def __init__(self,domain,debug=False):
1723       """       """
1724       @brief returns the number of unknowns       initializes a new Poisson equation
1725    
1726         @param domain: domain of the PDE
1727         @type domain: L{Domain<escript.Domain>}
1728         @param debug: if True debug informations are printed.
1729    
1730         """
1731         super(Helmholtz, self).__init__(domain,1,1,debug)
1732         self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1733                            "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1734                            "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1735                            "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1736                            "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1737                            "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1738                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1739         self.setSymmetryOn()
1740    
1741       def setValue(self,**coefficients):
1742       """       """
1743       if self.__numSolutions>0:       sets new values to coefficients
1744          return self.__numSolutions  
1745         @param coefficients: new values assigned to coefficients
1746         @keyword omega: value for coefficient M{S{omega}}
1747         @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1748         @keyword k: value for coefficeint M{k}
1749         @type k: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1750         @keyword f: value for right hand side M{f}
1751         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1752         @keyword alpha: value for right hand side M{S{alpha}}
1753         @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1754         @keyword g: value for right hand side M{g}
1755         @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1756         @keyword r: prescribed values M{r} for the solution in constraints.
1757         @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1758                   depending of reduced order is used for the representation of the equation.
1759         @keyword q: mask for location of constraints
1760         @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1761                   depending of reduced order is used for the representation of the equation.
1762         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1763         """
1764         super(Helmholtz, self).setValue(**coefficients)
1765    
1766       def getCoefficientOfGeneralPDE(self,name):
1767         """
1768         return the value of the coefficient name of the general PDE
1769    
1770         @param name: name of the coefficient requested.
1771         @type name: C{string}
1772         @return: the value of the coefficient  name
1773         @rtype: L{Data<escript.Data>}
1774         @raise IllegalCoefficient: if name is not one of coefficients
1775                      "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}.
1776         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1777         """
1778         if name == "A" :
1779             return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))*self.getCoefficient("k")
1780         elif name == "B" :
1781             return escript.Data()
1782         elif name == "C" :
1783             return escript.Data()
1784         elif name == "D" :
1785             return self.getCoefficient("omega")
1786         elif name == "X" :
1787             return escript.Data()
1788         elif name == "Y" :
1789             return self.getCoefficient("f")
1790         elif name == "d" :
1791             return self.getCoefficient("alpha")
1792         elif name == "y" :
1793             return self.getCoefficient("g")
1794         elif name == "d_contact" :
1795             return escript.Data()
1796         elif name == "y_contact" :
1797             return escript.Data()
1798         elif name == "r" :
1799             return self.getCoefficient("r")
1800         elif name == "q" :
1801             return self.getCoefficient("q")
1802       else:       else:
1803          raise ValueError,"Number of solution is undefined. Please specify argument numSolutions."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1804    
1805    class LameEquation(LinearPDE):
1806       """
1807       Class to define a Lame equation problem:
1808    
1809     def checkSymmetry(self):     M{-grad(S{mu}*(grad(u[i])[j]+grad(u[j])[i]))[j] - grad(S{lambda}*grad(u[j])[i])[j] = F_i -grad(S{sigma}[i,j])[j] }
       """  
       @brief returns if the Operator is symmetric. This is a very expensive operation!!! The symmetry flag is not altered.  
       """  
       raise SystemError,"checkSymmetry is not implemented yet"  
1810    
1811        return None     with natural boundary conditons:
1812    
1813     def getFlux(self,u):     M{n[j]*(S{mu}*(grad(u[i])[j]+grad(u[j])[i]) - S{lambda}*grad(u[j])[i]) = f_i -n[j]*S{sigma}[i,j] }
        """  
        @brief returns the flux J_ij for a given u  
1814    
1815              J_ij=A_{ijkl}u_{k,l}+B_{ijk}u_k-X_{ij}     and constraints:
1816    
1817         @param u argument of the operator     M{u[i]=r[i]} where M{q[i]>0}
1818    
1819         """     """
        raise SystemError,"getFlux is not implemented yet"  
        return None  
1820    
1821     def applyOperator(self,u):     def __init__(self,domain,debug=False):
1822         """        super(LameEquation, self).__init__(domain,\
1823         @brief applies the operator of the PDE to a given solution u in weak from                                           domain.getDim(),domain.getDim(),debug)
1824          self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
1825                              "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
1826                              "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1827                              "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
1828                              "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1829                              "r"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1830                              "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1831          self.setSymmetryOn()
1832    
1833       def setValues(self,**coefficients):
1834         """
1835         sets new values to coefficients
1836    
1837         @param coefficients: new values assigned to coefficients
1838         @keyword lame_mu: value for coefficient M{S{mu}}
1839         @type lame_mu: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1840         @keyword lame_lambda: value for coefficient M{S{lambda}}
1841         @type lame_lambda: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1842         @keyword F: value for internal force M{F}
1843         @type F: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}
1844         @keyword sigma: value for initial stress M{S{sigma}}
1845         @type sigma: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}
1846         @keyword f: value for extrenal force M{f}
1847         @type f: any type that can be casted to L{Vector<escript.Vector>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}
1848         @keyword r: prescribed values M{r} for the solution in constraints.
1849         @type r: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1850                   depending of reduced order is used for the representation of the equation.
1851         @keyword q: mask for location of constraints
1852         @type q: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1853                   depending of reduced order is used for the representation of the equation.
1854         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1855         """
1856         super(LameEquation, self).setValues(**coefficients)
1857    
1858       def getCoefficientOfGeneralPDE(self,name):
1859         """
1860         return the value of the coefficient name of the general PDE
1861    
1862         @param name: name of the coefficient requested.
1863         @type name: C{string}
1864         @return: the value of the coefficient  name
1865         @rtype: L{Data<escript.Data>}
1866         @raise IllegalCoefficient: if name is not one of coefficients
1867                      "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}.
1868         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1869         """
1870         if name == "A" :
1871             out =self.createCoefficientOfGeneralPDE("A")
1872             for i in range(self.getDim()):
1873               for j in range(self.getDim()):
1874                 out[i,i,j,j] += self.getCoefficient("lame_lambda")
1875                 out[i,j,j,i] += self.getCoefficient("lame_mu")
1876                 out[i,j,i,j] += self.getCoefficient("lame_mu")
1877             return out
1878         elif name == "B" :
1879             return escript.Data()
1880         elif name == "C" :
1881             return escript.Data()
1882         elif name == "D" :
1883             return escript.Data()
1884         elif name == "X" :
1885             return self.getCoefficient("sigma")
1886         elif name == "Y" :
1887             return self.getCoefficient("F")
1888         elif name == "d" :
1889             return escript.Data()
1890         elif name == "y" :
1891             return self.getCoefficient("f")
1892         elif name == "d_contact" :
1893             return escript.Data()
1894         elif name == "y_contact" :
1895             return escript.Data()
1896         elif name == "r" :
1897             return self.getCoefficient("r")
1898         elif name == "q" :
1899             return self.getCoefficient("q")
1900         else:
1901            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1902    
1903         @param u argument of the operator  class AdvectivePDE(LinearPDE):
1904       """
1905       In cases of PDEs dominated by the advection terms M{B} and M{C} against the adevctive terms M{A}
1906       up-winding has been used.  The L{AdvectivePDE} class applies SUPG upwinding to the advective terms.
1907    
1908         """     In the following we set
        return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())  
                                                                                                                                                             
    def getResidual(self,u):  
        """  
        @brief return the residual of u in the weak from  
1909    
1910         @param u     M{Z[j]=C[j]-B[j]}
1911         """  
1912         return self.applyOperator(u)-self.getRightHandSide()     or
1913    
1914       M{Z[i,k,l]=C[i,k,l]-B[i,l,k]}
1915    
1916       To measure the dominance of the advective terms over the diffusive term M{A} the
1917       X{Pelclet number} M{P} is used. It is defined as
1918    
1919       M{P=h|Z|/(2|A|)}
1920    
1921       where M{|.|} denotes the L{length<util.length>} of the arument and M{h} is the local cell size
1922       from L{getSize<escript.Domain.getSize>}. Where M{|A|==0} M{P} is M{S{infinity}}.
1923    
1924       From the X{Pelclet number} the stabilization parameters M{S{Xi}} and M{S{Xi}} are calculated:
1925    
1926       M{S{Xi}=S{xi}(P) h/|Z|}
1927    
1928       where M{S{xi}} is a suitable function of the Peclet number.
1929    
1930       In the case of a single PDE the coefficient are up-dated in the following way:
1931             - M{A[i,j] S{<-} A[i,j] + S{Xi} * Z[j] * Z[l]}
1932             - M{B[j] S{<-} B[j] + S{Xi} * C[j] * D}
1933             - M{C[j] S{<-} C[j] + S{Xi} * B[j] * D}
1934             - M{X[j] S{<-} X[j] + S{Xi} * Z[j] * Y}
1935    
1936       Similar for the case of a systems of PDEs:
1937             - M{A[i,j,k,l] S{<-} A[i,j,k,l]+ S{delta}[p,m] * S{Xi} * Z[p,i,j] * Z[m,k,l]}
1938             - M{B[i,j,k] S{<-} B[i,j,k] +  S{delta}[p,m] * S{Xi} * D[p,k] * C[m,i,j]}
1939             - M{C[i,k,l] S{<-} C[i,k,l] +  S{delta}[p,m] * S{Xi} * D[p,k] * B[m,l,i]}
1940             - M{X[i,j] S{<-} X[i,j] + S{delta}[p,m] * S{Xi}  * Y[p] * Z[m,i,j]}
1941    
1942       where M{S{delta}} is L{kronecker}.
1943       Using upwinding in this form, introduces an additonal error which is proprtional to the cell size M{h}
1944       but with the intension to stabilize the solution.
1945    
 class Poisson(LinearPDE):  
1946     """     """
1947     @brief Class to define a Poisson equstion problem:     def __init__(self,domain,numEquations=None,numSolutions=None,xi=None,debug=False):
1948                                                                                                                                                                      """
1949     class to define a linear PDE of the form        creates a linear, steady, second order PDE on a L{Domain<escript.Domain>}
1950                                                                                                                                                                
1951          -u_{,jj} = f        @param domain: domain of the PDE
1952                                                                                                                                                                      @type domain: L{Domain<escript.Domain>}
1953       with boundary conditons:        @param numEquations: number of equations. If numEquations==None the number of equations
1954                                                                                                                                                                                           is exracted from the PDE coefficients.
1955          n_j*u_{,j} = 0        @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
1956                                                                                                                                                                                           is exracted from the PDE coefficients.
1957      and constraints:        @param xi: defines a function which returns for any given Preclet number as L{Scalar<escript.Scalar>} object the
1958                                                                                                                                                                                 M{S{xi}}-value used to define the stabilization parameters. If equal to None, L{ELMAN_RAMAGE} is used.
1959           u=0 where q>0        @type xi: callable object which returns a L{Scalar<escript.Scalar>} object.
1960                                                                                                                                                                      @param debug: if True debug informations are printed.
1961     """        """
1962          super(AdvectivePDE, self).__init__(domain,\
1963     def __init__(self,domain=None,f=escript.Data(),q=escript.Data()):                                           numEquations,numSolutions,debug)
1964         LinearPDE.__init__(self,domain=identifyDomain(domain,{"f":f, "q":q}))        if xi==None:
1965         self._setValue(A=numarray.identity(self.getDomain().getDim()))           self.__xi=AdvectivePDE.ELMAN_RAMAGE
1966         self.setSymmetryOn()        else:
1967         self.setValue(f,q)           self.__xi=xi
1968          self.__Xi=escript.Data()
1969     def setValue(self,f=escript.Data(),q=escript.Data()):  
1970         self._setValue(Y=f,q=q)     def setValue(self,**coefficients):
1971          """
1972                                                                                                                                                                    sets new values to coefficients
1973    
1974          @param coefficients: new values assigned to coefficients
1975          @keyword A: value for coefficient A.
1976          @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1977          @keyword B: value for coefficient B
1978          @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1979          @keyword C: value for coefficient C
1980          @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1981          @keyword D: value for coefficient D
1982          @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1983          @keyword X: value for coefficient X
1984          @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1985          @keyword Y: value for coefficient Y
1986          @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1987          @keyword d: value for coefficient d
1988          @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1989          @keyword y: value for coefficient y
1990          @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1991          @keyword d_contact: value for coefficient d_contact
1992          @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1993                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1994          @keyword y_contact: value for coefficient y_contact
1995          @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1996                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1997          @keyword r: values prescribed to the solution at the locations of constraints
1998          @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1999                   depending of reduced order is used for the solution.
2000          @keyword q: mask for location of constraints
2001          @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2002                   depending of reduced order is used for the representation of the equation.
2003          @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2004    
2005          """
2006          if "A" in coefficients.keys()   or "B" in coefficients.keys() or "C" in coefficients.keys(): self.__Xi=escript.Data()
2007          super(AdvectivePDE, self).setValue(**coefficients)
2008    
2009       def ELMAN_RAMAGE(self,P):
2010         """
2011         Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.
2012         This function uses the method suggested by H.C. Elman and A. Ramage, I{SIAM J. Numer. Anal.}, B{40} (2002)
2013              - M{S{xi}(P)=0} for M{P<1}
2014              - M{S{xi}(P)=(1-1/P)/2} otherwise
2015    
2016         @param P: Preclet number
2017         @type P: L{Scalar<escript.Scalar>}
2018         @return: up-wind weightimg factor
2019         @rtype: L{Scalar<escript.Scalar>}
2020         """
2021         return util.wherePositive(P-1.)*0.5*(1.-1./(P+1.e-15))
2022    
2023       def SIMPLIFIED_BROOK_HUGHES(self,P):
2024         """
2025         Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.
2026         The original methods is
2027    
2028         M{S{xi}(P)=coth(P)-1/P}
2029    
2030         As the evaluation of M{coth} is expensive we are using the approximation:
2031    
2032             - M{S{xi}(P)=P/3} where M{P<3}
2033             - M{S{xi}(P)=1/2} otherwise
2034    
2035         @param P: Preclet number
2036         @type P: L{Scalar<escript.Scalar>}
2037         @return: up-wind weightimg factor
2038         @rtype: L{Scalar<escript.Scalar>}
2039         """
2040         c=util.whereNegative(P-3.)
2041         return P/6.*c+1./2.*(1.-c)
2042    
2043       def HALF(self,P):
2044         """
2045         Predefined function to set value M{1/2} for M{S{xi}}
2046    
2047         @param P: Preclet number
2048         @type P: L{Scalar<escript.Scalar>}
2049         @return: up-wind weightimg factor
2050         @rtype: L{Scalar<escript.Scalar>}
2051         """
2052         return escript.Scalar(0.5,P.getFunctionSpace())
2053    
2054       def __getXi(self):
2055          if self.__Xi.isEmpty():
2056             B=self.getCoefficient("B")
2057             C=self.getCoefficient("C")
2058             A=self.getCoefficient("A")
2059             h=self.getDomain().getSize()
2060             self.__Xi=escript.Scalar(0.,self.getFunctionSpaceForCoefficient("A"))
2061             if not C.isEmpty() or not B.isEmpty():
2062                if not C.isEmpty() and not B.isEmpty():
2063                    if self.getNumEquations()>1:
2064                       if self.getNumSolutions()>1:
2065                          flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))
2066                          for i in range(self.getNumEquations()):
2067                             for k in range(self.getNumSolutions()):
2068                                for l in range(self.getDim()): flux2+=(C[i,k,l]-B[i,l,k])**2
2069                          length_of_flux=util.sqrt(flux2)
2070                          # flux=C-util.reorderComponents(B,[0,2,1])
2071                       else:
2072                          flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))
2073                          for i in range(self.getNumEquations()):
2074                             for l in range(self.getDim()): flux2+=(C[i,l]-B[i,l])**2
2075                          length_of_flux=util.sqrt(flux2)
2076                          # flux=C-B
2077                    else:
2078                       if self.getNumSolutions()>1:
2079                          flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))
2080                          for k in range(self.getNumSolutions()):
2081                             for l in range(self.getDim()): flux2+=(C[k,l]-B[l,k])**2
2082                          # flux=C-util.reorderComponents(B,[1,0])
2083                          length_of_flux=util.sqrt(flux2)
2084                       else:
2085                          length_of_flux=util.length(C-B)
2086                elif C.isEmpty():
2087                  length_of_flux=util.length(B)
2088                else:
2089                  length_of_flux=util.length(C)
2090                flux_max=util.Lsup(length_of_flux)
2091                if flux_max>0.:
2092                  if A.isEmpty():
2093                      inv_A=1./self.SMALL_TOLERANCE
2094                      peclet_number=escript.Scalar(inv_A,length_of_flux.getFunctionSpace())
2095                      xi=self.__xi(self,peclet_number)
2096                  else:
2097                      # length_of_A=util.inner(flux,util.tensormutiply(A,flux))
2098                      length_of_A=util.length(A)
2099                      A_max=util.Lsup(length_of_A)
2100                      if A_max>0:
2101                           inv_A=1./(length_of_A+A_max*self.SMALL_TOLERANCE)
2102                      else:
2103                           inv_A=1./self.SMALL_TOLERANCE
2104                      peclet_number=length_of_flux*h/2*inv_A
2105                      xi=self.__xi(self,peclet_number)
2106                  self.__Xi=h*xi/(length_of_flux+flux_max*self.SMALL_TOLERANCE)
2107                  self.trace("preclet number = %e"%util.Lsup(peclet_number))
2108                else:
2109                  self.__Xi=escript.Scalar(0.,length_of_flux.getFunctionSpace())
2110          return self.__Xi
2111    
2112    
2113       def getCoefficientOfGeneralPDE(self,name):
2114         """
2115         return the value of the coefficient name of the general PDE
2116    
2117         @param name: name of the coefficient requested.
2118         @type name: C{string}
2119         @return: the value of the coefficient name
2120         @rtype: L{Data<escript.Data>}
2121         @raise IllegalCoefficient: if name is not one of coefficients
2122                      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}.
2123         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2124         """
2125         if not self.getNumEquations() == self.getNumSolutions():
2126              raise ValueError,"AdvectivePDE expects the number of solution componets and the number of equations to be equal."
2127    
2128         if name == "A" :
2129             A=self.getCoefficient("A")
2130             B=self.getCoefficient("B")
2131             C=self.getCoefficient("C")
2132             if B.isEmpty() and C.isEmpty():
2133                Aout=A
2134             else:
2135                if A.isEmpty():
2136                   Aout=self.createCoefficientOfGeneralPDE("A")
2137                else:
2138                   Aout=A[:]
2139                Xi=self.__getXi()
2140                if self.getNumEquations()>1:
2141                    for i in range(self.getNumEquations()):
2142                       for j in range(self.getDim()):
2143                          for k in range(self.getNumSolutions()):
2144                             for l in range(self.getDim()):
2145                                if not C.isEmpty() and not B.isEmpty():
2146                                   # tmp=C-util.reorderComponents(B,[0,2,1])
2147                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(tmp,[1,2,0]),tmp,offset=1)
2148                                   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])
2149                                elif C.isEmpty():
2150                                   for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*B[p,j,i]*B[p,l,k]
2151                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(B,[2,1,0]),util.reorder(B,[0,2,1]),offset=1)
2152                                else:
2153                                   for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*C[p,i,j]*C[p,k,l]
2154                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),C,offset=1)
2155                else:
2156                   if not C.isEmpty() and not B.isEmpty():
2157                       delta=(C-B)
2158                       Aout+=util.outer(Xi*delta,delta)
2159                   elif not B.isEmpty():
2160                       Aout+=util.outer(Xi*B,B)
2161                   elif not C.isEmpty():
2162                       Aout+=util.outer(Xi*C,C)
2163             return Aout
2164         elif name == "B" :
2165             # return self.getCoefficient("B")
2166             B=self.getCoefficient("B")
2167             C=self.getCoefficient("C")
2168             D=self.getCoefficient("D")
2169             if C.isEmpty() or D.isEmpty():
2170                Bout=B
2171             else:
2172                Xi=self.__getXi()
2173                if B.isEmpty():
2174                    Bout=self.createCoefficientOfGeneralPDE("B")
2175                else:
2176                    Bout=B[:]
2177                if self.getNumEquations()>1:
2178                   for k in range(self.getNumSolutions()):
2179                      for p in range(self.getNumEquations()):
2180                         tmp=Xi*D[p,k]
2181                         for i in range(self.getNumEquations()):
2182                            for j in range(self.getDim()):
2183                               Bout[i,j,k]+=tmp*C[p,i,j]
2184                               # Bout=Bout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),D,offset=1)
2185                else:
2186                   Bout+=(Xi*D)*C
2187             return Bout
2188         elif name == "C" :
2189             # return self.getCoefficient("C")
2190             B=self.getCoefficient("B")
2191             C=self.getCoefficient("C")
2192             D=self.getCoefficient("D")
2193             if B.isEmpty() or D.isEmpty():
2194                Cout=C
2195             else:
2196                Xi=self.__getXi()
2197                if C.isEmpty():
2198                    Cout=self.createCoefficientOfGeneralPDE("C")
2199                else:
2200                    Cout=C[:]
2201                if self.getNumEquations()>1:
2202                   for k in range(self.getNumSolutions()):
2203                       for p in range(self.getNumEquations()):
2204                          tmp=Xi*D[p,k]
2205                          for i in range(self.getNumEquations()):
2206                            for l in range(self.getDim()):
2207                                     Cout[i,k,l]+=tmp*B[p,l,i]
2208                                     # Cout=Cout+Xi*B[p,l,i]*D[p,k]
2209                else:
2210                   Cout+=(Xi*D)*B
2211             return Cout
2212         elif name == "D" :
2213             return self.getCoefficient("D")
2214         elif name == "X" :
2215             # return self.getCoefficient("X")
2216             X=self.getCoefficient("X")
2217             Y=self.getCoefficient("Y")
2218             B=self.getCoefficient("B")
2219             C=self.getCoefficient("C")
2220             if Y.isEmpty() or (B.isEmpty() and C.isEmpty()):
2221                Xout=X
2222             else:
2223                if X.isEmpty():
2224                    Xout=self.createCoefficientOfGeneralPDE("X")
2225                else:
2226                    Xout=X[:]
2227                Xi=self.__getXi()
2228                if self.getNumEquations()>1:
2229                     for p in range(self.getNumEquations()):
2230                        tmp=Xi*Y[p]
2231                        for i in range(self.getNumEquations()):
2232                           for j in range(self.getDim()):
2233                              if not C.isEmpty() and not B.isEmpty():
2234                                 Xout[i,j]+=tmp*(C[p,i,j]-B[p,j,i])
2235                                 # Xout=X_out+Xi*util.inner(Y,C-util.reorderComponents(B,[0,2,1]),offset=1)
2236                              elif C.isEmpty():
2237                                 Xout[i,j]-=tmp*B[p,j,i]
2238                                 # Xout=X_out-Xi*util.inner(Y,util.reorderComponents(B,[0,2,1]),offset=1)
2239                              else:
2240                                 Xout[i,j]+=tmp*C[p,i,j]
2241                                 # Xout=X_out+Xi*util.inner(Y,C,offset=1)
2242                else:
2243                  if not C.isEmpty() and not B.isEmpty():
2244                    Xout+=(Xi*Y)*(C-B)
2245                  elif C.isEmpty():
2246                    Xout-=(Xi*Y)*B
2247                  else:
2248                    Xout+=(Xi*Y)*C
2249             return Xout
2250         elif name == "Y" :
2251             return self.getCoefficient("Y")
2252         elif name == "d" :
2253             return self.getCoefficient("d")
2254         elif name == "y" :
2255             return self.getCoefficient("y")
2256         elif name == "d_contact" :
2257             return self.getCoefficient("d_contact")
2258         elif name == "y_contact" :
2259             return self.getCoefficient("y_contact")
2260         elif name == "r" :
2261             return self.getCoefficient("r")
2262         elif name == "q" :
2263             return self.getCoefficient("q")
2264         else:
2265            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2266    
2267  # $Log$  # $Log$
2268  # Revision 1.3  2004/12/17 07:43:10  jgs  # Revision 1.14  2005/09/22 01:54:57  jgs
2269  # *** empty log message ***  # Merge of development branch dev-02 back to main trunk on 2005-09-22
2270    #
2271    # Revision 1.13  2005/09/15 03:44:19  jgs
2272    # Merge of development branch dev-02 back to main trunk on 2005-09-15
2273    #
2274    # Revision 1.12  2005/09/01 03:31:28  jgs
2275    # Merge of development branch dev-02 back to main trunk on 2005-09-01
2276    #
2277    # Revision 1.11  2005/08/23 01:24:28  jgs
2278    # Merge of development branch dev-02 back to main trunk on 2005-08-23
2279    #
2280    # Revision 1.10  2005/08/12 01:45:36  jgs
2281    # erge of development branch dev-02 back to main trunk on 2005-08-12
2282    #
2283    # Revision 1.9.2.17  2005/09/21 07:03:33  matt
2284    # PDECoefficient and LinearPDE are now new style classes (introduced in Python
2285    # 2.2). Classes Poisson, Helmholtz, LameEquation and AdvectivePDE have been
2286    # modified to instead use portable/cooperative "super" calls to extend base
2287    # class methods.
2288    #
2289    # Revision 1.9.2.16  2005/09/16 01:54:37  matt
2290    # Removed redundant if-loop.
2291    #
2292    # Revision 1.9.2.15  2005/09/14 08:09:18  matt
2293    # Added "REDUCED" solution PDECoefficient descriptors for LinearPDEs.
2294    #
2295    # Revision 1.9.2.14  2005/09/07 06:26:16  gross
2296    # the solver from finley are put into the standalone package paso now
2297    #
2298    # Revision 1.9.2.13  2005/08/31 08:45:03  gross
2299    # in the case of lumping no new system is allocated if the constraint is changed.
2300    #
2301    # Revision 1.9.2.12  2005/08/31 07:10:23  gross
2302    # test for Lumping added
2303    #
2304    # Revision 1.9.2.11  2005/08/30 01:53:45  gross
2305    # bug in format fixed.
2306    #
2307    # Revision 1.9.2.10  2005/08/26 07:14:17  gross
2308    # a few more bugs in linearPDE fixed. remaining problem are finley problems
2309    #
2310    # Revision 1.9.2.9  2005/08/26 06:30:45  gross
2311    # fix for reported bug  0000004. test_linearPDE passes a few more tests
2312    #
2313    # Revision 1.9.2.8  2005/08/26 04:30:13  gross
2314    # gneric unit testing for linearPDE
2315    #
2316    # Revision 1.9.2.7  2005/08/25 07:06:50  gross
2317    # linearPDE documentation is parsed now by epydoc. there is still a problem with links into escriptcpp.so
2318    #
2319    # Revision 1.9.2.6  2005/08/24 05:01:24  gross
2320    # problem with resetting the matrix in case of resetting its values to 0 fixed.
2321    #
2322    # Revision 1.9.2.5  2005/08/24 02:03:28  gross
2323    # epydoc mark up partially fixed
2324    #
2325    # Revision 1.9.2.4  2005/08/22 07:11:09  gross
2326    # some problems with LinearPDEs fixed.
2327    #
2328    # Revision 1.9.2.3  2005/08/18 04:48:48  gross
2329    # the methods SetLumping*() are removed. Lumping is set trough setSolverMethod(LinearPDE.LUMPING)
2330    #
2331    # Revision 1.9.2.2  2005/08/18 04:39:32  gross
2332    # the constants have been removed from util.py as they not needed anymore. PDE related constants are accessed through LinearPDE attributes now
2333    #
2334    # Revision 1.9.2.1  2005/07/29 07:10:27  gross
2335    # new functions in util and a new pde type in linearPDEs
2336    #
2337    # Revision 1.1.2.25  2005/07/28 04:21:09  gross
2338    # Lame equation: (linear elastic, isotropic) added
2339    #
2340    # Revision 1.1.2.24  2005/07/22 06:37:11  gross
2341    # some extensions to modellib and linearPDEs
2342    #
2343    # Revision 1.1.2.23  2005/05/13 00:55:20  cochrane
2344    # Fixed up some docstrings.  Moved module-level functions to top of file so
2345    # that epydoc and doxygen can pick them up properly.
2346    #
2347    # Revision 1.1.2.22  2005/05/12 11:41:30  gross
2348    # some basic Models have been added
2349    #
2350    # Revision 1.1.2.21  2005/05/12 07:16:12  cochrane
2351    # Moved ELMAN_RAMAGE, SIMPLIFIED_BROOK_HUGHES, and HALF functions to bottom of
2352    # file so that the AdvectivePDE class is picked up by doxygen.  Some
2353    # reformatting of docstrings.  Addition of code to make equations come out
2354    # as proper LaTeX.
2355    #
2356    # Revision 1.1.2.20  2005/04/15 07:09:08  gross
2357    # some problems with functionspace and linearPDEs fixed.
2358    #
2359    # Revision 1.1.2.19  2005/03/04 05:27:07  gross
2360    # bug in SystemPattern fixed.
2361    #
2362    # Revision 1.1.2.18  2005/02/08 06:16:45  gross
2363    # Bugs in AdvectivePDE fixed, AdvectiveTest is stable but more testing is needed
2364    #
2365    # Revision 1.1.2.17  2005/02/08 05:56:19  gross
2366    # Reference Number handling added
2367    #
2368    # Revision 1.1.2.16  2005/02/07 04:41:28  gross
2369    # some function exposed to python to make mesh merging running
2370    #
2371    # Revision 1.1.2.15  2005/02/03 00:14:44  gross
2372    # timeseries add and ESySParameter.py renames esysXML.py for consistence
2373    #
2374    # Revision 1.1.2.14  2005/02/01 06:44:10  gross
2375    # new implementation of AdvectivePDE which now also updates right hand side. systems of PDEs are still not working
2376    #
2377    # Revision 1.1.2.13  2005/01/25 00:47:07  gross
2378    # updates in the documentation
2379    #
2380    # Revision 1.1.2.12  2005/01/12 01:28:04  matt
2381    # Added createCoefficient method for linearPDEs.
2382    #
2383    # Revision 1.1.2.11  2005/01/11 01:55:34  gross
2384    # a problem in linearPDE class fixed
2385    #
2386    # Revision 1.1.2.10  2005/01/07 01:13:29  gross
2387    # some bugs in linearPDE fixed
2388    #
2389    # Revision 1.1.2.9  2005/01/06 06:24:58  gross
2390    # some bugs in slicing fixed
2391    #
2392    # Revision 1.1.2.8  2005/01/05 04:21:40  gross
2393    # FunctionSpace checking/matchig in slicing added
2394    #
2395    # Revision 1.1.2.7  2004/12/29 10:03:41  gross
2396    # bug in setValue fixed
2397    #
2398    # Revision 1.1.2.6  2004/12/29 05:29:59  gross
2399    # AdvectivePDE successfully tested for Peclet number 1000000. there is still a problem with setValue and Data()
2400    #
2401    # Revision 1.1.2.5  2004/12/29 00:18:41  gross
2402    # AdvectivePDE added
2403    #
2404    # Revision 1.1.2.4  2004/12/24 06:05:41  gross
2405    # some changes in linearPDEs to add AdevectivePDE
2406  #  #
2407  # Revision 1.1.2.3  2004/12/16 00:12:34  gross  # Revision 1.1.2.3  2004/12/16 00:12:34  gross
2408  # __init__ of LinearPDE does not accept any coefficients anymore  # __init__ of LinearPDE does not accept any coefficient anymore
2409  #  #
2410  # Revision 1.1.2.2  2004/12/14 03:55:01  jgs  # Revision 1.1.2.2  2004/12/14 03:55:01  jgs
2411  # *** empty log message ***  # *** empty log message ***
# Line 998  class Poisson(LinearPDE): Line 2449  class Poisson(LinearPDE):
2449  # Revision 1.1  2004/08/28 12:58:06  gross  # Revision 1.1  2004/08/28 12:58:06  gross
2450  # SimpleSolve is not running yet: problem with == of functionsspace  # SimpleSolve is not running yet: problem with == of functionsspace
2451  #  #
 #  

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