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trunk/esys2/escript/py_src/linearPDEs.py revision 142 by jgs, Mon Jul 25 05:28:20 2005 UTC trunk/escript/py_src/linearPDEs.py revision 877 by gross, Wed Oct 25 03:06:58 2006 UTC
# Line 1  Line 1 
1  # $Id$  # $Id$
   
 ## @file linearPDEs.py  
   
2  """  """
3  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{AdvectivePDE}
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 __copyright__: copyrights
16    @var __license__: licence agreement
17    @var __url__: url entry point on documentation
18    @var __version__: version
19    @var __date__: date of the version
20  """  """
21    
22  import escript  import escript
23  import util  import util
24  import numarray  import numarray
25    
26    __author__="Lutz Gross, l.gross@uq.edu.au"
27    __copyright__="""  Copyright (c) 2006 by ACcESS MNRF
28                        http://www.access.edu.au
29                    Primary Business: Queensland, Australia"""
30    __license__="""Licensed under the Open Software License version 3.0
31                 http://www.opensource.org/licenses/osl-3.0.php"""
32    __url__="http://www.iservo.edu.au/esys"
33    __version__="$Revision$"
34    __date__="$Date$"
35    
 def _CompTuple2(t1,t2):  
    """  
    Compare two tuples  
36    
37     \param t1 The first tuple  class IllegalCoefficient(ValueError):
38     \param t2 The second tuple     """
39       raised if an illegal coefficient of the general ar particular PDE is requested.
40     """     """
41    
42     dif=t1[0]+t1[1]-(t2[0]+t2[1])  class IllegalCoefficientValue(ValueError):
43     if dif<0: return 1     """
44     elif dif>0: return -1     raised if an incorrect value for a coefficient is used.
45     else: return 0     """
   
 def ELMAN_RAMAGE(P):  
     return (P-1.).wherePositive()*0.5*(1.-1./(P+1.e-15))  
   
 def SIMPLIFIED_BROOK_HUGHES(P):  
     c=(P-3.).whereNegative()  
     return P/6.*c+1./2.*(1.-c)  
46    
47  def HALF(P):  class UndefinedPDEError(ValueError):
48      return escript.Scalar(0.5,P.getFunctionSpace())     """
49       raised if a PDE is not fully defined yet.
50       """
51    
52  class PDECoefficient:  class PDECoefficient(object):
53      """      """
54      A class for PDE coefficients      A class for describing a PDE coefficient
55    
56        @cvar INTERIOR: indicator that coefficient is defined on the interior of the PDE domain
57        @cvar BOUNDARY: indicator that coefficient is defined on the boundary of the PDE domain
58        @cvar CONTACT: indicator that coefficient is defined on the contact region within the PDE domain
59        @cvar SOLUTION: indicator that coefficient is defined trough a solution of the PDE
60        @cvar REDUCED: indicator that coefficient is defined trough a reduced solution of the PDE
61        @cvar BY_EQUATION: indicator that the dimension of the coefficient shape is defined by the number PDE equations
62        @cvar BY_SOLUTION: indicator that the dimension of the coefficient shape is defined by the number PDE solutions
63        @cvar BY_DIM: indicator that the dimension of the coefficient shape is defined by the spatial dimension
64        @cvar OPERATOR: indicator that the the coefficient alters the operator of the PDE
65        @cvar RIGHTHANDSIDE: indicator that the the coefficient alters the right hand side of the PDE
66        @cvar BOTH: indicator that the the coefficient alters the operator as well as the right hand side of the PDE
67    
68      """      """
     # identifier for location of Data objects defining COEFFICIENTS  
69      INTERIOR=0      INTERIOR=0
70      BOUNDARY=1      BOUNDARY=1
71      CONTACT=2      CONTACT=2
72      CONTINUOUS=3      SOLUTION=3
73      # identifier in the pattern of COEFFICIENTS:      REDUCED=4
74      # 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
75      # number of unknowns.      BY_SOLUTION=6
76      EQUATION=3      BY_DIM=7
77      SOLUTION=4      OPERATOR=10
78      DIM=5      RIGHTHANDSIDE=11
79      # indicator for what is altered if the coefficient is altered:      BOTH=12
80      OPERATOR=5  
     RIGHTHANDSIDE=6  
     BOTH=7  
81      def __init__(self,where,pattern,altering):      def __init__(self,where,pattern,altering):
82         """         """
83         Initialise a PDE Coefficient type         Initialise a PDE Coefficient type
84    
85           @param where: describes where the coefficient lives
86           @type where: one of L{INTERIOR}, L{BOUNDARY}, L{CONTACT}, L{SOLUTION}, L{REDUCED}
87           @param pattern: describes the shape of the coefficient and how the shape is build for a given
88                  spatial dimension and numbers of equation and solution in then PDE. For instance,
89                  (L{BY_EQUATION},L{BY_SOLUTION},L{BY_DIM}) descrbes a rank 3 coefficient which
90                  is instanciated as shape (3,2,2) in case of a three equations and two solution components
91                  on a 2-dimensional domain. In the case of single equation and a single solution component
92                  the shape compoments marked by L{BY_EQUATION} or L{BY_SOLUTION} are dropped. In this case
93                  the example would be read as (2,).
94           @type pattern: C{tuple} of L{BY_EQUATION}, L{BY_SOLUTION}, L{BY_DIM}
95           @param altering: indicates what part of the PDE is altered if the coefficiennt is altered
96           @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}
97    
98         """         """
99           super(PDECoefficient, self).__init__()
100         self.what=where         self.what=where
101         self.pattern=pattern         self.pattern=pattern
102         self.altering=altering         self.altering=altering
# Line 68  class PDECoefficient: Line 108  class PDECoefficient:
108         """         """
109         self.value=escript.Data()         self.value=escript.Data()
110    
111      def getFunctionSpace(self,domain):      def getFunctionSpace(self,domain,reducedEquationOrder=False,reducedSolutionOrder=False):
112         """         """
113         defines the FunctionSpace of the coefficient on the domain         defines the L{FunctionSpace<escript.FunctionSpace>} of the coefficient
114    
115         @param domain:         @param domain: domain on which the PDE uses the coefficient
116         """         @type domain: L{Domain<escript.Domain>}
117         if self.what==self.INTERIOR: return escript.Function(domain)         @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
118         elif self.what==self.BOUNDARY: return escript.FunctionOnBoundary(domain)         @type reducedEquationOrder: C{bool}
119         elif self.what==self.CONTACT: return escript.FunctionOnContactZero(domain)         @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
120         elif self.what==self.CONTINUOUS: return escript.ContinuousFunction(domain)         @type reducedSolutionOrder: C{bool}
121           @return:  L{FunctionSpace<escript.FunctionSpace>} of the coefficient
122           @rtype:  L{FunctionSpace<escript.FunctionSpace>}
123           """
124           if self.what==self.INTERIOR:
125                return escript.Function(domain)
126           elif self.what==self.BOUNDARY:
127                return escript.FunctionOnBoundary(domain)
128           elif self.what==self.CONTACT:
129                return escript.FunctionOnContactZero(domain)
130           elif self.what==self.SOLUTION:
131                if reducedEquationOrder and reducedSolutionOrder:
132                    return escript.ReducedSolution(domain)
133                else:
134                    return escript.Solution(domain)
135           elif self.what==self.REDUCED:
136                return escript.ReducedSolution(domain)
137    
138      def getValue(self):      def getValue(self):
139         """         """
140         returns the value of the coefficient:         returns the value of the coefficient
141    
142           @return:  value of the coefficient
143           @rtype:  L{Data<escript.Data>}
144         """         """
145         return self.value         return self.value
146        
147      def setValue(self,newValue):      def setValue(self,domain,numEquations=1,numSolutions=1,reducedEquationOrder=False,reducedSolutionOrder=False,newValue=None):
        """  
        set the value of the coefficient to new value  
148         """         """
149           set the value of the coefficient to a new value
150    
151           @param domain: domain on which the PDE uses the coefficient
152           @type domain: L{Domain<escript.Domain>}
153           @param numEquations: number of equations of the PDE
154           @type numEquations: C{int}
155           @param numSolutions: number of components of the PDE solution
156           @type numSolutions: C{int}
157           @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
158           @type reducedEquationOrder: C{bool}
159           @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
160           @type reducedSolutionOrder: C{bool}
161           @param newValue: number of components of the PDE solution
162           @type newValue: any object that can be converted into a L{Data<escript.Data>} object with the appropriate shape and L{FunctionSpace<escript.FunctionSpace>}
163           @raise IllegalCoefficientValue: if the shape of the assigned value does not match the shape of the coefficient
164           """
165           if newValue==None:
166               newValue=escript.Data()
167           elif isinstance(newValue,escript.Data):
168               if not newValue.isEmpty():
169                  try:
170                     newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
171                  except:
172                     raise IllegalCoefficientValue,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)
173           else:
174               newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
175           if not newValue.isEmpty():
176               if not self.getShape(domain,numEquations,numSolutions)==newValue.getShape():
177                   raise IllegalCoefficientValue,"Expected shape of coefficient is %s but actual shape is %s."%(self.getShape(domain,numEquations,numSolutions),newValue.getShape())
178         self.value=newValue         self.value=newValue
179        
180      def isAlteringOperator(self):      def isAlteringOperator(self):
181          """          """
182      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
183    
184            @return:  True if the operator of the PDE is changed when the coefficient is changed
185            @rtype:  C{bool}
186      """      """
187          if self.altering==self.OPERATOR or self.altering==self.BOTH:          if self.altering==self.OPERATOR or self.altering==self.BOTH:
188              return not None              return not None
# Line 102  class PDECoefficient: Line 191  class PDECoefficient:
191    
192      def isAlteringRightHandSide(self):      def isAlteringRightHandSide(self):
193          """          """
194      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
195    
196        @rtype:  C{bool}
197            @return:  True if the right hand side of the PDE is changed when the coefficient is changed
198      """      """
199          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:
200              return not None              return not None
201          else:          else:
202              return None              return None
203    
204      def estimateNumEquationsAndNumSolutions(self,shape=(),dim=3):      def estimateNumEquationsAndNumSolutions(self,domain,shape=()):
205         """         """
206         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
207    
208         @param shape:         @param domain: domain on which the PDE uses the coefficient
209         @param dim:         @type domain: L{Domain<escript.Domain>}
210           @param shape: suggested shape of the coefficient
211           @type shape: C{tuple} of C{int} values
212           @return: the number of equations and number of solutions of the PDE is the coefficient has shape s.
213                     If no appropriate numbers could be identified, C{None} is returned
214           @rtype: C{tuple} of two C{int} values or C{None}
215         """         """
216           dim=domain.getDim()
217         if len(shape)>0:         if len(shape)>0:
218             num=max(shape)+1             num=max(shape)+1
219         else:         else:
220             num=1             num=1
221         search=[]         search=[]
222         for u in range(num):         if self.definesNumEquation() and self.definesNumSolutions():
223            for e in range(num):            for u in range(num):
224               search.append((e,u))               for e in range(num):
225         search.sort(_CompTuple2)                  search.append((e,u))
226         for item in search:            search.sort(self.__CompTuple2)
227               s=self.buildShape(item[0],item[1],dim)            for item in search:
228                 s=self.getShape(domain,item[0],item[1])
229               if len(s)==0 and len(shape)==0:               if len(s)==0 and len(shape)==0:
230                   return (1,1)                   return (1,1)
231               else:               else:
232                   if s==shape: return item                   if s==shape: return item
233           elif self.definesNumEquation():
234              for e in range(num,0,-1):
235                 s=self.getShape(domain,e,0)
236                 if len(s)==0 and len(shape)==0:
237                     return (1,None)
238                 else:
239                     if s==shape: return (e,None)
240    
241           elif self.definesNumSolutions():
242              for u in range(num,0,-1):
243                 s=self.getShape(domain,0,u)
244                 if len(s)==0 and len(shape)==0:
245                     return (None,1)
246                 else:
247                     if s==shape: return (None,u)
248         return None         return None
249        def definesNumSolutions(self):
250           """
251           checks if the coefficient allows to estimate the number of solution components
252    
253      def buildShape(self,e=1,u=1,dim=3):         @return: True if the coefficient allows an estimate of the number of solution components
254          """         @rtype: C{bool}
255      builds the required shape for a given number of equations e, number of unknowns u and spatial dimension dim         """
256           for i in self.pattern:
257                 if i==self.BY_SOLUTION: return True
258           return False
259    
260      @param e:      def definesNumEquation(self):
261      @param u:         """
262      @param dim:         checks if the coefficient allows to estimate the number of equations
263      """  
264          s=()         @return: True if the coefficient allows an estimate of the number of equations
265          for i in self.pattern:         @rtype: C{bool}
266               if i==self.EQUATION:         """
267                  if e>1: s=s+(e,)         for i in self.pattern:
268               elif i==self.SOLUTION:               if i==self.BY_EQUATION: return True
269                  if u>1: s=s+(u,)         return False
270    
271        def __CompTuple2(self,t1,t2):
272          """
273          Compare two tuples of possible number of equations and number of solutions
274    
275          @param t1: The first tuple
276          @param t2: The second tuple
277    
278          """
279    
280          dif=t1[0]+t1[1]-(t2[0]+t2[1])
281          if dif<0: return 1
282          elif dif>0: return -1
283          else: return 0
284    
285        def getShape(self,domain,numEquations=1,numSolutions=1):
286           """
287           builds the required shape of the coefficient
288    
289           @param domain: domain on which the PDE uses the coefficient
290           @type domain: L{Domain<escript.Domain>}
291           @param numEquations: number of equations of the PDE
292           @type numEquations: C{int}
293           @param numSolutions: number of components of the PDE solution
294           @type numSolutions: C{int}
295           @return: shape of the coefficient
296           @rtype: C{tuple} of C{int} values
297           """
298           dim=domain.getDim()
299           s=()
300           for i in self.pattern:
301                 if i==self.BY_EQUATION:
302                    if numEquations>1: s=s+(numEquations,)
303                 elif i==self.BY_SOLUTION:
304                    if numSolutions>1: s=s+(numSolutions,)
305               else:               else:
306                  s=s+(dim,)                  s=s+(dim,)
307          return s         return s
308    
309  class LinearPDE:  class LinearPDE(object):
310     """     """
311     Class to handle a linear PDE     This class is used to define a general linear, steady, second order PDE
312         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  
313    
314     \f[     For a single PDE with a solution with a single component the linear PDE is defined in the following form:
      -(A_{ijkl}u_{k,l})_{,j} -(B_{ijk}u_k)_{,j} + C_{ikl}u_{k,l} +D_{ik}u_k = - (X_{ij})_{,j} + Y_i  
    \f]  
315    
316     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}
317    
318     \f[     where M{grad(F)} denotes the spatial derivative of M{F}. Einstein's summation convention,
319     n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i     ie. summation over indexes appearing twice in a term of a sum is performed, is used.
320     \f]     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
321       L{Function<escript.Function>} on the PDE or objects that can be converted into such L{Data<escript.Data>} objects.
322       M{A} is a rank two, M{B}, M{C} and M{X} are rank one and M{D} and M{Y} are scalar.
323    
324     and contact conditions     The following natural boundary conditions are considered:
325    
326     \f[     M{n[j]*(A[i,j]*grad(u)[l]+B[j]*u)+d*u=n[j]*X[j]+y}
    n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_contact_{ik}[u_k] = - n_j*X_{ij} + y_contact_i  
    \f]  
327    
328     and constraints:     where M{n} is the outer normal field calculated by L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
329       Notice that the coefficients M{A}, M{B} and M{X} are defined in the PDE. The coefficients M{d} and M{y} are
330       each a scalar in the L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
331    
    \f[  
    u_i=r_i \quad \mathrm{where} \quad q_i>0  
    \f]  
332    
333     """     Constraints for the solution prescribing the value of the solution at certain locations in the domain. They have the form
    TOL=1.e-13  
    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  
    ILU0=util.ILU0  
    JACOBI=util.JACOBI  
334    
335     def __init__(self,domain,numEquations=0,numSolutions=0):     M{u=r}  where M{q>0}
      """  
      initializes a new linear PDE.  
336    
337       @param args:     M{r} and M{q} are each scalar where M{q} is the characteristic function defining where the constraint is applied.
338       """     The constraints override any other condition set by the PDE or the boundary condition.
339       # COEFFICIENTS can be overwritten by subclasses:  
340       self.COEFFICIENTS={     The PDE is symmetrical if
341         "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM,PDECoefficient.SOLUTION,PDECoefficient.DIM),PDECoefficient.OPERATOR),  
342         "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),     M{A[i,j]=A[j,i]}  and M{B[j]=C[j]}
343         "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION,PDECoefficient.DIM),PDECoefficient.OPERATOR),  
344         "D"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),     For a system of PDEs and a solution with several components the PDE has the form
345         "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM),PDECoefficient.RIGHTHANDSIDE),  
346         "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),     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] }
347         "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),  
348         "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),     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.
349         "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),     The natural boundary conditions take the form:
350         "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),  
351         "r"         : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),     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]}
352         "q"         : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.SOLUTION,),PDECoefficient.BOTH)}  
353    
354       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
355    
356    
357       M{u[i]=r[i]}  where  M{q[i]>0}
358    
359       M{r} and M{q} are each rank one. Notice that at some locations not necessarily all components must have a constraint.
360    
361       The system of PDEs is symmetrical if
362    
363            - M{A[i,j,k,l]=A[k,l,i,j]}
364            - M{B[i,j,k]=C[k,i,j]}
365            - M{D[i,k]=D[i,k]}
366            - M{d[i,k]=d[k,i]}
367    
368       L{LinearPDE} also supports solution discontinuities over a contact region in the domain. To specify the conditions across the
369       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
370       defined as
371    
372       M{J[i,j]=A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]*u[k]-X[i,j]}
373    
374       For the case of single solution component and single PDE M{J} is defined
375    
376       M{J_{j}=A[i,j]*grad(u)[j]+B[i]*u-X[i]}
377    
378       In the context of discontinuities M{n} denotes the normal on the discontinuity pointing from side 0 towards side 1
379       calculated from L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnContactZero<escript.FunctionOnContactZero>}. For a system of PDEs
380       the contact condition takes the form
381    
382       M{n[j]*J0[i,j]=n[j]*J1[i,j]=y_contact[i]- d_contact[i,k]*jump(u)[k]}
383    
384       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
385       of the solution at side 1 and at side 0, denotes the jump of M{u} across discontinuity along the normal calcualted by
386       L{jump<util.jump>}.
387       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>}.
388       In case of a single PDE and a single component solution the contact condition takes the form
389    
390       M{n[j]*J0_{j}=n[j]*J1_{j}=y_contact-d_contact*jump(u)}
391    
392       In this case the the coefficient M{d_contact} and M{y_contact} are eaach scalar
393       both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
394    
395       @cvar DEFAULT: The default method used to solve the system of linear equations
396       @cvar DIRECT: The direct solver based on LDU factorization
397       @cvar CHOLEVSKY: The direct solver based on LDLt factorization (can only be applied for symmetric PDEs)
398       @cvar PCG: The preconditioned conjugate gradient method (can only be applied for symmetric PDEs)
399       @cvar CR: The conjugate residual method
400       @cvar CGS: The conjugate gardient square method
401       @cvar BICGSTAB: The stabilized BiConjugate Gradient method.
402       @cvar SSOR: The symmetric overrealaxtion method
403       @cvar ILU0: The incomplete LU factorization preconditioner  with no fill in
404       @cvar ILUT: The incomplete LU factorization preconditioner with will in
405       @cvar JACOBI: The Jacobi preconditioner
406       @cvar GMRES: The Gram-Schmidt minimum residual method
407       @cvar PRES20: Special GMRES with restart after 20 steps and truncation after 5 residuals
408       @cvar LUMPING: Matrix lumping.
409       @cvar NO_REORDERING: No matrix reordering allowed
410       @cvar MINIMUM_FILL_IN: Reorder matrix to reduce fill-in during factorization
411       @cvar NESTED_DISSECTION: Reorder matrix to improve load balancing during factorization
412       @cvar PASO: PASO solver package
413       @cvar SCSL: SGI SCSL solver library
414       @cvar MKL: Intel's MKL solver library
415       @cvar UMFPACK: the UMFPACK library
416       @cvar ITERATIVE: The default iterative solver
417       @cvar AMG: algebraic multi grid
418       @cvar RILU: recursive ILU
419    
420       """
421       DEFAULT= 0
422       DIRECT= 1
423       CHOLEVSKY= 2
424       PCG= 3
425       CR= 4
426       CGS= 5
427       BICGSTAB= 6
428       SSOR= 7
429       ILU0= 8
430       ILUT= 9
431       JACOBI= 10
432       GMRES= 11
433       PRES20= 12
434       LUMPING= 13
435       NO_REORDERING= 17
436       MINIMUM_FILL_IN= 18
437       NESTED_DISSECTION= 19
438       SCSL= 14
439       MKL= 15
440       UMFPACK= 16
441       ITERATIVE= 20
442       PASO= 21
443       AMG= 22
444       RILU = 23
445    
446       SMALL_TOLERANCE=1.e-13
447       __PACKAGE_KEY="package"
448       __METHOD_KEY="method"
449       __SYMMETRY_KEY="symmetric"
450       __TOLERANCE_KEY="tolerance"
451       __PRECONDITIONER_KEY="preconditioner"
452    
453    
454       def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):
455         """
456         initializes a new linear PDE
457    
458         @param domain: domain of the PDE
459         @type domain: L{Domain<escript.Domain>}
460         @param numEquations: number of equations. If numEquations==None the number of equations
461                              is exracted from the PDE coefficients.
462         @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
463                              is exracted from the PDE coefficients.
464         @param debug: if True debug informations are printed.
465    
466         """
467         super(LinearPDE, self).__init__()
468         #
469         #   the coefficients of the general PDE:
470         #
471         self.__COEFFICIENTS_OF_GENEARL_PDE={
472           "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
473           "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
474           "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
475           "D"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
476           "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
477           "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
478           "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
479           "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
480           "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
481           "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
482           "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
483           "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
484    
485         # COEFFICIENTS can be overwritten by subclasses:
486         self.COEFFICIENTS=self.__COEFFICIENTS_OF_GENEARL_PDE
487         self.__altered_coefficients=False
488       # initialize attributes       # initialize attributes
489       self.__debug=None       self.__debug=debug
490       self.__domain=domain       self.__domain=domain
491       self.__numEquations=numEquations       self.__numEquations=numEquations
492       self.__numSolutions=numSolutions       self.__numSolutions=numSolutions
493       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  
494    
495       # set some default values:       # set some default values:
496       self.__homogeneous_constraint=True       self.__reduce_equation_order=False
497       self.__row_function_space=escript.Solution(self.__domain)       self.__reduce_solution_order=False
      self.__column_function_space=escript.Solution(self.__domain)  
498       self.__tolerance=1.e-8       self.__tolerance=1.e-8
499       self.__solver_method=util.DEFAULT_METHOD       self.__solver_method=self.DEFAULT
500       self.__matrix_type=self.__domain.getSystemMatrixTypeId(util.DEFAULT_METHOD,False)       self.__solver_package=self.DEFAULT
501         self.__preconditioner=self.DEFAULT
502         self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT,self.DEFAULT,False)
503       self.__sym=False       self.__sym=False
      self.__lumping=False  
504    
505     def createCoefficient(self, name):       self.resetCoefficients()
506         self.trace("PDE Coeffients are %s"%str(self.COEFFICIENTS.keys()))
507       # =============================================================================
508       #    general stuff:
509       # =============================================================================
510       def __str__(self):
511         """
512         returns string representation of the PDE
513    
514         @return: a simple representation of the PDE
515         @rtype: C{str}
516         """
517         return "<LinearPDE %d>"%id(self)
518       # =============================================================================
519       #    debug :
520       # =============================================================================
521       def setDebugOn(self):
522       """       """
523       create a data object corresponding to coefficient name       switches on debugging
      @param name:  
524       """       """
525       return escript.Data(shape = getShapeOfCoefficient(name), \       self.__debug=not None
                          what = getFunctionSpaceForCoefficient(name))  
526    
527     def __del__(self):     def setDebugOff(self):
528       pass       """
529         switches off debugging
    def getCoefficient(self,name):  
530       """       """
531       return the value of the parameter name       self.__debug=None
532    
533       @param name:     def trace(self,text):
534       """       """
535       return self.COEFFICIENTS[name].getValue()       print the text message if debugging is swiched on.
536         @param text: message
537         @type text: C{string}
538         """
539         if self.__debug: print "%s: %s"%(str(self),text)
540    
541     def getCoefficientOfPDE(self,name):     # =============================================================================
542       # some service functions:
543       # =============================================================================
544       def getDomain(self):
545       """       """
546       return the value of the coefficient name of the general PDE.       returns the domain of the PDE
      This method is called by the assembling routine it can be  
      overwritten to map coefficients of a particualr PDE to the general PDE.  
547    
548       @param name:       @return: the domain of the PDE
549         @rtype: L{Domain<escript.Domain>}
550       """       """
551       return self.getCoefficient(name)       return self.__domain
552    
553     def hasCoefficient(self,name):     def getDim(self):
554        """       """
555        return true if name is the name of a coefficient       returns the spatial dimension of the PDE
556    
557        @param name:       @return: the spatial dimension of the PDE domain
558        """       @rtype: C{int}
559        return self.COEFFICIENTS.has_key(name)       """
560         return self.getDomain().getDim()
561    
562     def getFunctionSpaceForEquation(self):     def getNumEquations(self):
563       """       """
564       return true if the test functions should use reduced order       returns the number of equations
565    
566         @return: the number of equations
567         @rtype: C{int}
568         @raise UndefinedPDEError: if the number of equations is not be specified yet.
569       """       """
570       return self.__row_function_space       if self.__numEquations==None:
571             raise UndefinedPDEError,"Number of equations is undefined. Please specify argument numEquations."
572         else:
573             return self.__numEquations
574    
575     def getFunctionSpaceForSolution(self):     def getNumSolutions(self):
576       """       """
577       return true if the interpolation of the solution should use reduced order       returns the number of unknowns
578    
579         @return: the number of unknowns
580         @rtype: C{int}
581         @raise UndefinedPDEError: if the number of unknowns is not be specified yet.
582       """       """
583       return self.__column_function_space       if self.__numSolutions==None:
584            raise UndefinedPDEError,"Number of solution is undefined. Please specify argument numSolutions."
585         else:
586            return self.__numSolutions
587    
588     def setValue(self,**coefficients):     def reduceEquationOrder(self):
589        """       """
590        sets new values to coefficients       return status for order reduction for equation
591    
592        @param coefficients:       @return: return True is reduced interpolation order is used for the represenation of the equation
593        """       @rtype: L{bool}
594        self.__setValue(**coefficients)       """
595               return self.__reduce_equation_order
596    
597     def cleanCoefficients(self):     def reduceSolutionOrder(self):
598       """       """
599       resets all coefficients to default values.       return status for order reduction for the solution
600    
601         @return: return True is reduced interpolation order is used for the represenation of the solution
602         @rtype: L{bool}
603       """       """
604       for i in self.COEFFICIENTS.iterkeys():       return self.__reduce_solution_order
          self.COEFFICIENTS[i].resetValue()  
605    
606     def createNewCoefficient(self,name):     def getFunctionSpaceForEquation(self):
607       """       """
608       returns a new coefficient appropriate for coefficient name:       returns the L{FunctionSpace<escript.FunctionSpace>} used to discretize the equation
609    
610         @return: representation space of equation
611         @rtype: L{FunctionSpace<escript.FunctionSpace>}
612       """       """
613       return escript.Data(0,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))       if self.reduceEquationOrder():
614                   return escript.ReducedSolution(self.getDomain())
615         else:
616             return escript.Solution(self.getDomain())
617    
618     def getShapeOfCoefficient(self,name):     def getFunctionSpaceForSolution(self):
619       """       """
620       return the shape of the coefficient name       returns the L{FunctionSpace<escript.FunctionSpace>} used to represent the solution
621    
622       @param name:       @return: representation space of solution
623         @rtype: L{FunctionSpace<escript.FunctionSpace>}
624       """       """
625       if self.hasCoefficient(name):       if self.reduceSolutionOrder():
626          return self.COEFFICIENTS[name].buildShape(self.getNumEquations(),self.getNumSolutions(),self.getDomain().getDim())           return escript.ReducedSolution(self.getDomain())
627       else:       else:
628          raise ValueError,"Solution coefficient %s requested"%name           return escript.Solution(self.getDomain())
629    
630     def getFunctionSpaceForCoefficient(self,name):  
631       def getOperator(self):
632       """       """
633       return the atoms of the coefficient name       provides access to the operator of the PDE
634    
635       @param name:       @return: the operator of the PDE
636         @rtype: L{Operator<escript.Operator>}
637       """       """
638       if self.hasCoefficient(name):       m=self.getSystem()[0]
639          return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())       if self.isUsingLumping():
640             return self.copyConstraint(1./m)
641       else:       else:
642          raise ValueError,"Solution coefficient %s requested"%name           return m
643    
644     def alteredCoefficient(self,name):     def getRightHandSide(self):
645       """       """
646       announce that coefficient name has been changed       provides access to the right hand side of the PDE
647         @return: the right hand side of the PDE
648         @rtype: L{Data<escript.Data>}
649         """
650         r=self.getSystem()[1]
651         if self.isUsingLumping():
652             return self.copyConstraint(r)
653         else:
654             return r
655    
656       @param name:     def applyOperator(self,u=None):
657       """       """
658       if self.hasCoefficient(name):       applies the operator of the PDE to a given u or the solution of PDE if u is not present.
659          if self.COEFFICIENTS[name].isAlteringOperator(): self.__rebuildOperator()  
660          if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__rebuildRightHandSide()       @param u: argument of the operator. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
661                   the current solution is used.
662         @type u: L{Data<escript.Data>} or None
663         @return: image of u
664         @rtype: L{Data<escript.Data>}
665         """
666         if u==None:
667            return self.getOperator()*self.getSolution()
668       else:       else:
669          raise ValueError,"unknown coefficient %s requested"%name          return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
670    
671     # ===== debug ==============================================================     def getResidual(self,u=None):
672     def setDebugOn(self):       """
673         """       return the residual of u or the current solution if u is not present.
        """  
        self.__debug=not None  
674    
675     def setDebugOff(self):       @param u: argument in the residual calculation. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
676         """                 the current solution is used.
677         """       @type u: L{Data<escript.Data>} or None
678         self.__debug=None       @return: residual of u
679         @rtype: L{Data<escript.Data>}
680         """
681         return self.applyOperator(u)-self.getRightHandSide()
682    
683     def debug(self):     def checkSymmetry(self,verbose=True):
684          """
685          test the PDE for symmetry.
686    
687          @param verbose: if equal to True or not present a report on coefficients which are breaking the symmetry is printed.
688          @type verbose: C{bool}
689          @return:  True if the PDE is symmetric.
690          @rtype: L{Data<escript.Data>}
691          @note: This is a very expensive operation. It should be used for degugging only! The symmetry flag is not altered.
692          """
693          verbose=verbose or self.__debug
694          out=True
695          if self.getNumSolutions()!=self.getNumEquations():
696             if verbose: print "non-symmetric PDE because of different number of equations and solutions"
697             out=False
698          else:
699             A=self.getCoefficientOfGeneralPDE("A")
700             if not A.isEmpty():
701                tol=util.Lsup(A)*self.SMALL_TOLERANCE
702                if self.getNumSolutions()>1:
703                   for i in range(self.getNumEquations()):
704                      for j in range(self.getDim()):
705                         for k in range(self.getNumSolutions()):
706                            for l in range(self.getDim()):
707                                if util.Lsup(A[i,j,k,l]-A[k,l,i,j])>tol:
708                                   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)
709                                   out=False
710                else:
711                   for j in range(self.getDim()):
712                      for l in range(self.getDim()):
713                         if util.Lsup(A[j,l]-A[l,j])>tol:
714                            if verbose: print "non-symmetric PDE because A[%d,%d]!=A[%d,%d]"%(j,l,l,j)
715                            out=False
716             B=self.getCoefficientOfGeneralPDE("B")
717             C=self.getCoefficientOfGeneralPDE("C")
718             if B.isEmpty() and not C.isEmpty():
719                if verbose: print "non-symmetric PDE because B is not present but C is"
720                out=False
721             elif not B.isEmpty() and C.isEmpty():
722                if verbose: print "non-symmetric PDE because C is not present but B is"
723                out=False
724             elif not B.isEmpty() and not C.isEmpty():
725                tol=(util.Lsup(B)+util.Lsup(C))*self.SMALL_TOLERANCE/2.
726                if self.getNumSolutions()>1:
727                   for i in range(self.getNumEquations()):
728                       for j in range(self.getDim()):
729                          for k in range(self.getNumSolutions()):
730                             if util.Lsup(B[i,j,k]-C[k,i,j])>tol:
731                                  if verbose: print "non-symmetric PDE because B[%d,%d,%d]!=C[%d,%d,%d]"%(i,j,k,k,i,j)
732                                  out=False
733                else:
734                   for j in range(self.getDim()):
735                      if util.Lsup(B[j]-C[j])>tol:
736                         if verbose: print "non-symmetric PDE because B[%d]!=C[%d]"%(j,j)
737                         out=False
738             if self.getNumSolutions()>1:
739               D=self.getCoefficientOfGeneralPDE("D")
740               if not D.isEmpty():
741                 tol=util.Lsup(D)*self.SMALL_TOLERANCE
742                 for i in range(self.getNumEquations()):
743                    for k in range(self.getNumSolutions()):
744                      if util.Lsup(D[i,k]-D[k,i])>tol:
745                          if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)
746                          out=False
747               d=self.getCoefficientOfGeneralPDE("d")
748               if not d.isEmpty():
749                 tol=util.Lsup(d)*self.SMALL_TOLERANCE
750                 for i in range(self.getNumEquations()):
751                    for k in range(self.getNumSolutions()):
752                      if util.Lsup(d[i,k]-d[k,i])>tol:
753                          if verbose: print "non-symmetric PDE because d[%d,%d]!=d[%d,%d]"%(i,k,k,i)
754                          out=False
755               d_contact=self.getCoefficientOfGeneralPDE("d_contact")
756               if not d_contact.isEmpty():
757                 tol=util.Lsup(d_contact)*self.SMALL_TOLERANCE
758                 for i in range(self.getNumEquations()):
759                    for k in range(self.getNumSolutions()):
760                      if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
761                          if verbose: print "non-symmetric PDE because d_contact[%d,%d]!=d_contact[%d,%d]"%(i,k,k,i)
762                          out=False
763          return out
764    
765       def getSolution(self,**options):
766         """         """
767         returns true if the PDE is in the debug mode         returns the solution of the PDE. If the solution is not valid the PDE is solved.
768    
769           @return: the solution
770           @rtype: L{Data<escript.Data>}
771           @param options: solver options
772           @keyword verbose: True to get some information during PDE solution
773           @type verbose: C{bool}
774           @keyword reordering: reordering scheme to be used during elimination. Allowed values are
775                                L{NO_REORDERING}, L{MINIMUM_FILL_IN}, L{NESTED_DISSECTION}
776           @keyword iter_max: maximum number of iteration steps allowed.
777           @keyword drop_tolerance: threshold for drupping in L{ILUT}
778           @keyword drop_storage: maximum of allowed memory in L{ILUT}
779           @keyword truncation: maximum number of residuals in L{GMRES}
780           @keyword restart: restart cycle length in L{GMRES}
781         """         """
782         return self.__debug         if not self.__solution_isValid:
783              mat,f=self.getSystem()
784              if self.isUsingLumping():
785                 self.__solution=self.copyConstraint(f*mat)
786              else:
787                 options[self.__TOLERANCE_KEY]=self.getTolerance()
788                 options[self.__METHOD_KEY]=self.getSolverMethod()[0]
789                 options[self.__PRECONDITIONER_KEY]=self.getSolverMethod()[1]
790                 options[self.__PACKAGE_KEY]=self.getSolverPackage()
791                 options[self.__SYMMETRY_KEY]=self.isSymmetric()
792                 self.trace("PDE is resolved.")
793                 self.trace("solver options: %s"%str(options))
794                 self.__solution=mat.solve(f,options)
795              self.__solution_isValid=True
796           return self.__solution
797    
798     #===== Lumping ===========================     def getFlux(self,u=None):
799     def setLumpingOn(self):       """
800        """       returns the flux M{J} for a given M{u}
       indicates to use matrix lumping  
       """  
       if not self.isUsingLumping():  
          if self.debug() : print "PDE Debug: lumping is set on"  
          self.__rebuildOperator()  
          self.__lumping=True  
801    
802     def setLumpingOff(self):       M{J[i,j]=A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]u[k]-X[i,j]}
       """  
       switches off matrix lumping  
       """  
       if self.isUsingLumping():  
          if self.debug() : print "PDE Debug: lumping is set off"  
          self.__rebuildOperator()  
          self.__lumping=False  
803    
804     def setLumping(self,flag=False):       or
       """  
       set the matrix lumping flag to flag  
       """  
       if flag:  
          self.setLumpingOn()  
       else:  
          self.setLumpingOff()  
805    
806     def isUsingLumping(self):       M{J[j]=A[i,j]*grad(u)[l]+B[j]u-X[j]}
       """  
         
       """  
       return self.__lumping  
807    
808     #============ method business =========================================================       @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.
809     def setSolverMethod(self,solver=util.DEFAULT_METHOD):       @type u: L{Data<escript.Data>} or None
810         @return: flux
811         @rtype: L{Data<escript.Data>}
812         """
813         if u==None: u=self.getSolution()
814         return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u))+util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u)-util.self.getCoefficientOfGeneralPDE("X")
815       # =============================================================================
816       #   solver settings:
817       # =============================================================================
818       def setSolverMethod(self,solver=None,preconditioner=None):
819         """         """
820         sets a new solver         sets a new solver
821         """  
822         if not solver==self.getSolverMethod():         @param solver: sets a new solver method.
823           @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}
824           @param preconditioner: sets a new solver method.
825           @type preconditioner: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}, L{RILU}
826           """
827           if solver==None: solve=self.DEFAULT
828           if preconditioner==None: preconditioner=self.DEFAULT
829           if not (solver,preconditioner)==self.getSolverMethod():
830             self.__solver_method=solver             self.__solver_method=solver
831             if self.debug() : print "PDE Debug: New solver is %s"%solver             self.__preconditioner=preconditioner
832             self.__checkMatrixType()             self.__checkMatrixType()
833               self.trace("New solver is %s"%self.getSolverMethodName())
834    
835       def getSolverMethodName(self):
836           """
837           returns the name of the solver currently used
838    
839           @return: the name of the solver currently used.
840           @rtype: C{string}
841           """
842    
843           m=self.getSolverMethod()
844           p=self.getSolverPackage()
845           method=""
846           if m[0]==self.DEFAULT: method="DEFAULT"
847           elif m[0]==self.DIRECT: method= "DIRECT"
848           elif m[0]==self.ITERATIVE: method= "ITERATIVE"
849           elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
850           elif m[0]==self.PCG: method= "PCG"
851           elif m[0]==self.CR: method= "CR"
852           elif m[0]==self.CGS: method= "CGS"
853           elif m[0]==self.BICGSTAB: method= "BICGSTAB"
854           elif m[0]==self.SSOR: method= "SSOR"
855           elif m[0]==self.GMRES: method= "GMRES"
856           elif m[0]==self.PRES20: method= "PRES20"
857           elif m[0]==self.LUMPING: method= "LUMPING"
858           elif m[0]==self.AMG: method= "AMG"
859           if m[1]==self.DEFAULT: method+="+DEFAULT"
860           elif m[1]==self.JACOBI: method+= "+JACOBI"
861           elif m[1]==self.ILU0: method+= "+ILU0"
862           elif m[1]==self.ILUT: method+= "+ILUT"
863           elif m[1]==self.SSOR: method+= "+SSOR"
864           elif m[1]==self.AMG: method+= "+AMG"
865           elif m[1]==self.RILU: method+= "+RILU"
866           if p==self.DEFAULT: package="DEFAULT"
867           elif p==self.PASO: package= "PASO"
868           elif p==self.MKL: package= "MKL"
869           elif p==self.SCSL: package= "SCSL"
870           elif p==self.UMFPACK: package= "UMFPACK"
871           else : method="unknown"
872           return "%s solver of %s package"%(method,package)
873    
874    
875     def getSolverMethod(self):     def getSolverMethod(self):
876         """         """
877         returns the solver method         returns the solver method
878    
879           @return: the solver method currently be used.
880           @rtype: C{int}
881         """         """
882         return self.__solver_method         return self.__solver_method,self.__preconditioner
883    
884       def setSolverPackage(self,package=None):
885           """
886           sets a new solver package
887    
888           @param package: sets a new solver method.
889           @type package: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMFPACK}
890           """
891           if package==None: package=self.DEFAULT
892           if not package==self.getSolverPackage():
893               self.__solver_package=package
894               self.__checkMatrixType()
895               self.trace("New solver is %s"%self.getSolverMethodName())
896    
897       def getSolverPackage(self):
898           """
899           returns the package of the solver
900    
901           @return: the solver package currently being used.
902           @rtype: C{int}
903           """
904           return self.__solver_package
905    
906       def isUsingLumping(self):
907          """
908          checks if matrix lumping is used a solver method
909    
910          @return: True is lumping is currently used a solver method.
911          @rtype: C{bool}
912          """
913          return self.getSolverMethod()[0]==self.LUMPING
914    
    #============ tolerance business =========================================================  
915     def setTolerance(self,tol=1.e-8):     def setTolerance(self,tol=1.e-8):
916         """         """
917         resets the tolerance to tol.         resets the tolerance for the solver method to tol where for an appropriate norm M{|.|}
918    
919           M{|L{getResidual}()|<tol*|L{getRightHandSide}()|}
920    
921           defines the stopping criterion.
922    
923           @param tol: new tolerance for the solver. If the tol is lower then the current tolerence
924                       the system will be resolved.
925           @type tol: positive C{float}
926           @raise ValueError: if tolerance is not positive.
927         """         """
928         if not tol>0:         if not tol>0:
929             raise ValueException,"Tolerance as to be positive"             raise ValueError,"Tolerance as to be positive"
930         if tol<self.getTolerance(): self.__rebuildSolution()         if tol<self.getTolerance(): self.__invalidateSolution()
931         if self.debug() : print "PDE Debug: New tolerance %e",tol         self.trace("New tolerance %e"%tol)
932         self.__tolerance=tol         self.__tolerance=tol
933         return         return
934    
935     def getTolerance(self):     def getTolerance(self):
936         """         """
937         returns the tolerance set for the solution         returns the tolerance set for the solution
938    
939           @return: tolerance currently used.
940           @rtype: C{float}
941         """         """
942         return self.__tolerance         return self.__tolerance
943    
944     #===== symmetry  flag ==========================     # =============================================================================
945       #    symmetry  flag:
946       # =============================================================================
947     def isSymmetric(self):     def isSymmetric(self):
948        """        """
949        returns true is the operator is considered to be symmetric        checks if symmetry is indicated.
950    
951          @return: True is a symmetric PDE is indicated, otherwise False is returned
952          @rtype: C{bool}
953        """        """
954        return self.__sym        return self.__sym
955    
956     def setSymmetryOn(self):     def setSymmetryOn(self):
957        """        """
958        sets the symmetry flag to true        sets the symmetry flag.
959        """        """
960        if not self.isSymmetric():        if not self.isSymmetric():
961           if self.debug() : print "PDE Debug: Operator is set to be symmetric"           self.trace("PDE is set to be symmetric")
962           self.__sym=True           self.__sym=True
963           self.__checkMatrixType()           self.__checkMatrixType()
964    
965     def setSymmetryOff(self):     def setSymmetryOff(self):
966        """        """
967        sets the symmetry flag to false        removes the symmetry flag.
968        """        """
969        if self.isSymmetric():        if self.isSymmetric():
970           if self.debug() : print "PDE Debug: Operator is set to be unsymmetric"           self.trace("PDE is set to be unsymmetric")
971           self.__sym=False           self.__sym=False
972           self.__checkMatrixType()           self.__checkMatrixType()
973    
974     def setSymmetryTo(self,flag=False):     def setSymmetryTo(self,flag=False):
975       """        """
976       sets the symmetry flag to flag        sets the symmetry flag to flag
977    
978       @param flag:        @param flag: If flag, the symmetry flag is set otherwise the symmetry flag is released.
979       """        @type flag: C{bool}
980       if flag:        """
981          self.setSymmetryOn()        if flag:
982       else:           self.setSymmetryOn()
983          self.setSymmetryOff()        else:
984             self.setSymmetryOff()
985    
986     #===== order reduction ==========================     # =============================================================================
987       # function space handling for the equation as well as the solution
988       # =============================================================================
989     def setReducedOrderOn(self):     def setReducedOrderOn(self):
990       """       """
991       switches to on reduced order       switches on reduced order for solution and equation representation
992    
993         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
994       """       """
995       self.setReducedOrderForSolutionOn()       self.setReducedOrderForSolutionOn()
996       self.setReducedOrderForEquationOn()       self.setReducedOrderForEquationOn()
997    
998     def setReducedOrderOff(self):     def setReducedOrderOff(self):
999       """       """
1000       switches to full order       switches off reduced order for solution and equation representation
1001    
1002         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1003       """       """
1004       self.setReducedOrderForSolutionOff()       self.setReducedOrderForSolutionOff()
1005       self.setReducedOrderForEquationOff()       self.setReducedOrderForEquationOff()
1006    
1007     def setReducedOrderTo(self,flag=False):     def setReducedOrderTo(self,flag=False):
1008       """       """
1009       sets order according to flag       sets order reduction for both solution and equation representation according to flag.
1010         @param flag: if flag is True, the order reduction is switched on for both  solution and equation representation, otherwise or
1011       @param flag:                    if flag is not present order reduction is switched off
1012         @type flag: C{bool}
1013         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1014       """       """
1015       self.setReducedOrderForSolutionTo(flag)       self.setReducedOrderForSolutionTo(flag)
1016       self.setReducedOrderForEquationTo(flag)       self.setReducedOrderForEquationTo(flag)
                                                                                                                                                             
1017    
1018     #===== order reduction solution ==========================  
1019     def setReducedOrderForSolutionOn(self):     def setReducedOrderForSolutionOn(self):
1020       """       """
1021       switches to reduced order to interpolate solution       switches on reduced order for solution representation
1022    
1023         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1024       """       """
1025       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_solution_order:
1026       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1027           if self.debug() : print "PDE Debug: Reduced order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1028           self.__column_function_space=new_fs           self.trace("Reduced order is used to solution representation.")
1029           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=True
1030             self.__resetSystem()
1031    
1032     def setReducedOrderForSolutionOff(self):     def setReducedOrderForSolutionOff(self):
1033       """       """
1034       switches to full order to interpolate solution       switches off reduced order for solution representation
1035    
1036         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1037       """       """
1038       new_fs=escript.Solution(self.getDomain())       if self.__reduce_solution_order:
1039       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1040           if self.debug() : print "PDE Debug: Full order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1041           self.__column_function_space=new_fs           self.trace("Full order is used to interpolate solution.")
1042           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=False
1043             self.__resetSystem()
1044    
1045     def setReducedOrderForSolutionTo(self,flag=False):     def setReducedOrderForSolutionTo(self,flag=False):
1046       """       """
1047       sets order for test functions according to flag       sets order for test functions according to flag
1048    
1049       @param flag:       @param flag: if flag is True, the order reduction is switched on for solution representation, otherwise or
1050                      if flag is not present order reduction is switched off
1051         @type flag: C{bool}
1052         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1053       """       """
1054       if flag:       if flag:
1055          self.setReducedOrderForSolutionOn()          self.setReducedOrderForSolutionOn()
1056       else:       else:
1057          self.setReducedOrderForSolutionOff()          self.setReducedOrderForSolutionOff()
1058                                                                                                                                                              
    #===== order reduction equation ==========================  
1059     def setReducedOrderForEquationOn(self):     def setReducedOrderForEquationOn(self):
1060       """       """
1061       switches to reduced order for test functions       switches on reduced order for equation representation
1062    
1063         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1064       """       """
1065       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_equation_order:
1066       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1067           if self.debug() : print "PDE Debug: Reduced order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1068           self.__row_function_space=new_fs           self.trace("Reduced order is used for test functions.")
1069           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=True
1070             self.__resetSystem()
1071    
1072     def setReducedOrderForEquationOff(self):     def setReducedOrderForEquationOff(self):
1073       """       """
1074       switches to full order for test functions       switches off reduced order for equation representation
1075    
1076         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1077       """       """
1078       new_fs=escript.Solution(self.getDomain())       if self.__reduce_equation_order:
1079       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1080           if self.debug() : print "PDE Debug: Full order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1081           self.__row_function_space=new_fs           self.trace("Full order is used for test functions.")
1082           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=False
1083             self.__resetSystem()
1084    
1085     def setReducedOrderForEquationTo(self,flag=False):     def setReducedOrderForEquationTo(self,flag=False):
1086       """       """
1087       sets order for test functions according to flag       sets order for test functions according to flag
1088    
1089       @param flag:       @param flag: if flag is True, the order reduction is switched on for equation representation, otherwise or
1090                      if flag is not present order reduction is switched off
1091         @type flag: C{bool}
1092         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1093       """       """
1094       if flag:       if flag:
1095          self.setReducedOrderForEquationOn()          self.setReducedOrderForEquationOn()
1096       else:       else:
1097          self.setReducedOrderForEquationOff()          self.setReducedOrderForEquationOff()
1098                                                                                                                                                              
1099     # ==== initialization =====================================================================     # =============================================================================
1100       # private method:
1101       # =============================================================================
1102       def __checkMatrixType(self):
1103         """
1104         reassess the matrix type and, if a new matrix is needed, resets the system.
1105         """
1106         new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod()[0],self.getSolverPackage(),self.isSymmetric())
1107         if not new_matrix_type==self.__matrix_type:
1108             self.trace("Matrix type is now %d."%new_matrix_type)
1109             self.__matrix_type=new_matrix_type
1110             self.__resetSystem()
1111       #
1112       #   rebuild switches :
1113       #
1114       def __invalidateSolution(self):
1115           """
1116           indicates the PDE has to be resolved if the solution is requested
1117           """
1118           if self.__solution_isValid: self.trace("PDE has to be resolved.")
1119           self.__solution_isValid=False
1120    
1121       def __invalidateOperator(self):
1122           """
1123           indicates the operator has to be rebuilt next time it is used
1124           """
1125           if self.__operator_is_Valid: self.trace("Operator has to be rebuilt.")
1126           self.__invalidateSolution()
1127           self.__operator_is_Valid=False
1128    
1129       def __invalidateRightHandSide(self):
1130           """
1131           indicates the right hand side has to be rebuild next time it is used
1132           """
1133           if self.__righthandside_isValid: self.trace("Right hand side has to be rebuilt.")
1134           self.__invalidateSolution()
1135           self.__righthandside_isValid=False
1136    
1137       def __invalidateSystem(self):
1138           """
1139           annonced that everthing has to be rebuild:
1140           """
1141           if self.__righthandside_isValid: self.trace("System has to be rebuilt.")
1142           self.__invalidateSolution()
1143           self.__invalidateOperator()
1144           self.__invalidateRightHandSide()
1145    
1146       def __resetSystem(self):
1147           """
1148           annonced that everthing has to be rebuild:
1149           """
1150           self.trace("New System is built from scratch.")
1151           self.__operator=escript.Operator()
1152           self.__operator_is_Valid=False
1153           self.__righthandside=escript.Data()
1154           self.__righthandside_isValid=False
1155           self.__solution=escript.Data()
1156           self.__solution_isValid=False
1157       #
1158       #    system initialization:
1159       #
1160     def __getNewOperator(self):     def __getNewOperator(self):
1161         """         """
1162           returns an instance of a new operator
1163         """         """
1164           self.trace("New operator is allocated.")
1165         return self.getDomain().newOperator( \         return self.getDomain().newOperator( \
1166                             self.getNumEquations(), \                             self.getNumEquations(), \
1167                             self.getFunctionSpaceForEquation(), \                             self.getFunctionSpaceForEquation(), \
# Line 565  class LinearPDE: Line 1169  class LinearPDE:
1169                             self.getFunctionSpaceForSolution(), \                             self.getFunctionSpaceForSolution(), \
1170                             self.__matrix_type)                             self.__matrix_type)
1171    
1172     def __makeFreshRightHandSide(self):     def __getNewRightHandSide(self):
1173         """         """
1174           returns an instance of a new right hand side
1175         """         """
1176         if self.debug() : print "PDE Debug: New right hand side allocated"         self.trace("New right hand side is allocated.")
1177         if self.getNumEquations()>1:         if self.getNumEquations()>1:
1178             self.__righthandside=escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)             return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)
1179         else:         else:
1180             self.__righthandside=escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)             return escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)
        return self.__righthandside  
1181    
1182     def __getNewSolution(self):     def __getNewSolution(self):
1183         """         """
1184           returns an instance of a new solution
1185         """         """
1186         if self.debug() : print "PDE Debug: New right hand side allocated"         self.trace("New solution is allocated.")
1187         if self.getNumSolutions()>1:         if self.getNumSolutions()>1:
1188             return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)             return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)
1189         else:         else:
1190             return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)             return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)
1191    
1192       def __makeFreshSolution(self):
1193           """
1194           makes sure that the solution is instantiated and returns it initialized by zeros
1195           """
1196           if self.__solution.isEmpty():
1197               self.__solution=self.__getNewSolution()
1198           else:
1199               self.__solution*=0
1200               self.trace("Solution is reset to zero.")
1201           return self.__solution
1202    
1203       def __makeFreshRightHandSide(self):
1204           """
1205           makes sure that the right hand side is instantiated and returns it initialized by zeros
1206           """
1207           if self.__righthandside.isEmpty():
1208               self.__righthandside=self.__getNewRightHandSide()
1209           else:
1210               self.__righthandside*=0
1211               self.trace("Right hand side is reset to zero.")
1212           return self.__righthandside
1213    
1214     def __makeFreshOperator(self):     def __makeFreshOperator(self):
1215         """         """
1216           makes sure that the operator is instantiated and returns it initialized by zeros
1217         """         """
1218         if self.__operator.isEmpty():         if self.__operator.isEmpty():
1219             self.__operator=self.__getNewOperator()             self.__operator=self.__getNewOperator()
            if self.debug() : print "PDE Debug: New operator allocated"  
1220         else:         else:
1221             self.__operator.setValue(0.)             self.__operator.resetValues()
1222             self.__operator.resetSolver()             self.trace("Operator reset to zero")
            if self.debug() : print "PDE Debug: Operator reset to zero"  
1223         return self.__operator         return self.__operator
1224    
1225     #============ some serivice functions  =====================================================     def __applyConstraint(self):
1226     def getDomain(self):         """
1227           applies the constraints defined by q and r to the system
1228           """
1229           if not self.isUsingLumping():
1230              q=self.getCoefficientOfGeneralPDE("q")
1231              r=self.getCoefficientOfGeneralPDE("r")
1232              if not q.isEmpty() and not self.__operator.isEmpty():
1233                 # q is the row and column mask to indicate where constraints are set:
1234                 row_q=escript.Data(q,self.getFunctionSpaceForEquation())
1235                 col_q=escript.Data(q,self.getFunctionSpaceForSolution())
1236                 u=self.__getNewSolution()
1237                 if r.isEmpty():
1238                    r_s=self.__getNewSolution()
1239                 else:
1240                    r_s=escript.Data(r,self.getFunctionSpaceForSolution())
1241                 u.copyWithMask(r_s,col_q)
1242                 if not self.__righthandside.isEmpty():
1243                    self.__righthandside-=self.__operator*u
1244                    self.__righthandside=self.copyConstraint(self.__righthandside)
1245                 self.__operator.nullifyRowsAndCols(row_q,col_q,1.)
1246       # =============================================================================
1247       # function giving access to coefficients of the general PDE:
1248       # =============================================================================
1249       def getCoefficientOfGeneralPDE(self,name):
1250         """
1251         return the value of the coefficient name of the general PDE.
1252    
1253         @note: This method is called by the assembling routine it can be overwritten
1254               to map coefficients of a particular PDE to the general PDE.
1255         @param name: name of the coefficient requested.
1256         @type name: C{string}
1257         @return: the value of the coefficient  name
1258         @rtype: L{Data<escript.Data>}
1259         @raise IllegalCoefficient: if name is not one of coefficients
1260                      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}.
1261       """       """
1262       returns the domain of the PDE       if self.hasCoefficientOfGeneralPDE(name):
1263            return self.getCoefficient(name)
1264         else:
1265            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1266    
1267       def hasCoefficientOfGeneralPDE(self,name):
1268       """       """
1269       return self.__domain       checks if name is a the name of a coefficient of the general PDE.
1270    
1271         @param name: name of the coefficient enquired.
1272         @type name: C{string}
1273         @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1274         @rtype: C{bool}
1275    
    def getDim(self):  
1276       """       """
1277       returns the spatial dimension of the PDE       return self.__COEFFICIENTS_OF_GENEARL_PDE.has_key(name)
1278    
1279       def createCoefficientOfGeneralPDE(self,name):
1280       """       """
1281       return self.getDomain().getDim()       returns a new instance of a coefficient for coefficient name of the general PDE
1282    
1283     def getNumEquations(self):       @param name: name of the coefficient requested.
1284         @type name: C{string}
1285         @return: a coefficient name initialized to 0.
1286         @rtype: L{Data<escript.Data>}
1287         @raise IllegalCoefficient: if name is not one of coefficients
1288                      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}.
1289       """       """
1290       returns the number of equations       if self.hasCoefficientOfGeneralPDE(name):
1291            return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
1292         else:
1293            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1294    
1295       def getFunctionSpaceForCoefficientOfGeneralPDE(self,name):
1296       """       """
1297       if self.__numEquations>0:       return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name of the general PDE
1298           return self.__numEquations  
1299         @param name: name of the coefficient enquired.
1300         @type name: C{string}
1301         @return: the function space to be used for coefficient name
1302         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1303         @raise IllegalCoefficient: if name is not one of coefficients
1304                      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}.
1305         """
1306         if self.hasCoefficientOfGeneralPDE(name):
1307            return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
1308       else:       else:
1309           raise ValueError,"Number of equations is undefined. Please specify argument numEquations."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1310    
1311     def getNumSolutions(self):     def getShapeOfCoefficientOfGeneralPDE(self,name):
1312       """       """
1313       returns the number of unknowns       return the shape of the coefficient name of the general PDE
1314    
1315         @param name: name of the coefficient enquired.
1316         @type name: C{string}
1317         @return: the shape of the coefficient name
1318         @rtype: C{tuple} of C{int}
1319         @raise IllegalCoefficient: if name is not one of coefficients
1320                      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}.
1321       """       """
1322       if self.__numSolutions>0:       if self.hasCoefficientOfGeneralPDE(name):
1323          return self.__numSolutions          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1324       else:       else:
1325          raise ValueError,"Number of solution is undefined. Please specify argument numSolutions."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1326    
1327       # =============================================================================
1328       # functions giving access to coefficients of a particular PDE implementation:
1329       # =============================================================================
1330       def getCoefficient(self,name):
1331         """
1332         returns the value of the coefficient name
1333    
1334     def checkSymmetry(self,verbose=True):       @param name: name of the coefficient requested.
1335        """       @type name: C{string}
1336        returns if the Operator is symmetric. This is a very expensive operation!!! The symmetry flag is not altered.       @return: the value of the coefficient name
1337        """       @rtype: L{Data<escript.Data>}
1338        verbose=verbose or self.debug()       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1339        out=True       """
1340        if self.getNumSolutions()!=self.getNumEquations():       if self.hasCoefficient(name):
1341           if verbose: print "non-symmetric PDE because of different number of equations and solutions"           return self.COEFFICIENTS[name].getValue()
1342           out=False       else:
1343        else:          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
          A=self.getCoefficientOfPDE("A")  
          if not A.isEmpty():  
             tol=util.Lsup(A)*self.TOL  
             if self.getNumSolutions()>1:  
                for i in range(self.getNumEquations()):  
                   for j in range(self.getDim()):  
                      for k in range(self.getNumSolutions()):  
                         for l in range(self.getDim()):  
                             if util.Lsup(A[i,j,k,l]-A[k,l,i,j])>tol:  
                                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)  
                                out=False  
             else:  
                for j in range(self.getDim()):  
                   for l in range(self.getDim()):  
                      if util.Lsup(A[j,l]-A[l,j])>tol:  
                         if verbose: print "non-symmetric PDE because A[%d,%d]!=A[%d,%d]"%(j,l,l,j)  
                         out=False  
          B=self.getCoefficientOfPDE("B")  
          C=self.getCoefficientOfPDE("C")  
          if B.isEmpty() and not C.isEmpty():  
             if verbose: print "non-symmetric PDE because B is not present but C is"  
             out=False  
          elif not B.isEmpty() and C.isEmpty():  
             if verbose: print "non-symmetric PDE because C is not present but B is"  
             out=False  
          elif not B.isEmpty() and not C.isEmpty():  
             tol=(util.Lsup(B)+util.Lsup(C))*self.TOL/2.  
             if self.getNumSolutions()>1:  
                for i in range(self.getNumEquations()):  
                    for j in range(self.getDim()):  
                       for k in range(self.getNumSolutions()):  
                          if util.Lsup(B[i,j,k]-C[k,i,j])>tol:  
                               if verbose: print "non-symmetric PDE because B[%d,%d,%d]!=C[%d,%d,%d]"%(i,j,k,k,i,j)  
                               out=False  
             else:  
                for j in range(self.getDim()):  
                   if util.Lsup(B[j]-C[j])>tol:  
                      if verbose: print "non-symmetric PDE because B[%d]!=C[%d]"%(j,j)  
                      out=False  
          if self.getNumSolutions()>1:  
            D=self.getCoefficientOfPDE("D")  
            if not D.isEmpty():  
              tol=util.Lsup(D)*self.TOL  
              for i in range(self.getNumEquations()):  
                 for k in range(self.getNumSolutions()):  
                   if util.Lsup(D[i,k]-D[k,i])>tol:  
                       if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)  
                       out=False  
               
       return out  
1344    
1345     def getFlux(self,u):     def hasCoefficient(self,name):
1346         """       """
1347         returns the flux J_ij for a given u       return True if name is the name of a coefficient
1348    
1349         \f[       @param name: name of the coefficient enquired.
1350         J_ij=A_{ijkl}u_{k,l}+B_{ijk}u_k-X_{ij}       @type name: C{string}
1351         \f]       @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1352         @rtype: C{bool}
1353         """
1354         return self.COEFFICIENTS.has_key(name)
1355    
1356         @param u: argument of the operator     def createCoefficient(self, name):
1357         """       """
1358         raise SystemError,"getFlux is not implemented yet"       create a L{Data<escript.Data>} object corresponding to coefficient name
        return None  
1359    
1360     def applyOperator(self,u):       @return: a coefficient name initialized to 0.
1361         """       @rtype: L{Data<escript.Data>}
1362         applies the operator of the PDE to a given solution u in weak from       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1363         """
1364         if self.hasCoefficient(name):
1365            return escript.Data(0.,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))
1366         else:
1367            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1368    
1369         @param u: argument of the operator     def getFunctionSpaceForCoefficient(self,name):
1370         """       """
1371         return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())       return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name
                                                                                                                                                             
    def getResidual(self,u):  
        """  
        return the residual of u in the weak from  
1372    
1373         @param u:       @param name: name of the coefficient enquired.
1374         """       @type name: C{string}
1375         return self.applyOperator(u)-self.getRightHandSide()       @return: the function space to be used for coefficient name
1376         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1377         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1378         """
1379         if self.hasCoefficient(name):
1380            return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())
1381         else:
1382            raise ValueError,"unknown coefficient %s requested"%name
1383       def getShapeOfCoefficient(self,name):
1384         """
1385         return the shape of the coefficient name
1386    
1387         @param name: name of the coefficient enquired.
1388         @type name: C{string}
1389         @return: the shape of the coefficient name
1390         @rtype: C{tuple} of C{int}
1391         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1392         """
1393         if self.hasCoefficient(name):
1394            return self.COEFFICIENTS[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1395         else:
1396            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1397    
1398       def resetCoefficients(self):
1399         """
1400         resets all coefficients to there default values.
1401         """
1402         for i in self.COEFFICIENTS.iterkeys():
1403             self.COEFFICIENTS[i].resetValue()
1404    
1405       def alteredCoefficient(self,name):
1406         """
1407         announce that coefficient name has been changed
1408    
1409         @param name: name of the coefficient enquired.
1410         @type name: C{string}
1411         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1412         @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.
1413         """
1414         if self.hasCoefficient(name):
1415            self.trace("Coefficient %s has been altered."%name)
1416            if not ((name=="q" or name=="r") and self.isUsingLumping()):
1417               if self.COEFFICIENTS[name].isAlteringOperator(): self.__invalidateOperator()
1418               if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__invalidateRightHandSide()
1419         else:
1420            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1421    
1422       def copyConstraint(self,u):
1423          """
1424          copies the constraint into u and returns u.
1425    
1426          @param u: a function of rank 0 is a single PDE is solved and of shape (numSolution,) for a system of PDEs
1427          @type u: L{Data<escript.Data>}
1428          @return: the input u modified by the constraints.
1429          @rtype: L{Data<escript.Data>}
1430          @warning: u is altered if it has the appropriate L{FunctionSpace<escript.FunctionSpace>}
1431          """
1432          q=self.getCoefficientOfGeneralPDE("q")
1433          r=self.getCoefficientOfGeneralPDE("r")
1434          if not q.isEmpty():
1435             if u.isEmpty(): u=escript.Data(0.,q.getShape(),q.getFunctionSpace())
1436             if r.isEmpty():
1437                 r=escript.Data(0,u.getShape(),u.getFunctionSpace())
1438             else:
1439                 r=escript.Data(r,u.getFunctionSpace())
1440             u.copyWithMask(r,escript.Data(q,u.getFunctionSpace()))
1441          return u
1442    
1443     def __setValue(self,**coefficients):     def setValue(self,**coefficients):
1444        """        """
1445        sets new values to coefficient        sets new values to coefficients
1446    
1447        @param coefficients:        @param coefficients: new values assigned to coefficients
1448          @keyword A: value for coefficient A.
1449          @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1450          @keyword B: value for coefficient B
1451          @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1452          @keyword C: value for coefficient C
1453          @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1454          @keyword D: value for coefficient D
1455          @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1456          @keyword X: value for coefficient X
1457          @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1458          @keyword Y: value for coefficient Y
1459          @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1460          @keyword d: value for coefficient d
1461          @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1462          @keyword y: value for coefficient y
1463          @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1464          @keyword d_contact: value for coefficient d_contact
1465          @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1466                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1467          @keyword y_contact: value for coefficient y_contact
1468          @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1469                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1470          @keyword r: values prescribed to the solution at the locations of constraints
1471          @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1472                   depending of reduced order is used for the solution.
1473          @keyword q: mask for location of constraints
1474          @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1475                   depending of reduced order is used for the representation of the equation.
1476          @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1477        """        """
1478        # check if the coefficients are  legal:        # check if the coefficients are  legal:
1479        for i in coefficients.iterkeys():        for i in coefficients.iterkeys():
1480           if not self.hasCoefficient(i):           if not self.hasCoefficient(i):
1481              raise ValueError,"Attempt to set unknown coefficient %s"%i              raise IllegalCoefficient,"Attempt to set unknown coefficient %s"%i
1482        # if the number of unknowns or equations is still unknown we try to estimate them:        # if the number of unknowns or equations is still unknown we try to estimate them:
1483        if self.__numEquations<1 or self.__numSolutions<1:        if self.__numEquations==None or self.__numSolutions==None:
1484           for i,d in coefficients.iteritems():           for i,d in coefficients.iteritems():
1485              if hasattr(d,"shape"):              if hasattr(d,"shape"):
1486                  s=d.shape                  s=d.shape
# Line 739  class LinearPDE: Line 1490  class LinearPDE:
1490                  s=numarray.array(d).shape                  s=numarray.array(d).shape
1491              if s!=None:              if s!=None:
1492                  # get number of equations and number of unknowns:                  # get number of equations and number of unknowns:
1493                  res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(s,self.getDim())                  res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(self.getDomain(),s)
1494                  if res==None:                  if res==None:
1495                      raise ValueError,"Illegal shape %s of coefficient %s"%(s,i)                      raise IllegalCoefficientValue,"Illegal shape %s of coefficient %s"%(s,i)
1496                  else:                  else:
1497                      if self.__numEquations<1: self.__numEquations=res[0]                      if self.__numEquations==None: self.__numEquations=res[0]
1498                      if self.__numSolutions<1: self.__numSolutions=res[1]                      if self.__numSolutions==None: self.__numSolutions=res[1]
1499        if self.__numEquations<1: raise ValueError,"unidententified number of equations"        if self.__numEquations==None: raise UndefinedPDEError,"unidententified number of equations"
1500        if self.__numSolutions<1: raise ValueError,"unidententified number of solutions"        if self.__numSolutions==None: raise UndefinedPDEError,"unidententified number of solutions"
1501        # now we check the shape of the coefficient if numEquations and numSolutions are set:        # now we check the shape of the coefficient if numEquations and numSolutions are set:
1502        for i,d in coefficients.iteritems():        for i,d in coefficients.iteritems():
1503          if d==None:          try:
1504               d2=escript.Data()             self.COEFFICIENTS[i].setValue(self.getDomain(),self.getNumEquations(),self.getNumSolutions(),self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1505          elif isinstance(d,escript.Data):          except IllegalCoefficientValue,m:
1506               if d.isEmpty():             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
                 d2=d  
              else:  
                 d2=escript.Data(d,self.getFunctionSpaceForCoefficient(i))  
         else:  
               d2=escript.Data(d,self.getFunctionSpaceForCoefficient(i))  
         if not d2.isEmpty():  
            if not self.getShapeOfCoefficient(i)==d2.getShape():  
                raise ValueError,"Expected shape for coefficient %s is %s but actual shape is %s."%(i,self.getShapeOfCoefficient(i),d2.getShape())  
         # overwrite new values:  
         if self.debug(): print "PDE Debug: Coefficient %s has been altered."%i  
         self.COEFFICIENTS[i].setValue(d2)  
1507          self.alteredCoefficient(i)          self.alteredCoefficient(i)
         
       # reset the HomogeneousConstraintFlag:  
       self.__setHomogeneousConstraintFlag()  
       if len(coefficients)>0 and not self.isUsingLumping() and not self.__homogeneous_constraint: self.__rebuildSystem()  
   
    def __setHomogeneousConstraintFlag(self):  
       """  
       checks if the constraints are homogeneous and sets self.__homogeneous_constraint accordingly.  
       """  
       self.__homogeneous_constraint=True  
       q=self.getCoefficientOfPDE("q")  
       r=self.getCoefficientOfPDE("r")  
       if not q.isEmpty() and not r.isEmpty():  
          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."  
   
   
    # ==== rebuild switches =====================================================================  
    def __rebuildSolution(self,deep=False):  
        """  
        indicates the PDE has to be reolved if the solution is requested  
        """  
        if self.__solution_isValid and self.debug() : print "PDE Debug: PDE has to be resolved."  
        self.__solution_isValid=False  
        if deep: self.__solution=escript.Data()  
   
   
    def __rebuildOperator(self,deep=False):  
        """  
        indicates the operator has to be rebuilt next time it is used  
        """  
        if self.__operator_isValid and self.debug() : print "PDE Debug: Operator has to be rebuilt."  
        self.__rebuildSolution(deep)  
        self.__operator_isValid=False  
        if deep: self.__operator=escript.Operator()  
   
    def __rebuildRightHandSide(self,deep=False):  
        """  
        indicates the right hand side has to be rebuild next time it is used  
        """  
        if self.__righthandside_isValid and self.debug() : print "PDE Debug: Right hand side has to be rebuilt."  
        self.__rebuildSolution(deep)  
        self.__righthandside_isValid=False  
        if deep: self.__righthandside=escript.Data()  
   
    def __rebuildSystem(self,deep=False):  
        """  
        annonced that all coefficient name has been changed  
        """  
        self.__rebuildSolution(deep)  
        self.__rebuildOperator(deep)  
        self.__rebuildRightHandSide(deep)  
     
    def __checkMatrixType(self):  
      """  
      reassess the matrix type and, if needed, initiates an operator rebuild  
      """  
      new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod(),self.isSymmetric())  
      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)  
   
    #============ assembling =======================================================  
    def __copyConstraint(self):  
       """  
       copies the constrint condition into u  
       """  
       if not self.__righthandside.isEmpty():  
          q=self.getCoefficientOfPDE("q")  
          r=self.getCoefficientOfPDE("r")  
          if not q.isEmpty():  
              if r.isEmpty():  
                 r2=escript.Data(0,self.__righthandside.getShape(),self.__righthandside.getFunctionSpace())  
              else:  
                 r2=escript.Data(r,self.__righthandside.getFunctionSpace())  
              self.__righthandside.copyWithMask(r2,escript.Data(q,self.__righthandside.getFunctionSpace()))  
1508    
1509     def __applyConstraint(self):        self.__altered_coefficients=True
1510         """        # check if the systrem is inhomogeneous:
1511         applies the constraints defined by q and r to the system        if len(coefficients)>0 and not self.isUsingLumping():
1512         """           q=self.getCoefficientOfGeneralPDE("q")
1513         q=self.getCoefficientOfPDE("q")           r=self.getCoefficientOfGeneralPDE("r")
1514         r=self.getCoefficientOfPDE("r")           homogeneous_constraint=True
1515         if not q.isEmpty() and not self.__operator.isEmpty():           if not q.isEmpty() and not r.isEmpty():
1516            # q is the row and column mask to indicate where constraints are set:               if util.Lsup(q*r)>0.:
1517            row_q=escript.Data(q,self.getFunctionSpaceForEquation())                 self.trace("Inhomogeneous constraint detected.")
1518            col_q=escript.Data(q,self.getFunctionSpaceForSolution())                 self.__invalidateSystem()
           u=self.__getNewSolution()  
           if r.isEmpty():  
              r_s=self.__getNewSolution()  
           else:  
              r_s=escript.Data(r,self.getFunctionSpaceForSolution())  
           u.copyWithMask(r_s,col_q)  
           if self.isUsingLumping():  
              self.__operator.copyWithMask(escript.Data(1,q.getShape(),self.getFunctionSpaceForEquation()),row_q)  
           else:  
              if not self.__righthandside.isEmpty(): self.__righthandside-=self.__operator*u  
              self.__operator.nullifyRowsAndCols(row_q,col_q,1.)  
1519    
1520     def getSystem(self):     def getSystem(self):
1521         """         """
1522         return the operator and right hand side of the PDE         return the operator and right hand side of the PDE
1523    
1524           @return: the discrete version of the PDE
1525           @rtype: C{tuple} of L{Operator,<escript.Operator>} and L{Data<escript.Data>}.
1526         """         """
1527         if not self.__operator_isValid or not self.__righthandside_isValid:         if not self.__operator_is_Valid or not self.__righthandside_isValid:
1528            if self.isUsingLumping():            if self.isUsingLumping():
1529                if not self.__operator_isValid:                if not self.__operator_is_Valid:
1530                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():
1531                         raise TypeError,"Lumped matrix requires same order for equations and unknowns"                        raise TypeError,"Lumped matrix requires same order for equations and unknowns"
1532                   if not self.getCoefficientOfPDE("A").isEmpty():                   if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1533                            raise Warning,"Lumped matrix does not allow coefficient A"                        raise ValueError,"coefficient A in lumped matrix may not be present."
1534                   if not self.getCoefficientOfPDE("B").isEmpty():                   if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1535                            raise Warning,"Lumped matrix does not allow coefficient B"                        raise ValueError,"coefficient A in lumped matrix may not be present."
1536                   if not self.getCoefficientOfPDE("C").isEmpty():                   if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1537                            raise Warning,"Lumped matrix does not allow coefficient C"                        raise ValueError,"coefficient A in lumped matrix may not be present."
1538                   if self.debug() : print "PDE Debug: New lumped operator is built."                   D=self.getCoefficientOfGeneralPDE("D")
1539                   mat=self.__getNewOperator()                   if not D.isEmpty():
1540                   self.getDomain().addPDEToSystem(mat,escript.Data(), \                       if self.getNumSolutions()>1:
1541                             self.getCoefficientOfPDE("A"), \                          #D_times_e=util.matrixmult(D,numarray.ones((self.getNumSolutions(),)))
1542                             self.getCoefficientOfPDE("B"), \                          D_times_e=util.matrix_mult(D,numarray.ones((self.getNumSolutions(),)))
1543                             self.getCoefficientOfPDE("C"), \                       else:
1544                             self.getCoefficientOfPDE("D"), \                          D_times_e=D
1545                             escript.Data(), \                   else:
1546                             escript.Data(), \                      D_times_e=escript.Data()
1547                             self.getCoefficientOfPDE("d"), \                   d=self.getCoefficientOfGeneralPDE("d")
1548                             escript.Data(),\                   if not d.isEmpty():
1549                             self.getCoefficientOfPDE("d_contact"), \                       if self.getNumSolutions()>1:
1550                             escript.Data())                          #d_times_e=util.matrixmult(d,numarray.ones((self.getNumSolutions(),)))
1551                   self.__operator=mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)                          d_times_e=util.matrix_mult(d,numarray.ones((self.getNumSolutions(),)))
1552                   self.__applyConstraint()                       else:
1553                   self.__operator_isValid=True                          d_times_e=d
1554                     else:
1555                        d_times_e=escript.Data()
1556                     d_contact=self.getCoefficientOfGeneralPDE("d_contact")
1557                     if not d_contact.isEmpty():
1558                         if self.getNumSolutions()>1:
1559                            d_contact_times_e=util.matrixmult(d_contact,numarray.ones((self.getNumSolutions(),)))
1560                         else:
1561                            d_contact_times_e=d_contact
1562                     else:
1563                        d_contact_times_e=escript.Data()
1564        
1565                     self.__operator=self.__getNewRightHandSide()
1566                     self.getDomain().addPDEToRHS(self.__operator, \
1567                                                  escript.Data(), \
1568                                                  D_times_e, \
1569                                                  d_times_e,\
1570                                                  d_contact_times_e)
1571                     self.__operator=1./self.__operator
1572                     self.trace("New lumped operator has been built.")
1573                     self.__operator_is_Valid=True
1574                if not self.__righthandside_isValid:                if not self.__righthandside_isValid:
                  if self.debug() : print "PDE Debug: New right hand side is built."  
1575                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1576                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1577                                 self.getCoefficientOfPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1578                                 self.getCoefficientOfPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1579                                 self.getCoefficientOfPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1580                   self.__copyConstraint()                   self.trace("New right hand side as been built.")
1581                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1582            else:            else:
1583               if not self.__operator_isValid and not self.__righthandside_isValid:               if not self.__operator_is_Valid and not self.__righthandside_isValid:
                  if self.debug() : print "PDE Debug: New system is built."  
1584                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \
1585                                 self.getCoefficientOfPDE("A"), \                                 self.getCoefficientOfGeneralPDE("A"), \
1586                                 self.getCoefficientOfPDE("B"), \                                 self.getCoefficientOfGeneralPDE("B"), \
1587                                 self.getCoefficientOfPDE("C"), \                                 self.getCoefficientOfGeneralPDE("C"), \
1588                                 self.getCoefficientOfPDE("D"), \                                 self.getCoefficientOfGeneralPDE("D"), \
1589                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1590                                 self.getCoefficientOfPDE("Y"), \                                 self.getCoefficientOfGeneralPDE("Y"), \
1591                                 self.getCoefficientOfPDE("d"), \                                 self.getCoefficientOfGeneralPDE("d"), \
1592                                 self.getCoefficientOfPDE("y"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1593                                 self.getCoefficientOfPDE("d_contact"), \                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1594                                 self.getCoefficientOfPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1595                   self.__applyConstraint()                   self.__applyConstraint()
1596                   self.__copyConstraint()                   self.__righthandside=self.copyConstraint(self.__righthandside)
1597                   self.__operator_isValid=True                   self.trace("New system has been built.")
1598                     self.__operator_is_Valid=True
1599                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1600               elif not self.__righthandside_isValid:               elif not self.__righthandside_isValid:
                  if self.debug() : print "PDE Debug: New right hand side is built."  
1601                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1602                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1603                                 self.getCoefficientOfPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1604                                 self.getCoefficientOfPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1605                                 self.getCoefficientOfPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1606                   self.__copyConstraint()                   self.__righthandside=self.copyConstraint(self.__righthandside)
1607                     self.trace("New right hand side has been built.")
1608                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1609               elif not self.__operator_isValid:               elif not self.__operator_is_Valid:
                  if self.debug() : print "PDE Debug: New operator is built."  
1610                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \
1611                              self.getCoefficientOfPDE("A"), \                              self.getCoefficientOfGeneralPDE("A"), \
1612                              self.getCoefficientOfPDE("B"), \                              self.getCoefficientOfGeneralPDE("B"), \
1613                              self.getCoefficientOfPDE("C"), \                              self.getCoefficientOfGeneralPDE("C"), \
1614                              self.getCoefficientOfPDE("D"), \                              self.getCoefficientOfGeneralPDE("D"), \
1615                              escript.Data(), \                              escript.Data(), \
1616                              escript.Data(), \                              escript.Data(), \
1617                              self.getCoefficientOfPDE("d"), \                              self.getCoefficientOfGeneralPDE("d"), \
1618                              escript.Data(),\                              escript.Data(),\
1619                              self.getCoefficientOfPDE("d_contact"), \                              self.getCoefficientOfGeneralPDE("d_contact"), \
1620                              escript.Data())                              escript.Data())
1621                   self.__applyConstraint()                   self.__applyConstraint()
1622                   self.__operator_isValid=True                   self.trace("New operator has been built.")
1623                     self.__operator_is_Valid=True
1624         return (self.__operator,self.__righthandside)         return (self.__operator,self.__righthandside)
    def getOperator(self):  
        """  
        returns the operator of the PDE  
        """  
        return self.getSystem()[0]  
1625    
    def getRightHandSide(self):  
        """  
        returns the right hand side of the PDE  
        """  
        return self.getSystem()[1]  
1626    
1627     def solve(self,**options):  class Poisson(LinearPDE):
1628        """     """
1629        solve the PDE     Class to define a Poisson equation problem, which is genear L{LinearPDE} of the form
1630    
1631        @param options:     M{-grad(grad(u)[j])[j] = f}
       """  
       mat,f=self.getSystem()  
       if self.isUsingLumping():  
          out=f/mat  
       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  
1632    
1633     def getSolution(self,**options):     with natural boundary conditons
        """  
        returns the solution of the PDE  
1634    
1635         @param options:     M{n[j]*grad(u)[j] = 0 }
        """  
        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  
1636    
1637       and constraints:
1638    
1639       M{u=0} where M{q>0}
1640    
1641  def ELMAN_RAMAGE(P):     """
      """   """  
      return (P-1.).wherePositive()*0.5*(1.-1./(P+1.e-15))  
 def SIMPLIFIED_BROOK_HUGHES(P):  
      """   """  
      c=(P-3.).whereNegative()  
      return P/6.*c+1./2.*(1.-c)  
1642    
1643  def HALF(P):     def __init__(self,domain,debug=False):
1644      """ """       """
1645      return escript.Scalar(0.5,P.getFunctionSpace())       initializes a new Poisson equation
1646    
1647         @param domain: domain of the PDE
1648         @type domain: L{Domain<escript.Domain>}
1649         @param debug: if True debug informations are printed.
1650    
1651         """
1652         super(Poisson, self).__init__(domain,1,1,debug)
1653         self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1654                              "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1655         self.setSymmetryOn()
1656    
1657       def setValue(self,**coefficients):
1658         """
1659         sets new values to coefficients
1660    
1661         @param coefficients: new values assigned to coefficients
1662         @keyword f: value for right hand side M{f}
1663         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1664         @keyword q: mask for location of constraints
1665         @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>}
1666                   depending of reduced order is used for the representation of the equation.
1667         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1668         """
1669         super(Poisson, self).setValue(**coefficients)
1670    
1671       def getCoefficientOfGeneralPDE(self,name):
1672         """
1673         return the value of the coefficient name of the general PDE
1674         @param name: name of the coefficient requested.
1675         @type name: C{string}
1676         @return: the value of the coefficient  name
1677         @rtype: L{Data<escript.Data>}
1678         @raise IllegalCoefficient: if name is not one of coefficients
1679                      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}.
1680         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1681         """
1682         if name == "A" :
1683             return escript.Data(util.kronecker(self.getDim()),escript.Function(self.getDomain()))
1684         elif name == "B" :
1685             return escript.Data()
1686         elif name == "C" :
1687             return escript.Data()
1688         elif name == "D" :
1689             return escript.Data()
1690         elif name == "X" :
1691             return escript.Data()
1692         elif name == "Y" :
1693             return self.getCoefficient("f")
1694         elif name == "d" :
1695             return escript.Data()
1696         elif name == "y" :
1697             return escript.Data()
1698         elif name == "d_contact" :
1699             return escript.Data()
1700         elif name == "y_contact" :
1701             return escript.Data()
1702         elif name == "r" :
1703             return escript.Data()
1704         elif name == "q" :
1705             return self.getCoefficient("q")
1706         else:
1707            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1708    
1709    class Helmholtz(LinearPDE):
1710       """
1711       Class to define a Helmhotz equation problem, which is genear L{LinearPDE} of the form
1712    
1713       M{S{omega}*u - grad(k*grad(u)[j])[j] = f}
1714    
1715       with natural boundary conditons
1716    
1717       M{k*n[j]*grad(u)[j] = g- S{alpha}u }
1718    
1719       and constraints:
1720    
1721       M{u=r} where M{q>0}
1722    
 class AdvectivePDE(LinearPDE):  
1723     """     """
    Class to handle a linear PDE dominated by advective terms:  
     
    class to define a linear PDE of the form  
1724    
1725     \f[     def __init__(self,domain,debug=False):
1726     -(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       """
1727     \f]       initializes a new Poisson equation
1728    
1729         @param domain: domain of the PDE
1730         @type domain: L{Domain<escript.Domain>}
1731         @param debug: if True debug informations are printed.
1732    
1733         """
1734         super(Helmholtz, self).__init__(domain,1,1,debug)
1735         self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1736                            "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1737                            "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1738                            "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1739                            "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1740                            "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1741                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1742         self.setSymmetryOn()
1743    
1744       def setValue(self,**coefficients):
1745         """
1746         sets new values to coefficients
1747    
1748         @param coefficients: new values assigned to coefficients
1749         @keyword omega: value for coefficient M{S{omega}}
1750         @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1751         @keyword k: value for coefficeint M{k}
1752         @type k: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1753         @keyword f: value for right hand side M{f}
1754         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1755         @keyword alpha: value for right hand side M{S{alpha}}
1756         @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1757         @keyword g: value for right hand side M{g}
1758         @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1759         @keyword r: prescribed values M{r} for the solution in constraints.
1760         @type r: 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         @keyword q: mask for location of constraints
1763         @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1764                   depending of reduced order is used for the representation of the equation.
1765         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1766         """
1767         super(Helmholtz, self).setValue(**coefficients)
1768    
1769       def getCoefficientOfGeneralPDE(self,name):
1770         """
1771         return the value of the coefficient name of the general PDE
1772    
1773         @param name: name of the coefficient requested.
1774         @type name: C{string}
1775         @return: the value of the coefficient  name
1776         @rtype: L{Data<escript.Data>}
1777         @raise IllegalCoefficient: if name is not one of coefficients
1778                      "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}.
1779         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1780         """
1781         if name == "A" :
1782             return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))*self.getCoefficient("k")
1783         elif name == "B" :
1784             return escript.Data()
1785         elif name == "C" :
1786             return escript.Data()
1787         elif name == "D" :
1788             return self.getCoefficient("omega")
1789         elif name == "X" :
1790             return escript.Data()
1791         elif name == "Y" :
1792             return self.getCoefficient("f")
1793         elif name == "d" :
1794             return self.getCoefficient("alpha")
1795         elif name == "y" :
1796             return self.getCoefficient("g")
1797         elif name == "d_contact" :
1798             return escript.Data()
1799         elif name == "y_contact" :
1800             return escript.Data()
1801         elif name == "r" :
1802             return self.getCoefficient("r")
1803         elif name == "q" :
1804             return self.getCoefficient("q")
1805         else:
1806            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1807    
1808     with boundary conditons:  class LameEquation(LinearPDE):
1809       """
1810       Class to define a Lame equation problem:
1811    
1812     \f[     M{-grad(S{mu}*(grad(u[i])[j]+grad(u[j])[i]))[j] - grad(S{lambda}*grad(u[k])[k])[j] = F_i -grad(S{sigma}[ij])[j] }
    n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i  
    \f]  
1813    
1814     and contact conditions     with natural boundary conditons:
1815    
1816     \f[     M{n[j]*(S{mu}*(grad(u[i])[j]+grad(u[j])[i]) + S{lambda}*grad(u[k])[k]) = f_i +n[j]*S{sigma}[ij] }
    n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d^{contact}_{ik}[u_k] = - n_j*X_{ij} + y^{contact}_{i}  
    \f]  
1817    
1818     and constraints:     and constraints:
1819    
1820     \f[     M{u[i]=r[i]} where M{q[i]>0}
1821     u_i=r_i \quad \mathrm{where} \quad q_i>0  
    \f]  
1822     """     """
1823     def __init__(self,domain,numEquations=0,numSolutions=0,xi=ELMAN_RAMAGE):  
1824        LinearPDE.__init__(self,domain,numEquations,numSolutions)     def __init__(self,domain,debug=False):
1825        self.__xi=xi        super(LameEquation, self).__init__(domain,\
1826                                             domain.getDim(),domain.getDim(),debug)
1827          self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
1828                              "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
1829                              "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1830                              "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
1831                              "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1832                              "r"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1833                              "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1834          self.setSymmetryOn()
1835    
1836       def setValues(self,**coefficients):
1837         """
1838         sets new values to coefficients
1839    
1840         @param coefficients: new values assigned to coefficients
1841         @keyword lame_mu: value for coefficient M{S{mu}}
1842         @type lame_mu: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1843         @keyword lame_lambda: value for coefficient M{S{lambda}}
1844         @type lame_lambda: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1845         @keyword F: value for internal force M{F}
1846         @type F: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}
1847         @keyword sigma: value for initial stress M{S{sigma}}
1848         @type sigma: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}
1849         @keyword f: value for extrenal force M{f}
1850         @type f: any type that can be casted to L{Vector<escript.Vector>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}
1851         @keyword r: prescribed values M{r} for the solution in constraints.
1852         @type r: 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         @keyword q: mask for location of constraints
1855         @type q: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1856                   depending of reduced order is used for the representation of the equation.
1857         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1858         """
1859         super(LameEquation, self).setValues(**coefficients)
1860    
1861       def getCoefficientOfGeneralPDE(self,name):
1862         """
1863         return the value of the coefficient name of the general PDE
1864    
1865         @param name: name of the coefficient requested.
1866         @type name: C{string}
1867         @return: the value of the coefficient  name
1868         @rtype: L{Data<escript.Data>}
1869         @raise IllegalCoefficient: if name is not one of coefficients
1870                      "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}.
1871         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1872         """
1873         if name == "A" :
1874             out =self.createCoefficientOfGeneralPDE("A")
1875             for i in range(self.getDim()):
1876               for j in range(self.getDim()):
1877                 out[i,i,j,j] += self.getCoefficient("lame_lambda")
1878                 out[i,j,j,i] += self.getCoefficient("lame_mu")
1879                 out[i,j,i,j] += self.getCoefficient("lame_mu")
1880             return out
1881         elif name == "B" :
1882             return escript.Data()
1883         elif name == "C" :
1884             return escript.Data()
1885         elif name == "D" :
1886             return escript.Data()
1887         elif name == "X" :
1888             return self.getCoefficient("sigma")
1889         elif name == "Y" :
1890             return self.getCoefficient("F")
1891         elif name == "d" :
1892             return escript.Data()
1893         elif name == "y" :
1894             return self.getCoefficient("f")
1895         elif name == "d_contact" :
1896             return escript.Data()
1897         elif name == "y_contact" :
1898             return escript.Data()
1899         elif name == "r" :
1900             return self.getCoefficient("r")
1901         elif name == "q" :
1902             return self.getCoefficient("q")
1903         else:
1904            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1905    
1906    class AdvectivePDE(LinearPDE):
1907       """
1908       In cases of PDEs dominated by the advection terms M{B} and M{C} against the adevctive terms M{A}
1909       up-winding has been used.  The L{AdvectivePDE} class applies SUPG upwinding to the advective terms.
1910    
1911       In the following we set
1912    
1913       M{Z[j]=C[j]-B[j]}
1914    
1915       or
1916    
1917       M{Z[i,k,l]=C[i,k,l]-B[i,l,k]}
1918    
1919       To measure the dominance of the advective terms over the diffusive term M{A} the
1920       X{Pelclet number} M{P} is used. It is defined as
1921    
1922       M{P=h|Z|/(2|A|)}
1923    
1924       where M{|.|} denotes the L{length<util.length>} of the arument and M{h} is the local cell size
1925       from L{getSize<escript.Domain.getSize>}. Where M{|A|==0} M{P} is M{S{infinity}}.
1926    
1927       From the X{Pelclet number} the stabilization parameters M{S{Xi}} and M{S{Xi}} are calculated:
1928    
1929       M{S{Xi}=S{xi}(P) h/|Z|}
1930    
1931       where M{S{xi}} is a suitable function of the Peclet number.
1932    
1933       In the case of a single PDE the coefficient are up-dated in the following way:
1934             - M{A[i,j] S{<-} A[i,j] + S{Xi} * Z[j] * Z[l]}
1935             - M{B[j] S{<-} B[j] + S{Xi} * C[j] * D}
1936             - M{C[j] S{<-} C[j] + S{Xi} * B[j] * D}
1937             - M{X[j] S{<-} X[j] + S{Xi} * Z[j] * Y}
1938    
1939       Similar for the case of a systems of PDEs:
1940             - 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]}
1941             - M{B[i,j,k] S{<-} B[i,j,k] +  S{delta}[p,m] * S{Xi} * D[p,k] * C[m,i,j]}
1942             - M{C[i,k,l] S{<-} C[i,k,l] +  S{delta}[p,m] * S{Xi} * D[p,k] * B[m,l,i]}
1943             - M{X[i,j] S{<-} X[i,j] + S{delta}[p,m] * S{Xi}  * Y[p] * Z[m,i,j]}
1944    
1945       where M{S{delta}} is L{kronecker}.
1946       Using upwinding in this form, introduces an additonal error which is proprtional to the cell size M{h}
1947       but with the intension to stabilize the solution.
1948    
1949       """
1950       def __init__(self,domain,numEquations=None,numSolutions=None,xi=None,debug=False):
1951          """
1952          creates a linear, steady, second order PDE on a L{Domain<escript.Domain>}
1953    
1954          @param domain: domain of the PDE
1955          @type domain: L{Domain<escript.Domain>}
1956          @param numEquations: number of equations. If numEquations==None the number of equations
1957                               is exracted from the PDE coefficients.
1958          @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
1959                               is exracted from the PDE coefficients.
1960          @param xi: defines a function which returns for any given Preclet number as L{Scalar<escript.Scalar>} object the
1961                     M{S{xi}}-value used to define the stabilization parameters. If equal to None, L{ELMAN_RAMAGE} is used.
1962          @type xi: callable object which returns a L{Scalar<escript.Scalar>} object.
1963          @param debug: if True debug informations are printed.
1964          """
1965          super(AdvectivePDE, self).__init__(domain,\
1966                                             numEquations,numSolutions,debug)
1967          if xi==None:
1968             self.__xi=AdvectivePDE.ELMAN_RAMAGE
1969          else:
1970             self.__xi=xi
1971        self.__Xi=escript.Data()        self.__Xi=escript.Data()
1972    
1973     def __calculateXi(self,peclet_factor,Z,h):     def setValue(self,**coefficients):
1974         Z_max=util.Lsup(Z)        """
1975         if Z_max>0.:        sets new values to coefficients
1976            return h*self.__xi(Z*peclet_factor)/(Z+Z_max*self.TOL)  
1977         else:        @param coefficients: new values assigned to coefficients
1978            return 0.        @keyword A: value for coefficient A.
1979          @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1980          @keyword B: value for coefficient B
1981          @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1982          @keyword C: value for coefficient C
1983          @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1984          @keyword D: value for coefficient D
1985          @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1986          @keyword X: value for coefficient X
1987          @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1988          @keyword Y: value for coefficient Y
1989          @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1990          @keyword d: value for coefficient d
1991          @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1992          @keyword y: value for coefficient y
1993          @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1994          @keyword d_contact: value for coefficient d_contact
1995          @type d_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 y_contact: value for coefficient y_contact
1998          @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1999                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
2000          @keyword r: values prescribed to the solution at the locations of constraints
2001          @type r: 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 solution.
2003          @keyword q: mask for location of constraints
2004          @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2005                   depending of reduced order is used for the representation of the equation.
2006          @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2007    
2008          """
2009          if "A" in coefficients.keys()   or "B" in coefficients.keys() or "C" in coefficients.keys(): self.__Xi=escript.Data()
2010          super(AdvectivePDE, self).setValue(**coefficients)
2011    
2012       def ELMAN_RAMAGE(self,P):
2013         """
2014         Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.
2015         This function uses the method suggested by H.C. Elman and A. Ramage, I{SIAM J. Numer. Anal.}, B{40} (2002)
2016              - M{S{xi}(P)=0} for M{P<1}
2017              - M{S{xi}(P)=(1-1/P)/2} otherwise
2018    
2019         @param P: Preclet number
2020         @type P: L{Scalar<escript.Scalar>}
2021         @return: up-wind weightimg factor
2022         @rtype: L{Scalar<escript.Scalar>}
2023         """
2024         return util.wherePositive(P-1.)*0.5*(1.-1./(P+1.e-15))
2025    
2026       def SIMPLIFIED_BROOK_HUGHES(self,P):
2027         """
2028         Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.
2029         The original methods is
2030    
2031         M{S{xi}(P)=coth(P)-1/P}
2032    
2033         As the evaluation of M{coth} is expensive we are using the approximation:
2034    
2035             - M{S{xi}(P)=P/3} where M{P<3}
2036             - M{S{xi}(P)=1/2} otherwise
2037    
2038         @param P: Preclet number
2039         @type P: L{Scalar<escript.Scalar>}
2040         @return: up-wind weightimg factor
2041         @rtype: L{Scalar<escript.Scalar>}
2042         """
2043         c=util.whereNegative(P-3.)
2044         return P/6.*c+1./2.*(1.-c)
2045    
2046     def setValue(self,**args):     def HALF(self,P):
2047         if "A" in args.keys()   or "B" in args.keys() or "C" in args.keys(): self.__Xi=escript.Data()       """
2048         self._LinearPDE__setValue(**args)       Predefined function to set value M{1/2} for M{S{xi}}
2049              
2050     def getXi(self):       @param P: Preclet number
2051         @type P: L{Scalar<escript.Scalar>}
2052         @return: up-wind weightimg factor
2053         @rtype: L{Scalar<escript.Scalar>}
2054         """
2055         return escript.Scalar(0.5,P.getFunctionSpace())
2056    
2057       def __getXi(self):
2058        if self.__Xi.isEmpty():        if self.__Xi.isEmpty():
2059           B=self.getCoefficient("B")           B=self.getCoefficient("B")
2060           C=self.getCoefficient("C")           C=self.getCoefficient("C")
# Line 1060  class AdvectivePDE(LinearPDE): Line 2063  class AdvectivePDE(LinearPDE):
2063           self.__Xi=escript.Scalar(0.,self.getFunctionSpaceForCoefficient("A"))           self.__Xi=escript.Scalar(0.,self.getFunctionSpaceForCoefficient("A"))
2064           if not C.isEmpty() or not B.isEmpty():           if not C.isEmpty() or not B.isEmpty():
2065              if not C.isEmpty() and not B.isEmpty():              if not C.isEmpty() and not B.isEmpty():
                 Z2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))  
2066                  if self.getNumEquations()>1:                  if self.getNumEquations()>1:
2067                     if self.getNumSolutions()>1:                     if self.getNumSolutions()>1:
2068                          flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))
2069                        for i in range(self.getNumEquations()):                        for i in range(self.getNumEquations()):
2070                           for k in range(self.getNumSolutions()):                           for k in range(self.getNumSolutions()):
2071                              for l in range(self.getDim()): Z2+=(C[i,k,l]-B[i,l,k])**2                              for l in range(self.getDim()): flux2+=(C[i,k,l]-B[i,l,k])**2
2072                          length_of_flux=util.sqrt(flux2)
2073                          # flux=C-util.reorderComponents(B,[0,2,1])
2074                     else:                     else:
2075                          flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))
2076                        for i in range(self.getNumEquations()):                        for i in range(self.getNumEquations()):
2077                           for l in range(self.getDim()): Z2+=(C[i,l]-B[i,l])**2                           for l in range(self.getDim()): flux2+=(C[i,l]-B[i,l])**2
2078                          length_of_flux=util.sqrt(flux2)
2079                          # flux=C-B
2080                  else:                  else:
2081                     if self.getNumSolutions()>1:                     if self.getNumSolutions()>1:
2082                          flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))
2083                        for k in range(self.getNumSolutions()):                        for k in range(self.getNumSolutions()):
2084                           for l in range(self.getDim()): Z2+=(C[k,l]-B[l,k])**2                           for l in range(self.getDim()): flux2+=(C[k,l]-B[l,k])**2
2085                          # flux=C-util.reorderComponents(B,[1,0])
2086                          length_of_flux=util.sqrt(flux2)
2087                     else:                     else:
2088                        for l in range(self.getDim()): Z2+=(C[l]-B[l])**2                        length_of_flux=util.length(C-B)
                 length_of_Z=util.sqrt(Z2)  
2089              elif C.isEmpty():              elif C.isEmpty():
2090                length_of_Z=util.length(B)                length_of_flux=util.length(B)
2091              else:              else:
2092                length_of_Z=util.length(C)                length_of_flux=util.length(C)
2093                flux_max=util.Lsup(length_of_flux)
2094              Z_max=util.Lsup(length_of_Z)              if flux_max>0.:
2095              if Z_max>0.:                if A.isEmpty():
2096                 length_of_A=util.length(A)                    inv_A=1./self.SMALL_TOLERANCE
2097                 A_max=util.Lsup(length_of_A)                    peclet_number=escript.Scalar(inv_A,length_of_flux.getFunctionSpace())
2098                 if A_max>0:                    xi=self.__xi(self,peclet_number)
2099                      inv_A=1./(length_of_A+A_max*self.TOL)                else:
2100                 else:                    # length_of_A=util.inner(flux,util.tensormutiply(A,flux))
2101                      inv_A=1./self.TOL                    length_of_A=util.length(A)
2102                 peclet_number=length_of_Z*h/2*inv_A                    A_max=util.Lsup(length_of_A)
2103                 xi=self.__xi(peclet_number)                    if A_max>0:
2104                 self.__Xi=h*xi/(length_of_Z+Z_max*self.TOL)                         inv_A=1./(length_of_A+A_max*self.SMALL_TOLERANCE)
2105                 print "@ preclet number = %e"%util.Lsup(peclet_number),util.Lsup(xi),util.Lsup(length_of_Z)                    else:
2106                           inv_A=1./self.SMALL_TOLERANCE
2107                      peclet_number=length_of_flux*h/2*inv_A
2108                      xi=self.__xi(self,peclet_number)
2109                  self.__Xi=h*xi/(length_of_flux+flux_max*self.SMALL_TOLERANCE)
2110                  self.trace("preclet number = %e"%util.Lsup(peclet_number))
2111                else:
2112                  self.__Xi=escript.Scalar(0.,length_of_flux.getFunctionSpace())
2113        return self.__Xi        return self.__Xi
         
2114    
2115     def getCoefficientOfPDE(self,name):  
2116       def getCoefficientOfGeneralPDE(self,name):
2117       """       """
2118       return the value of the coefficient name of the general PDE       return the value of the coefficient name of the general PDE
2119    
2120       @param name:       @param name: name of the coefficient requested.
2121         @type name: C{string}
2122         @return: the value of the coefficient name
2123         @rtype: L{Data<escript.Data>}
2124         @raise IllegalCoefficient: if name is not one of coefficients
2125                      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}.
2126         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2127       """       """
2128       if not self.getNumEquations() == self.getNumSolutions():       if not self.getNumEquations() == self.getNumSolutions():
2129            raise ValueError,"AdvectivePDE expects the number of solution componets and the number of equations to be equal."            raise ValueError,"AdvectivePDE expects the number of solution componets and the number of equations to be equal."
2130    
2131       if name == "A" :       if name == "A" :
2132           A=self.getCoefficient("A")           A=self.getCoefficient("A")
2133           B=self.getCoefficient("B")           B=self.getCoefficient("B")
2134           C=self.getCoefficient("C")           C=self.getCoefficient("C")
2135           if B.isEmpty() and C.isEmpty():           if B.isEmpty() and C.isEmpty():
2136              Aout=A              Aout=A
2137           else:           else:
2138              if A.isEmpty():              if A.isEmpty():
2139                 Aout=self.createNewCoefficient("A")                 Aout=self.createCoefficientOfGeneralPDE("A")
2140              else:              else:
2141                 Aout=A[:]                 Aout=A[:]
2142              Xi=self.getXi()              Xi=self.__getXi()
2143              if self.getNumEquations()>1:              if self.getNumEquations()>1:
2144                  for i in range(self.getNumEquations()):                  for i in range(self.getNumEquations()):
2145                     for j in range(self.getDim()):                     for j in range(self.getDim()):
2146                        for k in range(self.getNumSolutions()):                        for k in range(self.getNumSolutions()):
2147                           for l in range(self.getDim()):                           for l in range(self.getDim()):
2148                              if not C.isEmpty() and not B.isEmpty():                              if not C.isEmpty() and not B.isEmpty():
2149                                   # tmp=C-util.reorderComponents(B,[0,2,1])
2150                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(tmp,[1,2,0]),tmp,offset=1)
2151                                 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])                                 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])
2152                              elif C.isEmpty():                              elif C.isEmpty():
2153                                 for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*B[p,j,i]*B[p,l,k]                                 for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*B[p,j,i]*B[p,l,k]
2154                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(B,[2,1,0]),util.reorder(B,[0,2,1]),offset=1)
2155                              else:                              else:
2156                                 for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*C[p,i,j]*C[p,k,l]                                 for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*C[p,i,j]*C[p,k,l]
2157                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),C,offset=1)
2158              else:              else:
2159                  for j in range(self.getDim()):                 if not C.isEmpty() and not B.isEmpty():
2160                     for l in range(self.getDim()):                     delta=(C-B)
2161                        if not C.isEmpty() and not B.isEmpty():                     Aout+=util.outer(Xi*delta,delta)
2162                            Aout[j,l]+=Xi*(C[j]-B[j])*(C[l]-B[l])                 elif not B.isEmpty():
2163                        elif C.isEmpty():                     Aout+=util.outer(Xi*B,B)
2164                            Aout[j,l]+=Xi*B[j]*B[l]                 elif not C.isEmpty():
2165                        else:                     Aout+=util.outer(Xi*C,C)
                           Aout[j,l]+=Xi*C[j]*C[l]  
2166           return Aout           return Aout
2167       elif name == "B" :       elif name == "B" :
2168             # return self.getCoefficient("B")
2169           B=self.getCoefficient("B")           B=self.getCoefficient("B")
2170           C=self.getCoefficient("C")           C=self.getCoefficient("C")
2171           D=self.getCoefficient("D")           D=self.getCoefficient("D")
2172           if C.isEmpty() or D.isEmpty():           if C.isEmpty() or D.isEmpty():
2173              Bout=B              Bout=B
2174           else:           else:
2175              Xi=self.getXi()              Xi=self.__getXi()
2176              if B.isEmpty():              if B.isEmpty():
2177                  Bout=self.createNewCoefficient("B")                  Bout=self.createCoefficientOfGeneralPDE("B")
2178              else:              else:
2179                  Bout=B[:]                  Bout=B[:]
2180              if self.getNumEquations()>1:              if self.getNumEquations()>1:
2181                 for k in range(self.getNumSolutions()):                 for k in range(self.getNumSolutions()):
2182                    for p in range(self.getNumEquations()):                    for p in range(self.getNumEquations()):
2183                       tmp=Xi*D[p,k]                       tmp=Xi*D[p,k]
2184                       for i in range(self.getNumEquations()):                       for i in range(self.getNumEquations()):
2185                          for j in range(self.getDim()):                          for j in range(self.getDim()):
2186                             Bout[i,j,k]+=tmp*C[p,i,j]                             Bout[i,j,k]+=tmp*C[p,i,j]
2187                               # Bout=Bout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),D,offset=1)
2188              else:              else:
2189                 tmp=Xi*D                 Bout+=(Xi*D)*C
                for j in range(self.getDim()): Bout[j]+=tmp*C[j]  
2190           return Bout           return Bout
2191       elif name == "C" :       elif name == "C" :
2192             # return self.getCoefficient("C")
2193           B=self.getCoefficient("B")           B=self.getCoefficient("B")
2194           C=self.getCoefficient("C")           C=self.getCoefficient("C")
2195           D=self.getCoefficient("D")           D=self.getCoefficient("D")
2196           if B.isEmpty() or D.isEmpty():           if B.isEmpty() or D.isEmpty():
2197              Cout=C              Cout=C
2198           else:           else:
2199              Xi=self.getXi()              Xi=self.__getXi()
2200              if C.isEmpty():              if C.isEmpty():
2201                  Cout=self.createNewCoefficient("C")                  Cout=self.createCoefficientOfGeneralPDE("C")
2202              else:              else:
2203                  Cout=C[:]                  Cout=C[:]
2204              if self.getNumEquations()>1:              if self.getNumEquations()>1:
# Line 1180  class AdvectivePDE(LinearPDE): Line 2208  class AdvectivePDE(LinearPDE):
2208                        for i in range(self.getNumEquations()):                        for i in range(self.getNumEquations()):
2209                          for l in range(self.getDim()):                          for l in range(self.getDim()):
2210                                   Cout[i,k,l]+=tmp*B[p,l,i]                                   Cout[i,k,l]+=tmp*B[p,l,i]
2211                                     # Cout=Cout+Xi*B[p,l,i]*D[p,k]
2212              else:              else:
2213                 tmp=Xi*D                 Cout+=(Xi*D)*B
                for j in range(self.getDim()): Cout[j]+=tmp*B[j]  
2214           return Cout           return Cout
2215       elif name == "D" :       elif name == "D" :
2216           return self.getCoefficient("D")           return self.getCoefficient("D")
2217       elif name == "X" :       elif name == "X" :
2218             # return self.getCoefficient("X")
2219           X=self.getCoefficient("X")           X=self.getCoefficient("X")
2220           Y=self.getCoefficient("Y")           Y=self.getCoefficient("Y")
2221           B=self.getCoefficient("B")           B=self.getCoefficient("B")
# Line 1195  class AdvectivePDE(LinearPDE): Line 2224  class AdvectivePDE(LinearPDE):
2224              Xout=X              Xout=X
2225           else:           else:
2226              if X.isEmpty():              if X.isEmpty():
2227                  Xout=self.createNewCoefficient("X")                  Xout=self.createCoefficientOfGeneralPDE("X")
2228              else:              else:
2229                  Xout=X[:]                  Xout=X[:]
2230              Xi=self.getXi()              Xi=self.__getXi()
2231              if self.getNumEquations()>1:              if self.getNumEquations()>1:
2232                   for p in range(self.getNumEquations()):                   for p in range(self.getNumEquations()):
2233                      tmp=Xi*Y[p]                      tmp=Xi*Y[p]
2234                      for i in range(self.getNumEquations()):                      for i in range(self.getNumEquations()):
2235                         for j in range(self.getDim()):                         for j in range(self.getDim()):
2236                            if not C.isEmpty() and not B.isEmpty():                            if not C.isEmpty() and not B.isEmpty():
2237                               Xout[i,j]+=tmp*(C[p,i,j]-B[p,j,i])                               Xout[i,j]+=tmp*(C[p,i,j]-B[p,j,i])
2238                                 # Xout=X_out+Xi*util.inner(Y,C-util.reorderComponents(B,[0,2,1]),offset=1)
2239                            elif C.isEmpty():                            elif C.isEmpty():
2240                               Xout[i,j]-=tmp*B[p,j,i]                               Xout[i,j]-=tmp*B[p,j,i]
2241                                 # Xout=X_out-Xi*util.inner(Y,util.reorderComponents(B,[0,2,1]),offset=1)
2242                            else:                            else:
2243                               Xout[i,j]+=tmp*C[p,i,j]                               Xout[i,j]+=tmp*C[p,i,j]
2244                                 # Xout=X_out+Xi*util.inner(Y,C,offset=1)
2245              else:              else:
2246                   tmp=Xi*Y                if not C.isEmpty() and not B.isEmpty():
2247                   for j in range(self.getDim()):                  Xout+=(Xi*Y)*(C-B)
2248                      if not C.isEmpty() and not B.isEmpty():                elif C.isEmpty():
2249                         Xout[j]+=tmp*(C[j]-B[j])                  Xout-=(Xi*Y)*B
2250                      elif C.isEmpty():                else:
2251                         Xout[j]-=tmp*B[j]                  Xout+=(Xi*Y)*C
                     else:  
                        Xout[j]+=tmp*C[j]  
2252           return Xout           return Xout
2253       elif name == "Y" :       elif name == "Y" :
2254           return self.getCoefficient("Y")           return self.getCoefficient("Y")
2255       elif name == "d" :       elif name == "d" :
2256           return self.getCoefficient("d")           return self.getCoefficient("d")
2257       elif name == "y" :       elif name == "y" :
2258           return self.getCoefficient("y")           return self.getCoefficient("y")
2259       elif name == "d_contact" :       elif name == "d_contact" :
2260           return self.getCoefficient("d_contact")           return self.getCoefficient("d_contact")
2261       elif name == "y_contact" :       elif name == "y_contact" :
2262           return self.getCoefficient("y_contact")           return self.getCoefficient("y_contact")
2263       elif name == "r" :       elif name == "r" :
          return self.getCoefficient("r")  
      elif name == "q" :  
          return self.getCoefficient("q")  
      else:  
          raise SystemError,"unknown PDE coefficient %s",name  
   
   
 class Poisson(LinearPDE):  
    """  
    Class to define a Poisson equation problem:  
   
    class to define a linear PDE of the form  
    \f[  
    -u_{,jj} = f  
    \f]  
   
    with boundary conditons:  
   
    \f[  
    n_j*u_{,j} = 0  
    \f]  
   
    and constraints:  
   
    \f[  
    u=0 \quad \mathrm{where} \quad q>0  
    \f]  
    """  
   
    def __init__(self,domain,f=escript.Data(),q=escript.Data()):  
        LinearPDE.__init__(self,domain,1,1)  
        self.COEFFICIENTS={  
        "f"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),  
        "q"         : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.BOTH)}  
        self.setSymmetryOn()  
        self.setValue(f,q)  
   
    def setValue(self,f=escript.Data(),q=escript.Data()):  
        """set value of PDE parameters f and q"""  
        self._LinearPDE__setValue(f=f,q=q)  
   
    def getCoefficientOfPDE(self,name):  
      """  
      return the value of the coefficient name of the general PDE  
   
      @param name:  
      """  
      if name == "A" :  
          return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))  
      elif name == "B" :  
          return escript.Data()  
      elif name == "C" :  
          return escript.Data()  
      elif name == "D" :  
          return escript.Data()  
      elif name == "X" :  
          return escript.Data()  
      elif name == "Y" :  
          return self.getCoefficient("f")  
      elif name == "d" :  
          return escript.Data()  
      elif name == "y" :  
          return escript.Data()  
      elif name == "d_contact" :  
          return escript.Data()  
      elif name == "y_contact" :  
          return escript.Data()  
      elif name == "r" :  
          return escript.Data()  
      elif name == "q" :  
          return self.getCoefficient("q")  
      else:  
          raise SystemError,"unknown PDE coefficient %s",name  
   
 class LameEquation(LinearPDE):  
    """  
    Class to define a Lame equation problem:  
   
    class to define a linear PDE of the form  
    \f[  
    -(\lambda (u_{i,j}+u_{j,i}))_{,j} - \mu u_{j,ji}} = F_i -\sigma_{ij,j}  
    \f]  
   
    with boundary conditons:  
   
    \f[  
    n_j(\lambda(u_{i,j}+u_{j,i})-sigma_{ij}) + n_i\mu u_{j,j} = f_i  
    \f]  
   
    and constraints:  
   
    \f[  
    u_i=r_i \quad \mathrm{where} \quad q_i>0  
    \f]  
    """  
   
    def __init__(self,domain,f=escript.Data(),q=escript.Data()):  
        LinearPDE.__init__(self,domain,domain.getDim(),domain.getDim())  
        self.COEFFICIENTS={  
        "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),  
        "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),  
        "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM),PDECoefficient.RIGHTHANDSIDE),  
        "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.EQUATION),PDECoefficient.RIGHTHANDSIDE),  
        "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),  
        "r"            : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.BOTH),  
        "q"            : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.BOTH)}  
        self.setSymmetryOn()  
   
    def setValue(self,lame_lambda=escript.Data(),lame_mu=escript.Data(),F=escript.Data(),sigma=escript.Data(),f=escript.Data(),r=escript.Data(),q=escript.Data()):  
        """set value of PDE parameters"""  
        self._LinearPDE__setValue(lame_lambda=lame_lambda, \  
                                  lame_mu=lame_mu, \  
                                  F=F, \  
                                  sigma=sigma, \  
                                  f=f, \  
                                  r=r, \  
                                  q=q)  
    def getCoefficientOfPDE(self,name):  
      """  
      return the value of the coefficient name of the general PDE  
   
      @param name:  
      """  
      if name == "A" :  
          A =self.createNewCoefficient("A")  
          for i in range(self.getDim()):  
            for j in range(self.getDim()):  
              out[i,i,j,j] += self.getCoefficient("lame_mu")  
              out[i,j,j,i] += self.getCoefficient("lame_lambda")  
              out[i,j,i,j] += self.getCoefficient("lame_lambda")  
          return out  
      elif name == "B" :  
          return escript.Data()  
      elif name == "C" :  
          return escript.Data()  
      elif name == "D" :  
          return escript.Data()  
      elif name == "X" :  
          return self.getCoefficient("sigma")  
      elif name == "Y" :  
          return self.getCoefficient("F")  
      elif name == "d" :  
          return escript.Data()  
      elif name == "y" :  
          return self.getCoefficient("f")  
      elif name == "d_contact" :  
          return escript.Data()  
      elif name == "y_contact" :  
          return escript.Data()  
      elif name == "r" :  
2264           return self.getCoefficient("r")           return self.getCoefficient("r")
2265       elif name == "q" :       elif name == "q" :
2266           return self.getCoefficient("q")           return self.getCoefficient("q")
2267       else:       else:
2268           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2269    
2270  # $Log$  # $Log$
2271  # Revision 1.9  2005/07/25 05:28:13  jgs  # Revision 1.14  2005/09/22 01:54:57  jgs
2272  # Merge of development branch back to main trunk on 2005-07-25  # Merge of development branch dev-02 back to main trunk on 2005-09-22
2273  #  #
2274  # Revision 1.8  2005/06/09 05:37:59  jgs  # Revision 1.13  2005/09/15 03:44:19  jgs
2275  # Merge of development branch back to main trunk on 2005-06-09  # Merge of development branch dev-02 back to main trunk on 2005-09-15
2276  #  #
2277  # Revision 1.7  2005/05/06 04:26:10  jgs  # Revision 1.12  2005/09/01 03:31:28  jgs
2278  # Merge of development branch back to main trunk on 2005-05-06  # Merge of development branch dev-02 back to main trunk on 2005-09-01
2279    #
2280    # Revision 1.11  2005/08/23 01:24:28  jgs
2281    # Merge of development branch dev-02 back to main trunk on 2005-08-23
2282    #
2283    # Revision 1.10  2005/08/12 01:45:36  jgs
2284    # erge of development branch dev-02 back to main trunk on 2005-08-12
2285    #
2286    # Revision 1.9.2.17  2005/09/21 07:03:33  matt
2287    # PDECoefficient and LinearPDE are now new style classes (introduced in Python
2288    # 2.2). Classes Poisson, Helmholtz, LameEquation and AdvectivePDE have been
2289    # modified to instead use portable/cooperative "super" calls to extend base
2290    # class methods.
2291    #
2292    # Revision 1.9.2.16  2005/09/16 01:54:37  matt
2293    # Removed redundant if-loop.
2294    #
2295    # Revision 1.9.2.15  2005/09/14 08:09:18  matt
2296    # Added "REDUCED" solution PDECoefficient descriptors for LinearPDEs.
2297    #
2298    # Revision 1.9.2.14  2005/09/07 06:26:16  gross
2299    # the solver from finley are put into the standalone package paso now
2300    #
2301    # Revision 1.9.2.13  2005/08/31 08:45:03  gross
2302    # in the case of lumping no new system is allocated if the constraint is changed.
2303    #
2304    # Revision 1.9.2.12  2005/08/31 07:10:23  gross
2305    # test for Lumping added
2306    #
2307    # Revision 1.9.2.11  2005/08/30 01:53:45  gross
2308    # bug in format fixed.
2309    #
2310    # Revision 1.9.2.10  2005/08/26 07:14:17  gross
2311    # a few more bugs in linearPDE fixed. remaining problem are finley problems
2312    #
2313    # Revision 1.9.2.9  2005/08/26 06:30:45  gross
2314    # fix for reported bug  0000004. test_linearPDE passes a few more tests
2315    #
2316    # Revision 1.9.2.8  2005/08/26 04:30:13  gross
2317    # gneric unit testing for linearPDE
2318    #
2319    # Revision 1.9.2.7  2005/08/25 07:06:50  gross
2320    # linearPDE documentation is parsed now by epydoc. there is still a problem with links into escriptcpp.so
2321    #
2322    # Revision 1.9.2.6  2005/08/24 05:01:24  gross
2323    # problem with resetting the matrix in case of resetting its values to 0 fixed.
2324    #
2325    # Revision 1.9.2.5  2005/08/24 02:03:28  gross
2326    # epydoc mark up partially fixed
2327    #
2328    # Revision 1.9.2.4  2005/08/22 07:11:09  gross
2329    # some problems with LinearPDEs fixed.
2330    #
2331    # Revision 1.9.2.3  2005/08/18 04:48:48  gross
2332    # the methods SetLumping*() are removed. Lumping is set trough setSolverMethod(LinearPDE.LUMPING)
2333    #
2334    # Revision 1.9.2.2  2005/08/18 04:39:32  gross
2335    # the constants have been removed from util.py as they not needed anymore. PDE related constants are accessed through LinearPDE attributes now
2336    #
2337    # Revision 1.9.2.1  2005/07/29 07:10:27  gross
2338    # new functions in util and a new pde type in linearPDEs
2339    #
2340    # Revision 1.1.2.25  2005/07/28 04:21:09  gross
2341    # Lame equation: (linear elastic, isotropic) added
2342  #  #
2343  # Revision 1.1.2.24  2005/07/22 06:37:11  gross  # Revision 1.1.2.24  2005/07/22 06:37:11  gross
2344  # some extensions to modellib and linearPDEs  # some extensions to modellib and linearPDEs
# Line 1509  class LameEquation(LinearPDE): Line 2452  class LameEquation(LinearPDE):
2452  # Revision 1.1  2004/08/28 12:58:06  gross  # Revision 1.1  2004/08/28 12:58:06  gross
2453  # SimpleSolve is not running yet: problem with == of functionsspace  # SimpleSolve is not running yet: problem with == of functionsspace
2454  #  #
 #  

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