/[escript]/trunk/escript/py_src/flows.py
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Wed Feb 11 06:48:28 2009 UTC (10 years, 7 months ago) by gross
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a new darcy flux solver.
1 ksteube 1809 ########################################################
2 gross 1414 #
3 ksteube 1809 # Copyright (c) 2003-2008 by University of Queensland
4     # Earth Systems Science Computational Center (ESSCC)
5     # http://www.uq.edu.au/esscc
6 gross 1414 #
7 ksteube 1809 # Primary Business: Queensland, Australia
8     # Licensed under the Open Software License version 3.0
9     # http://www.opensource.org/licenses/osl-3.0.php
10 gross 1414 #
11 ksteube 1809 ########################################################
12 gross 1414
13 ksteube 1809 __copyright__="""Copyright (c) 2003-2008 by University of Queensland
14     Earth Systems Science Computational Center (ESSCC)
15     http://www.uq.edu.au/esscc
16     Primary Business: Queensland, Australia"""
17     __license__="""Licensed under the Open Software License version 3.0
18     http://www.opensource.org/licenses/osl-3.0.php"""
19     __url__="http://www.uq.edu.au/esscc/escript-finley"
20    
21 gross 1414 """
22     Some models for flow
23    
24     @var __author__: name of author
25     @var __copyright__: copyrights
26     @var __license__: licence agreement
27     @var __url__: url entry point on documentation
28     @var __version__: version
29     @var __date__: date of the version
30     """
31    
32     __author__="Lutz Gross, l.gross@uq.edu.au"
33    
34     from escript import *
35     import util
36 gross 2100 from linearPDEs import LinearPDE, LinearPDESystem, LinearSinglePDE
37 gross 2264 from pdetools import HomogeneousSaddlePointProblem,Projector, ArithmeticTuple, PCG, NegativeNorm, GMRES
38 gross 1414
39 gross 2100 class DarcyFlow(object):
40     """
41 gross 2264 solves the problem
42 gross 1659
43 gross 2100 M{u_i+k_{ij}*p_{,j} = g_i}
44     M{u_{i,i} = f}
45 gross 1659
46 gross 2264 where M{p} represents the pressure and M{u} the Darcy flux. M{k} represents the permeability,
47 gross 1659
48 gross 2100 @note: The problem is solved in a least squares formulation.
49     """
50 gross 1659
51 gross 2208 def __init__(self, domain,useReduced=False):
52 gross 2100 """
53 gross 2208 initializes the Darcy flux problem
54 gross 2100 @param domain: domain of the problem
55     @type domain: L{Domain}
56     """
57     self.domain=domain
58     self.__pde_v=LinearPDESystem(domain)
59 gross 2208 if useReduced: self.__pde_v.setReducedOrderOn()
60     self.__pde_v.setSymmetryOn()
61 gross 2100 self.__pde_v.setValue(D=util.kronecker(domain), A=util.outer(util.kronecker(domain),util.kronecker(domain)))
62     self.__pde_p=LinearSinglePDE(domain)
63     self.__pde_p.setSymmetryOn()
64 gross 2208 if useReduced: self.__pde_p.setReducedOrderOn()
65 gross 2100 self.__f=Scalar(0,self.__pde_v.getFunctionSpaceForCoefficient("X"))
66     self.__g=Vector(0,self.__pde_v.getFunctionSpaceForCoefficient("Y"))
67 gross 2264 self.setTolerance()
68     self.setAbsoluteTolerance()
69     self.setSubProblemTolerance()
70 gross 1659
71 gross 2100 def setValue(self,f=None, g=None, location_of_fixed_pressure=None, location_of_fixed_flux=None, permeability=None):
72     """
73 gross 2208 assigns values to model parameters
74 gross 1659
75 gross 2208 @param f: volumetic sources/sinks
76     @type f: scalar value on the domain (e.g. L{Data})
77 gross 2100 @param g: flux sources/sinks
78 gross 2208 @type g: vector values on the domain (e.g. L{Data})
79 gross 2100 @param location_of_fixed_pressure: mask for locations where pressure is fixed
80 gross 2208 @type location_of_fixed_pressure: scalar value on the domain (e.g. L{Data})
81     @param location_of_fixed_flux: mask for locations where flux is fixed.
82     @type location_of_fixed_flux: vector values on the domain (e.g. L{Data})
83 gross 2264 @param permeability: permeability tensor. If scalar C{s} is given the tensor with
84     C{s} on the main diagonal is used. If vector C{v} is given the tensor with
85 gross 2208 C{v} on the main diagonal is used.
86     @type permeability: scalar, vector or tensor values on the domain (e.g. L{Data})
87 gross 1659
88 gross 2208 @note: the values of parameters which are not set by calling C{setValue} are not altered.
89     @note: at any point on the boundary of the domain the pressure (C{location_of_fixed_pressure} >0)
90     or the normal component of the flux (C{location_of_fixed_flux[i]>0} if direction of the normal
91     is along the M{x_i} axis.
92 gross 2100 """
93 gross 2264 if f !=None:
94 gross 2100 f=util.interpolate(f, self.__pde_v.getFunctionSpaceForCoefficient("X"))
95     if f.isEmpty():
96     f=Scalar(0,self.__pde_v.getFunctionSpaceForCoefficient("X"))
97     else:
98     if f.getRank()>0: raise ValueError,"illegal rank of f."
99     self.f=f
100 gross 2264 if g !=None:
101 gross 2100 g=util.interpolate(g, self.__pde_p.getFunctionSpaceForCoefficient("Y"))
102     if g.isEmpty():
103     g=Vector(0,self.__pde_v.getFunctionSpaceForCoefficient("Y"))
104     else:
105     if not g.getShape()==(self.domain.getDim(),):
106     raise ValueError,"illegal shape of g"
107     self.__g=g
108 gross 1659
109 gross 2100 if location_of_fixed_pressure!=None: self.__pde_p.setValue(q=location_of_fixed_pressure)
110     if location_of_fixed_flux!=None: self.__pde_v.setValue(q=location_of_fixed_flux)
111 gross 1659
112 gross 2100 if permeability!=None:
113     perm=util.interpolate(permeability,self.__pde_p.getFunctionSpaceForCoefficient("A"))
114     if perm.getRank()==0:
115     perm=perm*util.kronecker(self.domain.getDim())
116     elif perm.getRank()==1:
117     perm, perm2=Tensor(0.,self.__pde_p.getFunctionSpaceForCoefficient("A")), perm
118     for i in range(self.domain.getDim()): perm[i,i]=perm2[i]
119     elif perm.getRank()==2:
120     pass
121     else:
122     raise ValueError,"illegal rank of permeability."
123     self.__permeability=perm
124     self.__pde_p.setValue(A=util.transposed_tensor_mult(self.__permeability,self.__permeability))
125 gross 1659
126 gross 2264 def setTolerance(self,rtol=1e-4):
127     """
128     sets the relative tolerance C{rtol} used to terminate the solution process. The iteration is terminated if
129 gross 1659
130 gross 2264 M{|g-v-Qp| <= atol + rtol * min( max( |g-v|, |Qp| ), max( |v|, |g-Qp| ) ) }
131    
132     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}}.
133    
134     @param rtol: relative tolerance for the pressure
135     @type rtol: non-negative C{float}
136 gross 2100 """
137 gross 2264 if rtol<0:
138     raise ValueError,"Relative tolerance needs to be non-negative."
139     self.__rtol=rtol
140     def getTolerance(self):
141 gross 2100 """
142 gross 2264 returns the relative tolerance
143 gross 1659
144 gross 2264 @return: current relative tolerance
145     @rtype: C{float}
146 caltinay 2169 """
147 gross 2264 return self.__rtol
148 gross 1659
149 gross 2264 def setAbsoluteTolerance(self,atol=0.):
150 gross 2208 """
151 gross 2264 sets the absolute tolerance C{atol} used to terminate the solution process. The iteration is terminated if
152 gross 1659
153 gross 2264 M{|g-v-Qp| <= atol + rtol * min( max( |g-v|, |Qp| ), max( |v|, |g-Qp| ) ) }
154 gross 2208
155 gross 2264 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}}.
156 gross 2208
157 gross 2264 @param atol: absolute tolerance for the pressure
158     @type atol: non-negative C{float}
159     """
160     if atol<0:
161     raise ValueError,"Absolute tolerance needs to be non-negative."
162     self.__atol=atol
163     def getAbsoluteTolerance(self):
164     """
165     returns the absolute tolerance
166    
167     @return: current absolute tolerance
168     @rtype: C{float}
169     """
170     return self.__atol
171 gross 2208
172 gross 2264 def setSubProblemTolerance(self,rtol=None):
173     """
174     Sets the relative tolerance to solve the subproblem(s). If C{rtol} is not present
175     C{self.getTolerance()**2} is used.
176 gross 2208
177 gross 2264 @param rtol: relative tolerence
178     @type rtol: positive C{float}
179     """
180     if rtol == None:
181     if self.getTolerance()<=0.:
182     raise ValueError,"A positive relative tolerance must be set."
183     self.__sub_tol=max(util.EPSILON**(0.75),self.getTolerance()**2)
184     else:
185     if rtol<=0:
186     raise ValueError,"sub-problem tolerance must be positive."
187     self.__sub_tol=max(util.EPSILON**(0.75),rtol)
188 gross 2208
189 gross 2264 def getSubProblemTolerance(self):
190     """
191     Returns the subproblem reduction factor.
192 gross 2208
193 gross 2264 @return: subproblem reduction factor
194     @rtype: C{float}
195     """
196     return self.__sub_tol
197 gross 2208
198 gross 2264 def solve(self,u0,p0, max_iter=100, verbose=False, show_details=False, max_num_corrections=10):
199     """
200     solves the problem.
201 gross 1659
202 gross 2208 The iteration is terminated if the residual norm is less then self.getTolerance().
203 gross 1659
204 gross 2208 @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.
205     @type u0: vector value on the domain (e.g. L{Data}).
206     @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.
207     @type p0: scalar value on the domain (e.g. L{Data}).
208     @param verbose: if set some information on iteration progress are printed
209     @type verbose: C{bool}
210     @param show_details: if set information on the subiteration process are printed.
211     @type show_details: C{bool}
212     @return: flux and pressure
213     @rtype: C{tuple} of L{Data}.
214 gross 2264
215 gross 2208 @note: The problem is solved as a least squares form
216 gross 2100
217 gross 2208 M{(I+D^*D)u+Qp=D^*f+g}
218     M{Q^*u+Q^*Qp=Q^*g}
219 gross 2100
220 gross 2264 where M{D} is the M{div} operator and M{(Qp)_i=k_{ij}p_{,j}} for the permeability M{k_{ij}}.
221     We eliminate the flux form the problem by setting
222 caltinay 2169
223 gross 2208 M{u=(I+D^*D)^{-1}(D^*f-g-Qp)} with u=u0 on location_of_fixed_flux
224 caltinay 2169
225 gross 2208 form the first equation. Inserted into the second equation we get
226 caltinay 2169
227 gross 2208 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
228 gross 2264
229     which is solved using the PCG method (precondition is M{Q^*Q}). In each iteration step
230 gross 2208 PDEs with operator M{I+D^*D} and with M{Q^*Q} needs to be solved using a sub iteration scheme.
231     """
232     self.verbose=verbose
233     self.show_details= show_details and self.verbose
234 gross 2264 rtol=self.getTolerance()
235     atol=self.getAbsoluteTolerance()
236     if self.verbose: print "DarcyFlux: initial sub tolerance = %e"%self.getSubProblemTolerance()
237 caltinay 2169
238 gross 2264 num_corrections=0
239     converged=False
240     p=p0
241     norm_r=None
242     while not converged:
243     v=self.getFlux(p, fixed_flux=u0, show_details=self.show_details)
244     Qp=self.__Q(p)
245     norm_v=self.__L2(v)
246     norm_Qp=self.__L2(Qp)
247     if norm_v == 0.:
248     if norm_Qp == 0.:
249     return v,p
250     else:
251     fac=norm_Qp
252     else:
253     if norm_Qp == 0.:
254     fac=norm_v
255     else:
256     fac=2./(1./norm_v+1./norm_Qp)
257     ATOL=(atol+rtol*fac)
258     if self.verbose:
259     print "DarcyFlux: L2 norm of v = %e."%norm_v
260     print "DarcyFlux: L2 norm of k.grad(p) = %e."%norm_Qp
261     print "DarcyFlux: absolute tolerance ATOL = %e."%ATOL
262     if norm_r == None or norm_r>ATOL:
263     if num_corrections>max_num_corrections:
264     raise ValueError,"maximum number of correction steps reached."
265     p,r, norm_r=PCG(self.__g-util.interpolate(v,Function(self.domain))-Qp,self.__Aprod,p,self.__Msolve_PCG,self.__inner_PCG,atol=0.1*ATOL, rtol=0.,iter_max=max_iter, verbose=self.verbose)
266     num_corrections+=1
267     else:
268     converged=True
269     return v,p
270     #
271     #
272     # r_hat=g-util.interpolate(v,Function(self.domain))-Qp
273     # #===========================================================================
274     # norm_r_hat=self.__L2(r_hat)
275     # norm_v=self.__L2(v)
276     # norm_g=self.__L2(g)
277     # norm_gv=self.__L2(g-v)
278     # norm_Qp=self.__L2(Qp)
279     # norm_gQp=self.__L2(g-Qp)
280     # fac=min(max(norm_v,norm_gQp),max(norm_Qp,norm_gv))
281     # fac=min(norm_v,norm_Qp,norm_gv)
282     # norm_r_hat_PCG=util.sqrt(self.__inner_PCG(self.__Msolve_PCG(r_hat),r_hat))
283     # print "norm_r_hat = ",norm_r_hat,norm_r_hat_PCG, norm_r_hat_PCG/norm_r_hat
284     # if r!=None:
285     # print "diff = ",self.__L2(r-r_hat)/norm_r_hat
286     # sub_tol=min(rtol/self.__L2(r-r_hat)*norm_r_hat,1.)*self.getSubProblemTolerance()
287     # self.setSubProblemTolerance(sub_tol)
288     # print "subtol_new=",self.getSubProblemTolerance()
289     # print "norm_v = ",norm_v
290     # print "norm_gv = ",norm_gv
291     # print "norm_Qp = ",norm_Qp
292     # print "norm_gQp = ",norm_gQp
293     # print "norm_g = ",norm_g
294     # print "max(norm_v,norm_gQp)=",max(norm_v,norm_gQp)
295     # print "max(norm_Qp,norm_gv)=",max(norm_Qp,norm_gv)
296     # if fac == 0:
297     # if self.verbose: print "DarcyFlux: trivial case!"
298     # return v,p
299     # #===============================================================================
300     # # norm_v=util.sqrt(self.__inner_PCG(self.__Msolve_PCG(v),v))
301     # # norm_Qp=self.__L2(Qp)
302     # norm_r_hat=util.sqrt(self.__inner_PCG(self.__Msolve_PCG(r_hat),r_hat))
303     # # print "**** norm_v, norm_Qp :",norm_v,norm_Qp
304     #
305     # ATOL=(atol+rtol*2./(1./norm_v+1./norm_Qp))
306     # if self.verbose:
307     # print "DarcyFlux: residual = %e"%norm_r_hat
308     # print "DarcyFlux: absolute tolerance ATOL = %e."%ATOL
309     # if norm_r_hat <= ATOL:
310     # print "DarcyFlux: iteration finalized."
311     # converged=True
312     # else:
313     # # p=GMRES(r_hat,self.__Aprod, p, self.__inner_GMRES, atol=ATOL, rtol=0., iter_max=max_iter, iter_restart=20, verbose=self.verbose,P_R=self.__Msolve_PCG)
314     # # p,r=PCG(r_hat,self.__Aprod,p,self.__Msolve_PCG,self.__inner_PCG,atol=ATOL*min(0.1,norm_r_hat_PCG/norm_r_hat), rtol=0.,iter_max=max_iter, verbose=self.verbose)
315     # p,r, norm_r=PCG(r_hat,self.__Aprod,p,self.__Msolve_PCG,self.__inner_PCG,atol=0.1*ATOL, rtol=0.,iter_max=max_iter, verbose=self.verbose)
316     # print "norm_r =",norm_r
317     # return v,p
318     def __L2(self,v):
319     return util.sqrt(util.integrate(util.length(util.interpolate(v,Function(self.domain)))**2))
320    
321     def __Q(self,p):
322     return util.tensor_mult(self.__permeability,util.grad(p))
323    
324     def __Aprod(self,dp):
325     self.__pde_v.setTolerance(self.getSubProblemTolerance())
326 gross 2208 if self.show_details: print "DarcyFlux: Applying operator"
327 gross 2264 Qdp=self.__Q(dp)
328     self.__pde_v.setValue(Y=-Qdp,X=Data(), r=Data())
329 gross 2208 du=self.__pde_v.getSolution(verbose=self.show_details)
330 gross 2264 return Qdp+du
331     def __inner_GMRES(self,r,s):
332     return util.integrate(util.inner(r,s))
333    
334 gross 2100 def __inner_PCG(self,p,r):
335 gross 2264 return util.integrate(util.inner(self.__Q(p), r))
336 gross 2100
337     def __Msolve_PCG(self,r):
338 gross 2264 self.__pde_p.setTolerance(self.getSubProblemTolerance())
339 gross 2208 if self.show_details: print "DarcyFlux: Applying preconditioner"
340 gross 2264 self.__pde_p.setValue(X=util.transposed_tensor_mult(self.__permeability,r), Y=Data(), r=Data())
341 gross 2208 return self.__pde_p.getSolution(verbose=self.show_details)
342 gross 2100
343 gross 2264
344     def getFlux(self,p=None, fixed_flux=Data(), show_details=False):
345     """
346     returns the flux for a given pressure C{p} where the flux is equal to C{fixed_flux}
347     on locations where C{location_of_fixed_flux} is positive (see L{setValue}).
348     Note that C{g} and C{f} are used, see L{setValue}.
349    
350     @param p: pressure.
351     @type p: scalar value on the domain (e.g. L{Data}).
352     @param fixed_flux: flux on the locations of the domain marked be C{location_of_fixed_flux}.
353     @type fixed_flux: vector values on the domain (e.g. L{Data}).
354     @param tol: relative tolerance to be used.
355     @type tol: positive C{float}.
356     @return: flux
357     @rtype: L{Data}
358     @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}}
359     for the permeability M{k_{ij}}
360     """
361     self.__pde_v.setTolerance(self.getSubProblemTolerance())
362     g=self.__g
363     f=self.__f
364     self.__pde_v.setValue(X=f*util.kronecker(self.domain), r=fixed_flux)
365     if p == None:
366     self.__pde_v.setValue(Y=g)
367     else:
368     self.__pde_v.setValue(Y=g-self.__Q(p))
369     return self.__pde_v.getSolution(verbose=show_details)
370    
371 gross 1414 class StokesProblemCartesian(HomogeneousSaddlePointProblem):
372 gross 2251 """
373 gross 2264 solves
374 gross 1414
375 gross 2208 -(eta*(u_{i,j}+u_{j,i}))_j + p_i = f_i-stress_{ij,j}
376     u_{i,i}=0
377 gross 1414
378 gross 2208 u=0 where fixed_u_mask>0
379     eta*(u_{i,j}+u_{j,i})*n_j-p*n_i=surface_stress +stress_{ij}n_j
380 gross 1414
381 gross 2264 if surface_stress is not given 0 is assumed.
382 gross 1414
383 gross 2251 typical usage:
384 gross 1414
385 gross 2208 sp=StokesProblemCartesian(domain)
386     sp.setTolerance()
387     sp.initialize(...)
388     v,p=sp.solve(v0,p0)
389 gross 2251 """
390     def __init__(self,domain,**kwargs):
391 gross 2100 """
392 gross 2208 initialize the Stokes Problem
393 gross 2100
394 gross 2208 @param domain: domain of the problem. The approximation order needs to be two.
395 gross 2100 @type domain: L{Domain}
396 gross 2208 @warning: The apprximation order needs to be two otherwise you may see oscilations in the pressure.
397 gross 2100 """
398 gross 1414 HomogeneousSaddlePointProblem.__init__(self,**kwargs)
399     self.domain=domain
400     self.vol=util.integrate(1.,Function(self.domain))
401     self.__pde_u=LinearPDE(domain,numEquations=self.domain.getDim(),numSolutions=self.domain.getDim())
402     self.__pde_u.setSymmetryOn()
403 gross 2100 # self.__pde_u.setSolverMethod(self.__pde_u.DIRECT)
404     # self.__pde_u.setSolverMethod(preconditioner=LinearPDE.RILU)
405 gross 2264
406 gross 1414 self.__pde_prec=LinearPDE(domain)
407     self.__pde_prec.setReducedOrderOn()
408 gross 2156 # self.__pde_prec.setSolverMethod(self.__pde_prec.LUMPING)
409 gross 1414 self.__pde_prec.setSymmetryOn()
410    
411 gross 2251 def initialize(self,f=Data(),fixed_u_mask=Data(),eta=1,surface_stress=Data(),stress=Data()):
412 gross 2208 """
413     assigns values to the model parameters
414 gross 2100
415 gross 2208 @param f: external force
416     @type f: L{Vector} object in L{FunctionSpace} L{Function} or similar
417     @param fixed_u_mask: mask of locations with fixed velocity.
418     @type fixed_u_mask: L{Vector} object on L{FunctionSpace} L{Solution} or similar
419     @param eta: viscosity
420     @type eta: L{Scalar} object on L{FunctionSpace} L{Function} or similar
421     @param surface_stress: normal surface stress
422     @type eta: L{Vector} object on L{FunctionSpace} L{FunctionOnBoundary} or similar
423     @param stress: initial stress
424     @type stress: L{Tensor} object on L{FunctionSpace} L{Function} or similar
425     @note: All values needs to be set.
426 gross 2264
427 gross 2208 """
428     self.eta=eta
429     A =self.__pde_u.createCoefficient("A")
430     self.__pde_u.setValue(A=Data())
431     for i in range(self.domain.getDim()):
432     for j in range(self.domain.getDim()):
433 gross 2264 A[i,j,j,i] += 1.
434 gross 2208 A[i,j,i,j] += 1.
435 gross 2264 self.__pde_prec.setValue(D=1/self.eta)
436 gross 2251 self.__pde_u.setValue(A=A*self.eta,q=fixed_u_mask)
437     self.__f=f
438     self.__surface_stress=surface_stress
439 gross 2208 self.__stress=stress
440 gross 1414
441 gross 2251 def inner_pBv(self,p,v):
442     """
443     returns inner product of element p and div(v)
444 gross 1414
445 gross 2251 @param p: a pressure increment
446     @param v: a residual
447     @return: inner product of element p and div(v)
448     @rtype: C{float}
449 gross 2100 """
450 gross 2251 return util.integrate(-p*util.div(v))
451 gross 2208
452 gross 2251 def inner_p(self,p0,p1):
453 gross 2100 """
454 gross 2251 Returns inner product of p0 and p1
455 gross 1414
456 gross 2251 @param p0: a pressure
457     @param p1: a pressure
458     @return: inner product of p0 and p1
459 gross 2208 @rtype: C{float}
460 gross 2100 """
461     s0=util.interpolate(p0/self.eta,Function(self.domain))
462     s1=util.interpolate(p1/self.eta,Function(self.domain))
463     return util.integrate(s0*s1)
464 artak 1550
465 gross 2251 def norm_v(self,v):
466 gross 2100 """
467 gross 2251 returns the norm of v
468 gross 2208
469 gross 2251 @param v: a velovity
470     @return: norm of v
471     @rtype: non-negative C{float}
472 gross 2100 """
473 gross 2251 return util.sqrt(util.integrate(util.length(util.grad(v))))
474 gross 2100
475 gross 2251 def getV(self, p, v0):
476 gross 1414 """
477 gross 2251 return the value for v for a given p (overwrite)
478    
479     @param p: a pressure
480 gross 2264 @param v0: a initial guess for the value v to return.
481 gross 2251 @return: v given as M{v= A^{-1} (f-B^*p)}
482 gross 1414 """
483     self.__pde_u.setTolerance(self.getSubProblemTolerance())
484 gross 2251 self.__pde_u.setValue(Y=self.__f, y=self.__surface_stress, r=v0)
485 gross 2100 if self.__stress.isEmpty():
486 gross 2251 self.__pde_u.setValue(X=p*util.kronecker(self.domain))
487 gross 2100 else:
488 gross 2251 self.__pde_u.setValue(X=self.__stress+p*util.kronecker(self.domain))
489 gross 2100 out=self.__pde_u.getSolution(verbose=self.show_details)
490 gross 2208 return out
491 gross 1414
492 gross 2251
493     raise NotImplementedError,"no v calculation implemented."
494    
495 gross 2264
496 gross 2251 def norm_Bv(self,v):
497     """
498     Returns Bv (overwrite).
499    
500     @rtype: equal to the type of p
501     @note: boundary conditions on p should be zero!
502     """
503     return util.sqrt(util.integrate(util.div(v)**2))
504    
505     def solve_AinvBt(self,p):
506     """
507     Solves M{Av=B^*p} with accuracy L{self.getSubProblemTolerance()}
508    
509     @param p: a pressure increment
510 gross 2264 @return: the solution of M{Av=B^*p}
511 gross 2251 @note: boundary conditions on v should be zero!
512     """
513     self.__pde_u.setTolerance(self.getSubProblemTolerance())
514     self.__pde_u.setValue(Y=Data(), y=Data(), r=Data(),X=-p*util.kronecker(self.domain))
515     out=self.__pde_u.getSolution(verbose=self.show_details)
516     return out
517    
518     def solve_precB(self,v):
519     """
520     applies preconditioner for for M{BA^{-1}B^*} to M{Bv}
521     with accuracy L{self.getSubProblemTolerance()} (overwrite).
522    
523     @param v: velocity increment
524     @return: M{p=P(Bv)} where M{P^{-1}} is an approximation of M{BA^{-1}B^*}
525     @note: boundary conditions on p are zero.
526     """
527     self.__pde_prec.setValue(Y=-util.div(v))
528 gross 1414 self.__pde_prec.setTolerance(self.getSubProblemTolerance())
529 gross 2251 return self.__pde_prec.getSolution(verbose=self.show_details)

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