Diff of /trunk/escript/py_src/flows.py

revision 2100 by gross, Wed Nov 26 08:13:00 2008 UTC revision 2620 by gross, Thu Aug 20 06:24:00 2009 UTC
# Line 1  Line 1
1  ########################################################  ########################################################
2  #  #
3  # Copyright (c) 2003-2008 by University of Queensland  # Copyright (c) 2003-2009 by University of Queensland
4  # Earth Systems Science Computational Center (ESSCC)  # Earth Systems Science Computational Center (ESSCC)
5  # http://www.uq.edu.au/esscc  # http://www.uq.edu.au/esscc
6  #  #
# Line 10  Line 10
10  #  #
11  ########################################################  ########################################################
12
14  Earth Systems Science Computational Center (ESSCC)  Earth Systems Science Computational Center (ESSCC)
15  http://www.uq.edu.au/esscc  http://www.uq.edu.au/esscc
20
21  """  """
22  Some models for flow  Some models for flow
# Line 33  __author__="Lutz Gross, l.gross@uq.edu.a Line 33  __author__="Lutz Gross, l.gross@uq.edu.a
33
34  from escript import *  from escript import *
35  import util  import util
36  from linearPDEs import LinearPDE, LinearPDESystem, LinearSinglePDE  from linearPDEs import LinearPDE, LinearPDESystem, LinearSinglePDE, SolverOptions
37  from pdetools import HomogeneousSaddlePointProblem,Projector, ArithmeticTuple, PCG  from pdetools import HomogeneousSaddlePointProblem,Projector, ArithmeticTuple, PCG, NegativeNorm, GMRES
38
39  class DarcyFlow(object):  class DarcyFlow(object):
40      """      """
41      solves the problem      solves the problem
42
43      M{u_i+k_{ij}*p_{,j} = g_i}      M{u_i+k_{ij}*p_{,j} = g_i}
44      M{u_{i,i} = f}      M{u_{i,i} = f}
45
46      where M{p} represents the pressure and M{u} the Darcy flux. M{k} represents the permeability,      where M{p} represents the pressure and M{u} the Darcy flux. M{k} represents the permeability,
47
48      @note: The problem is solved in a least squares formulation.      @note: The problem is solved in a least squares formulation.
49      """      """
50
51      def __init__(self, domain):      def __init__(self, domain, weight=None, useReduced=False, adaptSubTolerance=True):
52          """          """
53          initializes the Darcy flux problem          initializes the Darcy flux problem
54          @param domain: domain of the problem          @param domain: domain of the problem
55          @type domain: L{Domain}          @type domain: L{Domain}
56        @param useReduced: uses reduced oreder on flux and pressure
57        @type useReduced: C{bool}
58        @param adaptSubTolerance: switches on automatic subtolerance selection
60          """          """
61          self.domain=domain          self.domain=domain
62            if weight == None:
63               s=self.domain.getSize()
64               self.__l=(3.*util.longestEdge(self.domain)*s/util.sup(s))**2
65               # self.__l=(3.*util.longestEdge(self.domain))**2
66               # self.__l=(0.1*util.longestEdge(self.domain)*s/util.sup(s))**2
67            else:
68               self.__l=weight
69          self.__pde_v=LinearPDESystem(domain)          self.__pde_v=LinearPDESystem(domain)
70          self.__pde_v.setValue(D=util.kronecker(domain), A=util.outer(util.kronecker(domain),util.kronecker(domain)))          if useReduced: self.__pde_v.setReducedOrderOn()
71          self.__pde_v.setSymmetryOn()          self.__pde_v.setSymmetryOn()
72            self.__pde_v.setValue(D=util.kronecker(domain), A=self.__l*util.outer(util.kronecker(domain),util.kronecker(domain)))
73          self.__pde_p=LinearSinglePDE(domain)          self.__pde_p=LinearSinglePDE(domain)
74          self.__pde_p.setSymmetryOn()          self.__pde_p.setSymmetryOn()
75            if useReduced: self.__pde_p.setReducedOrderOn()
76          self.__f=Scalar(0,self.__pde_v.getFunctionSpaceForCoefficient("X"))          self.__f=Scalar(0,self.__pde_v.getFunctionSpaceForCoefficient("X"))
77          self.__g=Vector(0,self.__pde_v.getFunctionSpaceForCoefficient("Y"))          self.__g=Vector(0,self.__pde_v.getFunctionSpaceForCoefficient("Y"))
78            self.setTolerance()
79            self.setAbsoluteTolerance()
81        self.verbose=False
82        def getSolverOptionsFlux(self):
83        """
84        Returns the solver options used to solve the flux problems
85
86        M{(I+D^*D)u=F}
87
88        @return: L{SolverOptions}
89        """
90        return self.__pde_v.getSolverOptions()
91        def setSolverOptionsFlux(self, options=None):
92        """
93        Sets the solver options used to solve the flux problems
94
95        M{(I+D^*D)u=F}
96
97        If C{options} is not present, the options are reset to default
98        @param options: L{SolverOptions}
99        @note: if the adaption of subtolerance is choosen, the tolerance set by C{options} will be overwritten before the solver is called.
100        """
101        return self.__pde_v.setSolverOptions(options)
102        def getSolverOptionsPressure(self):
103        """
104        Returns the solver options used to solve the pressure problems
105
106        M{(Q^*Q)p=Q^*G}
107
108        @return: L{SolverOptions}
109        """
110        return self.__pde_p.getSolverOptions()
111        def setSolverOptionsPressure(self, options=None):
112        """
113        Sets the solver options used to solve the pressure problems
114
115        M{(Q^*Q)p=Q^*G}
116
117        If C{options} is not present, the options are reset to default
118        @param options: L{SolverOptions}
119        @note: if the adaption of subtolerance is choosen, the tolerance set by C{options} will be overwritten before the solver is called.
120        """
121        return self.__pde_p.setSolverOptions(options)
122
123      def setValue(self,f=None, g=None, location_of_fixed_pressure=None, location_of_fixed_flux=None, permeability=None):      def setValue(self,f=None, g=None, location_of_fixed_pressure=None, location_of_fixed_flux=None, permeability=None):
124          """          """
# Line 75  class DarcyFlow(object): Line 132  class DarcyFlow(object):
132          @type location_of_fixed_pressure: scalar value on the domain (e.g. L{Data})          @type location_of_fixed_pressure: scalar value on the domain (e.g. L{Data})
133          @param location_of_fixed_flux:  mask for locations where flux is fixed.          @param location_of_fixed_flux:  mask for locations where flux is fixed.
134          @type location_of_fixed_flux: vector values on the domain (e.g. L{Data})          @type location_of_fixed_flux: vector values on the domain (e.g. L{Data})
135          @param permeability: permeability tensor. If scalar C{s} is given the tensor with          @param permeability: permeability tensor. If scalar C{s} is given the tensor with
136                               C{s} on the main diagonal is used. If vector C{v} is given the tensor with                               C{s} on the main diagonal is used. If vector C{v} is given the tensor with
137                               C{v} on the main diagonal is used.                               C{v} on the main diagonal is used.
138          @type permeability: scalar, vector or tensor values on the domain (e.g. L{Data})          @type permeability: scalar, vector or tensor values on the domain (e.g. L{Data})
139
# Line 85  class DarcyFlow(object): Line 142  class DarcyFlow(object):
142                 or the normal component of the flux (C{location_of_fixed_flux[i]>0} if direction of the normal                 or the normal component of the flux (C{location_of_fixed_flux[i]>0} if direction of the normal
143                 is along the M{x_i} axis.                 is along the M{x_i} axis.
144          """          """
145          if f !=None:          if f !=None:
146             f=util.interpolate(f, self.__pde_v.getFunctionSpaceForCoefficient("X"))             f=util.interpolate(f, self.__pde_v.getFunctionSpaceForCoefficient("X"))
147             if f.isEmpty():             if f.isEmpty():
148                 f=Scalar(0,self.__pde_v.getFunctionSpaceForCoefficient("X"))                 f=Scalar(0,self.__pde_v.getFunctionSpaceForCoefficient("X"))
149             else:             else:
150                 if f.getRank()>0: raise ValueError,"illegal rank of f."                 if f.getRank()>0: raise ValueError,"illegal rank of f."
151             self.f=f             self.__f=f
152          if g !=None:            if g !=None:
153             g=util.interpolate(g, self.__pde_p.getFunctionSpaceForCoefficient("Y"))             g=util.interpolate(g, self.__pde_p.getFunctionSpaceForCoefficient("Y"))
154             if g.isEmpty():             if g.isEmpty():
155               g=Vector(0,self.__pde_v.getFunctionSpaceForCoefficient("Y"))               g=Vector(0,self.__pde_v.getFunctionSpaceForCoefficient("Y"))
# Line 118  class DarcyFlow(object): Line 175  class DarcyFlow(object):
175             self.__permeability=perm             self.__permeability=perm
176             self.__pde_p.setValue(A=util.transposed_tensor_mult(self.__permeability,self.__permeability))             self.__pde_p.setValue(A=util.transposed_tensor_mult(self.__permeability,self.__permeability))
177
178        def setTolerance(self,rtol=1e-4):
179            """
180            sets the relative tolerance C{rtol} used to terminate the solution process. The iteration is terminated if
181
182            M{|g-v-Qp| <= atol + rtol * min( max( |g-v|, |Qp| ), max( |v|, |g-Qp| ) ) }
183
184            where C{atol} is an absolut tolerance (see L{setAbsoluteTolerance}), M{|f|^2 = integrate(length(f)^2)} and M{(Qp)_i=k_{ij}p_{,j}} for the permeability M{k_{ij}}.
185
186      def getFlux(self,p, fixed_flux=Data(),tol=1.e-8):          @param rtol: relative tolerance for the pressure
187            @type rtol: non-negative C{float}
188          """          """
189          returns the flux for a given pressure C{p} where the flux is equal to C{fixed_flux}          if rtol<0:
190          on locations where C{location_of_fixed_flux} is positive (see L{setValue}).              raise ValueError,"Relative tolerance needs to be non-negative."
191          Note that C{g} and C{f} are used, L{setValue}.          self.__rtol=rtol
192                def getTolerance(self):
@param p: pressure.
@type p: scalar value on the domain (e.g. L{Data}).
@param fixed_flux: flux on the locations of the domain marked be C{location_of_fixed_flux}.
@type fixed_flux: vector values on the domain (e.g. L{Data}).
@param tol: relative tolerance to be used.
@type tol: positive float.
@return: flux
@rtype: L{Data}
@note: the method uses the least squares solution M{u=(I+D^*D)^{-1}(D^*f-g-Qp)} where M{D} is the M{div} operator and M{(Qp)_i=k_{ij}p_{,j}}
for the permeability M{k_{ij}}
193          """          """
194          self.__pde_v.setTolerance(tol)          returns the relative tolerance
195          self.__pde_v.setValue(Y=self.__g, X=self.__f*util.kronecker(self.domain), r=boundary_flux)
196          return self.__pde_v.getSolution()          @return: current relative tolerance
197            @rtype: C{float}
198            """
199            return self.__rtol
200
201        def setAbsoluteTolerance(self,atol=0.):
202            """
203            sets the absolute tolerance C{atol} used to terminate the solution process. The iteration is terminated if
204
205            M{|g-v-Qp| <= atol + rtol * min( max( |g-v|, |Qp| ), max( |v|, |g-Qp| ) ) }
206
207            where C{rtol} is an absolut tolerance (see L{setTolerance}), M{|f|^2 = integrate(length(f)^2)} and M{(Qp)_i=k_{ij}p_{,j}} for the permeability M{k_{ij}}.
208
209      def solve(self,u0,p0,atol=0,rtol=1e-8, max_iter=100, verbose=False, show_details=False, sub_rtol=1.e-8):          @param atol: absolute tolerance for the pressure
210           """          @type atol: non-negative C{float}
211            """
212            if atol<0:
213                raise ValueError,"Absolute tolerance needs to be non-negative."
214            self.__atol=atol
215        def getAbsoluteTolerance(self):
216           """
217           returns the absolute tolerance
218
219           @return: current absolute tolerance
220           @rtype: C{float}
221           """
222           return self.__atol
223        def getSubProblemTolerance(self):
224        """
225        Returns a suitable subtolerance
226        @type: C{float}
227        """
228        return max(util.EPSILON**(0.75),self.getTolerance()**2)
229        def setSubProblemTolerance(self):
230             """
231             Sets the relative tolerance to solve the subproblem(s) if subtolerance adaption is selected.
232             """
234             sub_tol=self.getSubProblemTolerance()
235                 self.getSolverOptionsFlux().setTolerance(sub_tol)
236             self.getSolverOptionsFlux().setAbsoluteTolerance(0.)
237             self.getSolverOptionsPressure().setTolerance(sub_tol)
238             self.getSolverOptionsPressure().setAbsoluteTolerance(0.)
239             if self.verbose: print "DarcyFlux: relative subtolerance is set to %e."%sub_tol
240
241        def solve(self,u0,p0, max_iter=100, verbose=False, max_num_corrections=10):
242             """
243           solves the problem.           solves the problem.
244
245           The iteration is terminated if the error in the pressure is less then C{rtol * |q| + atol} where           The iteration is terminated if the residual norm is less then self.getTolerance().
C{|q|} denotes the norm of the right hand side (see escript user's guide for details).
246
247           @param u0: initial guess for the flux. At locations in the domain marked by C{location_of_fixed_flux} the value of C{u0} is kept unchanged.           @param u0: initial guess for the flux. At locations in the domain marked by C{location_of_fixed_flux} the value of C{u0} is kept unchanged.
248           @type u0: vector value on the domain (e.g. L{Data}).           @type u0: vector value on the domain (e.g. L{Data}).
249           @param p0: initial guess for the pressure. At locations in the domain marked by C{location_of_fixed_pressure} the value of C{p0} is kept unchanged.           @param p0: initial guess for the pressure. At locations in the domain marked by C{location_of_fixed_pressure} the value of C{p0} is kept unchanged.
250           @type p0: scalar value on the domain (e.g. L{Data}).           @type p0: scalar value on the domain (e.g. L{Data}).
@param atol: absolute tolerance for the pressure
@type atol: non-negative C{float}
@param rtol: relative tolerance for the pressure
@type rtol: non-negative C{float}
@param sub_rtol: tolerance to be used in the sub iteration. It is recommended that M{sub_rtol<rtol*5.e-3}
@type sub_rtol: positive-negative C{float}
251           @param verbose: if set some information on iteration progress are printed           @param verbose: if set some information on iteration progress are printed
252           @type verbose: C{bool}           @type verbose: C{bool}
@param show_details:  if set information on the subiteration process are printed.
@type show_details: C{bool}
253           @return: flux and pressure           @return: flux and pressure
254           @rtype: C{tuple} of L{Data}.           @rtype: C{tuple} of L{Data}.
255
256           @note: The problem is solved as a least squares form           @note: The problem is solved as a least squares form
257
258           M{(I+D^*D)u+Qp=D^*f+g}           M{(I+D^*D)u+Qp=D^*f+g}
259           M{Q^*u+Q^*Qp=Q^*g}           M{Q^*u+Q^*Qp=Q^*g}
260
261           where M{D} is the M{div} operator and M{(Qp)_i=k_{ij}p_{,j}} for the permeability M{k_{ij}}.           where M{D} is the M{div} operator and M{(Qp)_i=k_{ij}p_{,j}} for the permeability M{k_{ij}}.
262           We eliminate the flux form the problem by setting           We eliminate the flux form the problem by setting
263
264           M{u=(I+D^*D)^{-1}(D^*f-g-Qp)} with u=u0 on location_of_fixed_flux           M{u=(I+D^*D)^{-1}(D^*f-g-Qp)} with u=u0 on location_of_fixed_flux
265
266           form the first equation. Inserted into the second equation we get           form the first equation. Inserted into the second equation we get
267
268           M{Q^*(I-(I+D^*D)^{-1})Qp= Q^*(g-(I+D^*D)^{-1}(D^*f+g))} with p=p0  on location_of_fixed_pressure           M{Q^*(I-(I+D^*D)^{-1})Qp= Q^*(g-(I+D^*D)^{-1}(D^*f+g))} with p=p0  on location_of_fixed_pressure
269
270           which is solved using the PCG method (precondition is M{Q^*Q}). In each iteration step           which is solved using the PCG method (precondition is M{Q^*Q}). In each iteration step
271           PDEs with operator M{I+D^*D} and with M{Q^*Q} needs to be solved using a sub iteration scheme.           PDEs with operator M{I+D^*D} and with M{Q^*Q} needs to be solved using a sub iteration scheme.
272           """           """
273           self.verbose=verbose           self.verbose=verbose
274           self.show_details= show_details and self.verbose           rtol=self.getTolerance()
275           self.__pde_v.setTolerance(sub_rtol)           atol=self.getAbsoluteTolerance()
276           self.__pde_p.setTolerance(sub_rtol)       self.setSubProblemTolerance()
277           p2=p0*self.__pde_p.getCoefficient("q")
278           u2=u0*self.__pde_v.getCoefficient("q")           num_corrections=0
280           f=self.__f-util.div(u2)           p=p0
281           self.__pde_v.setValue(Y=g, X=f*util.kronecker(self.domain), r=Data())           norm_r=None
282           dv=self.__pde_v.getSolution(verbose=show_details)           while not converged:
283           self.__pde_p.setValue(X=util.transposed_tensor_mult(self.__permeability,g-dv))                 v=self.getFlux(p, fixed_flux=u0)
284           self.__pde_p.setValue(r=Data())                 Qp=self.__Q(p)
285           dp=self.__pde_p.getSolution(verbose=self.show_details)                 norm_v=self.__L2(v)
286           norm_rhs=self.__inner_PCG(dp,ArithmeticTuple(g,dv))                 norm_Qp=self.__L2(Qp)
287           if norm_rhs<0:                 if norm_v == 0.:
288               raise NegativeNorm,"negative norm. Maybe the sub-tolerance is too large."                    if norm_Qp == 0.:
289           ATOL=util.sqrt(norm_rhs)*rtol +atol                       return v,p
290           if not ATOL>0:                    else:
291               raise ValueError,"Negative absolute tolerance (rtol = %e, norm right hand side =%, atol =%e)."%(rtol, util.sqrt(norm_rhs), atol)                      fac=norm_Qp
292           rhs=ArithmeticTuple(g,dv)                 else:
293           dp,r=PCG(rhs,self.__Aprod_PCG,self.__Msolve_PCG,self.__inner_PCG,atol=ATOL, rtol=0.,iter_max=max_iter, x=p0, verbose=self.verbose, initial_guess=False)                    if norm_Qp == 0.:
294           return u2+r[1],p2+dp                      fac=norm_v
295                              else:
296      def __Aprod_PCG(self,p):                      fac=2./(1./norm_v+1./norm_Qp)
297            if self.show_details: print "DarcyFlux: Applying operator"                 ATOL=(atol+rtol*fac)
299            self.__pde_v.setValue(Y=Qp,X=Data())                      print "DarcyFlux: L2 norm of v = %e."%norm_v
300            w=self.__pde_v.getSolution(verbose=self.show_details)                      print "DarcyFlux: L2 norm of k.grad(p) = %e."%norm_Qp
301            return ArithmeticTuple(Qp,w)                      print "DarcyFlux: L2 defect u = %e."%(util.integrate(util.length(self.__g-util.interpolate(v,Function(self.domain))-Qp)**2)**(0.5),)
302                        print "DarcyFlux: L2 defect div(v) = %e."%(util.integrate((self.__f-util.div(v))**2)**(0.5),)
303                        print "DarcyFlux: absolute tolerance ATOL = %e."%ATOL
304                   if norm_r == None or norm_r>ATOL:
305                       if num_corrections>max_num_corrections:
306                             raise ValueError,"maximum number of correction steps reached."
307                       p,r, norm_r=PCG(self.__g-util.interpolate(v,Function(self.domain))-Qp,self.__Aprod,p,self.__Msolve_PCG,self.__inner_PCG,atol=0.5*ATOL, rtol=0.,iter_max=max_iter, verbose=self.verbose)
308                       num_corrections+=1
309                   else:
310                       converged=True
311             return v,p
312        def __L2(self,v):
313             return util.sqrt(util.integrate(util.length(util.interpolate(v,Function(self.domain)))**2))
314
315        def __Q(self,p):
317
318        def __Aprod(self,dp):
319              if self.getSolverOptionsFlux().isVerbose(): print "DarcyFlux: Applying operator"
320              Qdp=self.__Q(dp)
321              self.__pde_v.setValue(Y=-Qdp,X=Data(), r=Data())
322              du=self.__pde_v.getSolution()
323              # self.__pde_v.getOperator().saveMM("proj.mm")
324              return Qdp+du
325        def __inner_GMRES(self,r,s):
326             return util.integrate(util.inner(r,s))
327
328      def __inner_PCG(self,p,r):      def __inner_PCG(self,p,r):
return util.integrate(util.inner(a,r[0]-r[1]))
330
331      def __Msolve_PCG(self,r):      def __Msolve_PCG(self,r):
332            if self.show_details: print "DarcyFlux: Applying preconditioner"        if self.getSolverOptionsPressure().isVerbose(): print "DarcyFlux: Applying preconditioner"
333            self.__pde_p.setValue(X=util.transposed_tensor_mult(self.__permeability,r[0]-r[1]))            self.__pde_p.setValue(X=util.transposed_tensor_mult(self.__permeability,r), Y=Data(), r=Data())
334            return self.__pde_p.getSolution(verbose=self.show_details)            # self.__pde_p.getOperator().saveMM("prec.mm")
335              return self.__pde_p.getSolution()
336
337        def getFlux(self,p=None, fixed_flux=Data()):
338            """
339            returns the flux for a given pressure C{p} where the flux is equal to C{fixed_flux}
340            on locations where C{location_of_fixed_flux} is positive (see L{setValue}).
341            Note that C{g} and C{f} are used, see L{setValue}.
342
343            @param p: pressure.
344            @type p: scalar value on the domain (e.g. L{Data}).
345            @param fixed_flux: flux on the locations of the domain marked be C{location_of_fixed_flux}.
346            @type fixed_flux: vector values on the domain (e.g. L{Data}).
347            @param tol: relative tolerance to be used.
348            @type tol: positive C{float}.
349            @return: flux
350            @rtype: L{Data}
351            @note: the method uses the least squares solution M{u=(I+D^*D)^{-1}(D^*f-g-Qp)} where M{D} is the M{div} operator and M{(Qp)_i=k_{ij}p_{,j}}
352                   for the permeability M{k_{ij}}
353            """
354        self.setSubProblemTolerance()
355            g=self.__g
356            f=self.__f
357            self.__pde_v.setValue(X=self.__l*f*util.kronecker(self.domain), r=fixed_flux)
358            if p == None:
359               self.__pde_v.setValue(Y=g)
360            else:
361               self.__pde_v.setValue(Y=g-self.__Q(p))
362            return self.__pde_v.getSolution()
363
365        """       """
366        solves       solves
367
368            -(eta*(u_{i,j}+u_{j,i}))_j + p_i = f_i-stress_{ij,j}            -(eta*(u_{i,j}+u_{j,i}))_j + p_i = f_i-stress_{ij,j}
369                  u_{i,i}=0                  u_{i,i}=0
# Line 230  class StokesProblemCartesian(Homogeneous Line 371  class StokesProblemCartesian(Homogeneous
372            eta*(u_{i,j}+u_{j,i})*n_j-p*n_i=surface_stress +stress_{ij}n_j            eta*(u_{i,j}+u_{j,i})*n_j-p*n_i=surface_stress +stress_{ij}n_j
373
374        if surface_stress is not given 0 is assumed.       if surface_stress is not given 0 is assumed.
375
376        typical usage:       typical usage:
377
378              sp=StokesProblemCartesian(domain)              sp=StokesProblemCartesian(domain)
379              sp.setTolerance()              sp.setTolerance()
380              sp.initialize(...)              sp.initialize(...)
381              v,p=sp.solve(v0,p0)              v,p=sp.solve(v0,p0)
382        """       """
383        def __init__(self,domain,**kwargs):       def __init__(self,domain,adaptSubTolerance=True, **kwargs):
384           """           """
385           initialize the Stokes Problem           initialize the Stokes Problem
386
387           @param domain: domain of the problem. The approximation order needs to be two.           @param domain: domain of the problem. The approximation order needs to be two.
388           @type domain: L{Domain}           @type domain: L{Domain}
389         @param adaptSubTolerance: If True the tolerance for subproblem is set automatically.
391           @warning: The apprximation order needs to be two otherwise you may see oscilations in the pressure.           @warning: The apprximation order needs to be two otherwise you may see oscilations in the pressure.
392           """           """
394           self.domain=domain           self.domain=domain
395           self.vol=util.integrate(1.,Function(self.domain))           self.vol=util.integrate(1.,Function(self.domain))
396           self.__pde_u=LinearPDE(domain,numEquations=self.domain.getDim(),numSolutions=self.domain.getDim())           self.__pde_u=LinearPDE(domain,numEquations=self.domain.getDim(),numSolutions=self.domain.getDim())
397           self.__pde_u.setSymmetryOn()           self.__pde_u.setSymmetryOn()
398           # self.__pde_u.setSolverMethod(self.__pde_u.DIRECT)
# self.__pde_u.setSolverMethod(preconditioner=LinearPDE.RILU)

399           self.__pde_prec=LinearPDE(domain)           self.__pde_prec=LinearPDE(domain)
400           self.__pde_prec.setReducedOrderOn()           self.__pde_prec.setReducedOrderOn()
self.__pde_prec.setSolverMethod(self.__pde_prec.LUMPING)
401           self.__pde_prec.setSymmetryOn()           self.__pde_prec.setSymmetryOn()
402
403           self.__pde_proj=LinearPDE(domain)           self.__pde_proj=LinearPDE(domain)
404           self.__pde_proj.setReducedOrderOn()           self.__pde_proj.setReducedOrderOn()
405         self.__pde_proj.setValue(D=1)
406           self.__pde_proj.setSymmetryOn()           self.__pde_proj.setSymmetryOn()
self.__pde_proj.setValue(D=1.)
407
409             """
410         returns the solver options used  solve the equation for velocity.
411
412         @rtype: L{SolverOptions}
413         """
414         return self.__pde_u.getSolverOptions()
415         def setSolverOptionsVelocity(self, options=None):
416             """
417         set the solver options for solving the equation for velocity.
418
419         @param options: new solver  options
420         @type options: L{SolverOptions}
421         """
422             self.__pde_u.setSolverOptions(options)
423         def getSolverOptionsPressure(self):
424             """
425         returns the solver options used  solve the equation for pressure.
426         @rtype: L{SolverOptions}
427         """
428         return self.__pde_prec.getSolverOptions()
429         def setSolverOptionsPressure(self, options=None):
430             """
431         set the solver options for solving the equation for pressure.
432         @param options: new solver  options
433         @type options: L{SolverOptions}
434         """
435         self.__pde_prec.setSolverOptions(options)
436
437         def setSolverOptionsDiv(self, options=None):
438             """
439         set the solver options for solving the equation to project the divergence of
440         the velocity onto the function space of presure.
441
442         @param options: new solver options
443         @type options: L{SolverOptions}
444         """
445         self.__pde_prec.setSolverOptions(options)
446         def getSolverOptionsDiv(self):
447             """
448         returns the solver options for solving the equation to project the divergence of
449         the velocity onto the function space of presure.
450
451         @rtype: L{SolverOptions}
452         """
453         return self.__pde_prec.getSolverOptions()
454         def setSubProblemTolerance(self):
455             """
456         Updates the tolerance for subproblems
457             """
459                 sub_tol=self.getSubProblemTolerance()
460             self.getSolverOptionsDiv().setTolerance(sub_tol)
461             self.getSolverOptionsDiv().setAbsoluteTolerance(0.)
462             self.getSolverOptionsPressure().setTolerance(sub_tol)
463             self.getSolverOptionsPressure().setAbsoluteTolerance(0.)
464             self.getSolverOptionsVelocity().setTolerance(sub_tol)
465             self.getSolverOptionsVelocity().setAbsoluteTolerance(0.)
466
467
469          """          """
470          assigns values to the model parameters          assigns values to the model parameters
471
# Line 280  class StokesProblemCartesian(Homogeneous Line 480  class StokesProblemCartesian(Homogeneous
480          @param stress: initial stress          @param stress: initial stress
481      @type stress: L{Tensor} object on L{FunctionSpace} L{Function} or similar      @type stress: L{Tensor} object on L{FunctionSpace} L{Function} or similar
482          @note: All values needs to be set.          @note: All values needs to be set.

483          """          """
484          self.eta=eta          self.eta=eta
485          A =self.__pde_u.createCoefficient("A")          A =self.__pde_u.createCoefficient("A")
486      self.__pde_u.setValue(A=Data())      self.__pde_u.setValue(A=Data())
487          for i in range(self.domain.getDim()):          for i in range(self.domain.getDim()):
488          for j in range(self.domain.getDim()):          for j in range(self.domain.getDim()):
489              A[i,j,j,i] += 1.              A[i,j,j,i] += 1.
490              A[i,j,i,j] += 1.              A[i,j,i,j] += 1.
491      self.__pde_prec.setValue(D=1/self.eta)          n=self.domain.getNormal()
494            self.__f=f
495            self.__surface_stress=surface_stress
496          self.__stress=stress          self.__stress=stress
497
498        def B(self,v):       def Bv(self,v):
499          """           """
500          returns div(v)           returns inner product of element p and div(v)
@rtype: equal to the type of p
501
502          @note: boundary conditions on p should be zero!           @param p: a pressure increment
503          """           @param v: a residual
504          if self.show_details: print "apply divergence:"           @return: inner product of element p and div(v)
self.__pde_proj.setValue(Y=-util.div(v))
self.__pde_proj.setTolerance(self.getSubProblemTolerance())
return self.__pde_proj.getSolution(verbose=self.show_details)

def inner_pBv(self,p,Bv):
"""
returns inner product of element p and Bv  (overwrite)

@type p: equal to the type of p
@type Bv: equal to the type of result of operator B
505           @rtype: C{float}           @rtype: C{float}

@rtype: equal to the type of p
506           """           """
507           s0=util.interpolate(p,Function(self.domain))           self.__pde_proj.setValue(Y=-util.div(v))
508           s1=util.interpolate(Bv,Function(self.domain))           return self.__pde_proj.getSolution()
return util.integrate(s0*s1)
509
510        def inner_p(self,p0,p1):       def inner_pBv(self,p,Bv):
511           """           """
512           returns inner product of element p0 and p1  (overwrite)           returns inner product of element p and Bv=-div(v)
513
514           @type p0: equal to the type of p           @param p: a pressure increment
515           @type p1: equal to the type of p           @param v: a residual
516             @return: inner product of element p and Bv=-div(v)
517           @rtype: C{float}           @rtype: C{float}
518             """
519             return util.integrate(util.interpolate(p,Function(self.domain))*util.interpolate(Bv,Function(self.domain)))
520
521           @rtype: equal to the type of p       def inner_p(self,p0,p1):
522             """
523             Returns inner product of p0 and p1
524
525             @param p0: a pressure
526             @param p1: a pressure
527             @return: inner product of p0 and p1
528             @rtype: C{float}
529           """           """
530           s0=util.interpolate(p0/self.eta,Function(self.domain))           s0=util.interpolate(p0/self.eta,Function(self.domain))
531           s1=util.interpolate(p1/self.eta,Function(self.domain))           s1=util.interpolate(p1/self.eta,Function(self.domain))
532           return util.integrate(s0*s1)           return util.integrate(s0*s1)
533
534        def inner_v(self,v0,v1):       def norm_v(self,v):
535           """           """
536           returns inner product of two element v0 and v1  (overwrite)           returns the norm of v

@type v0: equal to the type of v
@type v1: equal to the type of v
@rtype: C{float}
537
538           @rtype: equal to the type of v           @param v: a velovity
539             @return: norm of v
540             @rtype: non-negative C{float}
541           """           """
return util.integrate(util.inner(gv0,gv1))
543
544        def solve_A(self,u,p):       def getV(self, p, v0):
545           """           """
546           solves Av=f-Au-B^*p (v=0 on fixed_u_mask)           return the value for v for a given p (overwrite)
547
548             @param p: a pressure
549             @param v0: a initial guess for the value v to return.
550             @return: v given as M{v= A^{-1} (f-B^*p)}
551           """           """
552           if self.show_details: print "solve for velocity:"           self.__pde_u.setValue(Y=self.__f, y=self.__surface_stress, r=v0)
self.__pde_u.setTolerance(self.getSubProblemTolerance())
553           if self.__stress.isEmpty():           if self.__stress.isEmpty():
555           else:           else:
557           out=self.__pde_u.getSolution(verbose=self.show_details)           out=self.__pde_u.getSolution()
558             return  out
559
560         def norm_Bv(self,Bv):
561            """
562            Returns Bv (overwrite).
563
564            @rtype: equal to the type of p
565            @note: boundary conditions on p should be zero!
566            """
567            return util.sqrt(util.integrate(util.interpolate(Bv,Function(self.domain))**2))
568
569         def solve_AinvBt(self,p):
570             """
571             Solves M{Av=B^*p} with accuracy L{self.getSubProblemTolerance()}
572
573             @param p: a pressure increment
574             @return: the solution of M{Av=B^*p}
575             @note: boundary conditions on v should be zero!
576             """
577             self.__pde_u.setValue(Y=Data(), y=Data(), r=Data(),X=-p*util.kronecker(self.domain))
578             out=self.__pde_u.getSolution()
579           return  out           return  out
580
581        def solve_prec(self,p):       def solve_prec(self,Bv):
582           if self.show_details: print "apply preconditioner:"           """
583           self.__pde_prec.setTolerance(self.getSubProblemTolerance())           applies preconditioner for for M{BA^{-1}B^*} to M{Bv}
584           self.__pde_prec.setValue(Y=p)           with accuracy L{self.getSubProblemTolerance()}
585           q=self.__pde_prec.getSolution(verbose=self.show_details)
586           return q           @param v: velocity increment
587             @return: M{p=P(Bv)} where M{P^{-1}} is an approximation of M{BA^{-1}B^*}
588             @note: boundary conditions on p are zero.
589             """
590             self.__pde_prec.setValue(Y=Bv)
591             return self.__pde_prec.getSolution()

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