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Revision 2351 - (hide annotations)
Tue Mar 31 08:26:41 2009 UTC (10 years, 5 months ago) by gross
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some fixes in the transport 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 jfenwick 2344 __url__="https://launchpad.net/escript-finley"
20 ksteube 1809
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 2351 def __init__(self, domain, weight=None, 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 gross 2351 if weight == None:
59     self.__l=10.*util.longestEdge(self.domain)**2
60     else:
61     self.__l=weight
62 gross 2100 self.__pde_v=LinearPDESystem(domain)
63 gross 2208 if useReduced: self.__pde_v.setReducedOrderOn()
64     self.__pde_v.setSymmetryOn()
65 gross 2267 self.__pde_v.setValue(D=util.kronecker(domain), A=self.__l*util.outer(util.kronecker(domain),util.kronecker(domain)))
66 gross 2351 # self.__pde_v.setSolverMethod(preconditioner=self.__pde_v.ILU0)
67 gross 2100 self.__pde_p=LinearSinglePDE(domain)
68     self.__pde_p.setSymmetryOn()
69 gross 2208 if useReduced: self.__pde_p.setReducedOrderOn()
70 gross 2100 self.__f=Scalar(0,self.__pde_v.getFunctionSpaceForCoefficient("X"))
71     self.__g=Vector(0,self.__pde_v.getFunctionSpaceForCoefficient("Y"))
72 gross 2264 self.setTolerance()
73     self.setAbsoluteTolerance()
74     self.setSubProblemTolerance()
75 gross 1659
76 gross 2100 def setValue(self,f=None, g=None, location_of_fixed_pressure=None, location_of_fixed_flux=None, permeability=None):
77     """
78 gross 2208 assigns values to model parameters
79 gross 1659
80 gross 2208 @param f: volumetic sources/sinks
81     @type f: scalar value on the domain (e.g. L{Data})
82 gross 2100 @param g: flux sources/sinks
83 gross 2208 @type g: vector values on the domain (e.g. L{Data})
84 gross 2100 @param location_of_fixed_pressure: mask for locations where pressure is fixed
85 gross 2208 @type location_of_fixed_pressure: scalar value on the domain (e.g. L{Data})
86     @param location_of_fixed_flux: mask for locations where flux is fixed.
87     @type location_of_fixed_flux: vector values on the domain (e.g. L{Data})
88 gross 2264 @param permeability: permeability tensor. If scalar C{s} is given the tensor with
89     C{s} on the main diagonal is used. If vector C{v} is given the tensor with
90 gross 2208 C{v} on the main diagonal is used.
91     @type permeability: scalar, vector or tensor values on the domain (e.g. L{Data})
92 gross 1659
93 gross 2208 @note: the values of parameters which are not set by calling C{setValue} are not altered.
94     @note: at any point on the boundary of the domain the pressure (C{location_of_fixed_pressure} >0)
95     or the normal component of the flux (C{location_of_fixed_flux[i]>0} if direction of the normal
96     is along the M{x_i} axis.
97 gross 2100 """
98 gross 2264 if f !=None:
99 gross 2100 f=util.interpolate(f, self.__pde_v.getFunctionSpaceForCoefficient("X"))
100     if f.isEmpty():
101     f=Scalar(0,self.__pde_v.getFunctionSpaceForCoefficient("X"))
102     else:
103     if f.getRank()>0: raise ValueError,"illegal rank of f."
104 gross 2267 self.__f=f
105 gross 2264 if g !=None:
106 gross 2100 g=util.interpolate(g, self.__pde_p.getFunctionSpaceForCoefficient("Y"))
107     if g.isEmpty():
108     g=Vector(0,self.__pde_v.getFunctionSpaceForCoefficient("Y"))
109     else:
110     if not g.getShape()==(self.domain.getDim(),):
111     raise ValueError,"illegal shape of g"
112     self.__g=g
113 gross 1659
114 gross 2100 if location_of_fixed_pressure!=None: self.__pde_p.setValue(q=location_of_fixed_pressure)
115     if location_of_fixed_flux!=None: self.__pde_v.setValue(q=location_of_fixed_flux)
116 gross 1659
117 gross 2100 if permeability!=None:
118     perm=util.interpolate(permeability,self.__pde_p.getFunctionSpaceForCoefficient("A"))
119     if perm.getRank()==0:
120     perm=perm*util.kronecker(self.domain.getDim())
121     elif perm.getRank()==1:
122     perm, perm2=Tensor(0.,self.__pde_p.getFunctionSpaceForCoefficient("A")), perm
123     for i in range(self.domain.getDim()): perm[i,i]=perm2[i]
124     elif perm.getRank()==2:
125     pass
126     else:
127     raise ValueError,"illegal rank of permeability."
128     self.__permeability=perm
129     self.__pde_p.setValue(A=util.transposed_tensor_mult(self.__permeability,self.__permeability))
130 gross 1659
131 gross 2264 def setTolerance(self,rtol=1e-4):
132     """
133     sets the relative tolerance C{rtol} used to terminate the solution process. The iteration is terminated if
134 gross 1659
135 gross 2264 M{|g-v-Qp| <= atol + rtol * min( max( |g-v|, |Qp| ), max( |v|, |g-Qp| ) ) }
136    
137     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}}.
138    
139     @param rtol: relative tolerance for the pressure
140     @type rtol: non-negative C{float}
141 gross 2100 """
142 gross 2264 if rtol<0:
143     raise ValueError,"Relative tolerance needs to be non-negative."
144     self.__rtol=rtol
145     def getTolerance(self):
146 gross 2100 """
147 gross 2264 returns the relative tolerance
148 gross 1659
149 gross 2264 @return: current relative tolerance
150     @rtype: C{float}
151 caltinay 2169 """
152 gross 2264 return self.__rtol
153 gross 1659
154 gross 2264 def setAbsoluteTolerance(self,atol=0.):
155 gross 2208 """
156 gross 2264 sets the absolute tolerance C{atol} used to terminate the solution process. The iteration is terminated if
157 gross 1659
158 gross 2264 M{|g-v-Qp| <= atol + rtol * min( max( |g-v|, |Qp| ), max( |v|, |g-Qp| ) ) }
159 gross 2208
160 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}}.
161 gross 2208
162 gross 2264 @param atol: absolute tolerance for the pressure
163     @type atol: non-negative C{float}
164     """
165     if atol<0:
166     raise ValueError,"Absolute tolerance needs to be non-negative."
167     self.__atol=atol
168     def getAbsoluteTolerance(self):
169     """
170     returns the absolute tolerance
171    
172     @return: current absolute tolerance
173     @rtype: C{float}
174     """
175     return self.__atol
176 gross 2208
177 gross 2264 def setSubProblemTolerance(self,rtol=None):
178     """
179     Sets the relative tolerance to solve the subproblem(s). If C{rtol} is not present
180     C{self.getTolerance()**2} is used.
181 gross 2208
182 gross 2264 @param rtol: relative tolerence
183     @type rtol: positive C{float}
184     """
185     if rtol == None:
186     if self.getTolerance()<=0.:
187     raise ValueError,"A positive relative tolerance must be set."
188     self.__sub_tol=max(util.EPSILON**(0.75),self.getTolerance()**2)
189     else:
190     if rtol<=0:
191     raise ValueError,"sub-problem tolerance must be positive."
192     self.__sub_tol=max(util.EPSILON**(0.75),rtol)
193 gross 2208
194 gross 2264 def getSubProblemTolerance(self):
195     """
196     Returns the subproblem reduction factor.
197 gross 2208
198 gross 2264 @return: subproblem reduction factor
199     @rtype: C{float}
200     """
201     return self.__sub_tol
202 gross 2208
203 gross 2264 def solve(self,u0,p0, max_iter=100, verbose=False, show_details=False, max_num_corrections=10):
204     """
205     solves the problem.
206 gross 1659
207 gross 2208 The iteration is terminated if the residual norm is less then self.getTolerance().
208 gross 1659
209 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.
210     @type u0: vector value on the domain (e.g. L{Data}).
211     @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.
212     @type p0: scalar value on the domain (e.g. L{Data}).
213     @param verbose: if set some information on iteration progress are printed
214     @type verbose: C{bool}
215     @param show_details: if set information on the subiteration process are printed.
216     @type show_details: C{bool}
217     @return: flux and pressure
218     @rtype: C{tuple} of L{Data}.
219 gross 2264
220 gross 2208 @note: The problem is solved as a least squares form
221 gross 2100
222 gross 2208 M{(I+D^*D)u+Qp=D^*f+g}
223     M{Q^*u+Q^*Qp=Q^*g}
224 gross 2100
225 gross 2264 where M{D} is the M{div} operator and M{(Qp)_i=k_{ij}p_{,j}} for the permeability M{k_{ij}}.
226     We eliminate the flux form the problem by setting
227 caltinay 2169
228 gross 2208 M{u=(I+D^*D)^{-1}(D^*f-g-Qp)} with u=u0 on location_of_fixed_flux
229 caltinay 2169
230 gross 2208 form the first equation. Inserted into the second equation we get
231 caltinay 2169
232 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
233 gross 2264
234     which is solved using the PCG method (precondition is M{Q^*Q}). In each iteration step
235 gross 2208 PDEs with operator M{I+D^*D} and with M{Q^*Q} needs to be solved using a sub iteration scheme.
236     """
237 gross 2277 self.verbose=verbose or True
238 gross 2208 self.show_details= show_details and self.verbose
239 gross 2264 rtol=self.getTolerance()
240     atol=self.getAbsoluteTolerance()
241     if self.verbose: print "DarcyFlux: initial sub tolerance = %e"%self.getSubProblemTolerance()
242 caltinay 2169
243 gross 2264 num_corrections=0
244     converged=False
245     p=p0
246     norm_r=None
247     while not converged:
248     v=self.getFlux(p, fixed_flux=u0, show_details=self.show_details)
249     Qp=self.__Q(p)
250     norm_v=self.__L2(v)
251     norm_Qp=self.__L2(Qp)
252     if norm_v == 0.:
253     if norm_Qp == 0.:
254     return v,p
255     else:
256     fac=norm_Qp
257     else:
258     if norm_Qp == 0.:
259     fac=norm_v
260     else:
261     fac=2./(1./norm_v+1./norm_Qp)
262     ATOL=(atol+rtol*fac)
263     if self.verbose:
264     print "DarcyFlux: L2 norm of v = %e."%norm_v
265     print "DarcyFlux: L2 norm of k.grad(p) = %e."%norm_Qp
266     print "DarcyFlux: absolute tolerance ATOL = %e."%ATOL
267     if norm_r == None or norm_r>ATOL:
268     if num_corrections>max_num_corrections:
269     raise ValueError,"maximum number of correction steps reached."
270     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)
271     num_corrections+=1
272     else:
273     converged=True
274     return v,p
275     #
276     #
277     # r_hat=g-util.interpolate(v,Function(self.domain))-Qp
278     # #===========================================================================
279     # norm_r_hat=self.__L2(r_hat)
280     # norm_v=self.__L2(v)
281     # norm_g=self.__L2(g)
282     # norm_gv=self.__L2(g-v)
283     # norm_Qp=self.__L2(Qp)
284     # norm_gQp=self.__L2(g-Qp)
285     # fac=min(max(norm_v,norm_gQp),max(norm_Qp,norm_gv))
286     # fac=min(norm_v,norm_Qp,norm_gv)
287     # norm_r_hat_PCG=util.sqrt(self.__inner_PCG(self.__Msolve_PCG(r_hat),r_hat))
288     # print "norm_r_hat = ",norm_r_hat,norm_r_hat_PCG, norm_r_hat_PCG/norm_r_hat
289     # if r!=None:
290     # print "diff = ",self.__L2(r-r_hat)/norm_r_hat
291     # sub_tol=min(rtol/self.__L2(r-r_hat)*norm_r_hat,1.)*self.getSubProblemTolerance()
292     # self.setSubProblemTolerance(sub_tol)
293     # print "subtol_new=",self.getSubProblemTolerance()
294     # print "norm_v = ",norm_v
295     # print "norm_gv = ",norm_gv
296     # print "norm_Qp = ",norm_Qp
297     # print "norm_gQp = ",norm_gQp
298     # print "norm_g = ",norm_g
299     # print "max(norm_v,norm_gQp)=",max(norm_v,norm_gQp)
300     # print "max(norm_Qp,norm_gv)=",max(norm_Qp,norm_gv)
301     # if fac == 0:
302     # if self.verbose: print "DarcyFlux: trivial case!"
303     # return v,p
304     # #===============================================================================
305     # # norm_v=util.sqrt(self.__inner_PCG(self.__Msolve_PCG(v),v))
306     # # norm_Qp=self.__L2(Qp)
307     # norm_r_hat=util.sqrt(self.__inner_PCG(self.__Msolve_PCG(r_hat),r_hat))
308     # # print "**** norm_v, norm_Qp :",norm_v,norm_Qp
309     #
310     # ATOL=(atol+rtol*2./(1./norm_v+1./norm_Qp))
311     # if self.verbose:
312     # print "DarcyFlux: residual = %e"%norm_r_hat
313     # print "DarcyFlux: absolute tolerance ATOL = %e."%ATOL
314     # if norm_r_hat <= ATOL:
315     # print "DarcyFlux: iteration finalized."
316     # converged=True
317     # else:
318     # # 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)
319     # # 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)
320     # 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)
321     # print "norm_r =",norm_r
322     # return v,p
323     def __L2(self,v):
324     return util.sqrt(util.integrate(util.length(util.interpolate(v,Function(self.domain)))**2))
325    
326     def __Q(self,p):
327     return util.tensor_mult(self.__permeability,util.grad(p))
328    
329     def __Aprod(self,dp):
330     self.__pde_v.setTolerance(self.getSubProblemTolerance())
331 gross 2208 if self.show_details: print "DarcyFlux: Applying operator"
332 gross 2264 Qdp=self.__Q(dp)
333     self.__pde_v.setValue(Y=-Qdp,X=Data(), r=Data())
334 gross 2349 du=self.__pde_v.getSolution(verbose=self.show_details, iter_max = 100000)
335 gross 2264 return Qdp+du
336     def __inner_GMRES(self,r,s):
337     return util.integrate(util.inner(r,s))
338    
339 gross 2100 def __inner_PCG(self,p,r):
340 gross 2264 return util.integrate(util.inner(self.__Q(p), r))
341 gross 2100
342     def __Msolve_PCG(self,r):
343 gross 2264 self.__pde_p.setTolerance(self.getSubProblemTolerance())
344 gross 2208 if self.show_details: print "DarcyFlux: Applying preconditioner"
345 gross 2264 self.__pde_p.setValue(X=util.transposed_tensor_mult(self.__permeability,r), Y=Data(), r=Data())
346 gross 2349 return self.__pde_p.getSolution(verbose=self.show_details, iter_max = 100000)
347 gross 2100
348 gross 2264 def getFlux(self,p=None, fixed_flux=Data(), show_details=False):
349     """
350     returns the flux for a given pressure C{p} where the flux is equal to C{fixed_flux}
351     on locations where C{location_of_fixed_flux} is positive (see L{setValue}).
352     Note that C{g} and C{f} are used, see L{setValue}.
353    
354     @param p: pressure.
355     @type p: scalar value on the domain (e.g. L{Data}).
356     @param fixed_flux: flux on the locations of the domain marked be C{location_of_fixed_flux}.
357     @type fixed_flux: vector values on the domain (e.g. L{Data}).
358     @param tol: relative tolerance to be used.
359     @type tol: positive C{float}.
360     @return: flux
361     @rtype: L{Data}
362     @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}}
363     for the permeability M{k_{ij}}
364     """
365     self.__pde_v.setTolerance(self.getSubProblemTolerance())
366     g=self.__g
367     f=self.__f
368 gross 2267 self.__pde_v.setValue(X=self.__l*f*util.kronecker(self.domain), r=fixed_flux)
369 gross 2264 if p == None:
370     self.__pde_v.setValue(Y=g)
371     else:
372     self.__pde_v.setValue(Y=g-self.__Q(p))
373 gross 2349 return self.__pde_v.getSolution(verbose=show_details, iter_max=100000)
374 gross 2264
375 gross 1414 class StokesProblemCartesian(HomogeneousSaddlePointProblem):
376 gross 2251 """
377 gross 2264 solves
378 gross 1414
379 gross 2208 -(eta*(u_{i,j}+u_{j,i}))_j + p_i = f_i-stress_{ij,j}
380     u_{i,i}=0
381 gross 1414
382 gross 2208 u=0 where fixed_u_mask>0
383     eta*(u_{i,j}+u_{j,i})*n_j-p*n_i=surface_stress +stress_{ij}n_j
384 gross 1414
385 gross 2264 if surface_stress is not given 0 is assumed.
386 gross 1414
387 gross 2251 typical usage:
388 gross 1414
389 gross 2208 sp=StokesProblemCartesian(domain)
390     sp.setTolerance()
391     sp.initialize(...)
392     v,p=sp.solve(v0,p0)
393 gross 2251 """
394     def __init__(self,domain,**kwargs):
395 gross 2100 """
396 gross 2208 initialize the Stokes Problem
397 gross 2100
398 gross 2208 @param domain: domain of the problem. The approximation order needs to be two.
399 gross 2100 @type domain: L{Domain}
400 gross 2208 @warning: The apprximation order needs to be two otherwise you may see oscilations in the pressure.
401 gross 2100 """
402 gross 1414 HomogeneousSaddlePointProblem.__init__(self,**kwargs)
403     self.domain=domain
404     self.vol=util.integrate(1.,Function(self.domain))
405     self.__pde_u=LinearPDE(domain,numEquations=self.domain.getDim(),numSolutions=self.domain.getDim())
406     self.__pde_u.setSymmetryOn()
407 gross 2100 # self.__pde_u.setSolverMethod(self.__pde_u.DIRECT)
408 gross 2351 # self.__pde_u.setSolverMethod(preconditioner=LinearPDE.ILU0)
409 gross 2264
410 gross 1414 self.__pde_prec=LinearPDE(domain)
411     self.__pde_prec.setReducedOrderOn()
412 gross 2156 # self.__pde_prec.setSolverMethod(self.__pde_prec.LUMPING)
413 gross 1414 self.__pde_prec.setSymmetryOn()
414    
415 gross 2251 def initialize(self,f=Data(),fixed_u_mask=Data(),eta=1,surface_stress=Data(),stress=Data()):
416 gross 2208 """
417     assigns values to the model parameters
418 gross 2100
419 gross 2208 @param f: external force
420     @type f: L{Vector} object in L{FunctionSpace} L{Function} or similar
421     @param fixed_u_mask: mask of locations with fixed velocity.
422     @type fixed_u_mask: L{Vector} object on L{FunctionSpace} L{Solution} or similar
423     @param eta: viscosity
424     @type eta: L{Scalar} object on L{FunctionSpace} L{Function} or similar
425     @param surface_stress: normal surface stress
426     @type eta: L{Vector} object on L{FunctionSpace} L{FunctionOnBoundary} or similar
427     @param stress: initial stress
428     @type stress: L{Tensor} object on L{FunctionSpace} L{Function} or similar
429     @note: All values needs to be set.
430 gross 2264
431 gross 2208 """
432     self.eta=eta
433     A =self.__pde_u.createCoefficient("A")
434     self.__pde_u.setValue(A=Data())
435     for i in range(self.domain.getDim()):
436     for j in range(self.domain.getDim()):
437 gross 2264 A[i,j,j,i] += 1.
438 gross 2208 A[i,j,i,j] += 1.
439 gross 2264 self.__pde_prec.setValue(D=1/self.eta)
440 gross 2251 self.__pde_u.setValue(A=A*self.eta,q=fixed_u_mask)
441     self.__f=f
442     self.__surface_stress=surface_stress
443 gross 2208 self.__stress=stress
444 gross 1414
445 gross 2251 def inner_pBv(self,p,v):
446     """
447     returns inner product of element p and div(v)
448 gross 1414
449 gross 2251 @param p: a pressure increment
450     @param v: a residual
451     @return: inner product of element p and div(v)
452     @rtype: C{float}
453 gross 2100 """
454 gross 2251 return util.integrate(-p*util.div(v))
455 gross 2208
456 gross 2251 def inner_p(self,p0,p1):
457 gross 2100 """
458 gross 2251 Returns inner product of p0 and p1
459 gross 1414
460 gross 2251 @param p0: a pressure
461     @param p1: a pressure
462     @return: inner product of p0 and p1
463 gross 2208 @rtype: C{float}
464 gross 2100 """
465     s0=util.interpolate(p0/self.eta,Function(self.domain))
466     s1=util.interpolate(p1/self.eta,Function(self.domain))
467     return util.integrate(s0*s1)
468 artak 1550
469 gross 2251 def norm_v(self,v):
470 gross 2100 """
471 gross 2251 returns the norm of v
472 gross 2208
473 gross 2251 @param v: a velovity
474     @return: norm of v
475     @rtype: non-negative C{float}
476 gross 2100 """
477 gross 2251 return util.sqrt(util.integrate(util.length(util.grad(v))))
478 gross 2100
479 gross 2251 def getV(self, p, v0):
480 gross 1414 """
481 gross 2251 return the value for v for a given p (overwrite)
482    
483     @param p: a pressure
484 gross 2264 @param v0: a initial guess for the value v to return.
485 gross 2251 @return: v given as M{v= A^{-1} (f-B^*p)}
486 gross 1414 """
487     self.__pde_u.setTolerance(self.getSubProblemTolerance())
488 gross 2251 self.__pde_u.setValue(Y=self.__f, y=self.__surface_stress, r=v0)
489 gross 2100 if self.__stress.isEmpty():
490 gross 2251 self.__pde_u.setValue(X=p*util.kronecker(self.domain))
491 gross 2100 else:
492 gross 2251 self.__pde_u.setValue(X=self.__stress+p*util.kronecker(self.domain))
493 gross 2100 out=self.__pde_u.getSolution(verbose=self.show_details)
494 gross 2208 return out
495 gross 1414
496 gross 2251
497     raise NotImplementedError,"no v calculation implemented."
498    
499 gross 2264
500 gross 2251 def norm_Bv(self,v):
501     """
502     Returns Bv (overwrite).
503    
504     @rtype: equal to the type of p
505     @note: boundary conditions on p should be zero!
506     """
507     return util.sqrt(util.integrate(util.div(v)**2))
508    
509     def solve_AinvBt(self,p):
510     """
511     Solves M{Av=B^*p} with accuracy L{self.getSubProblemTolerance()}
512    
513     @param p: a pressure increment
514 gross 2264 @return: the solution of M{Av=B^*p}
515 gross 2251 @note: boundary conditions on v should be zero!
516     """
517     self.__pde_u.setTolerance(self.getSubProblemTolerance())
518     self.__pde_u.setValue(Y=Data(), y=Data(), r=Data(),X=-p*util.kronecker(self.domain))
519     out=self.__pde_u.getSolution(verbose=self.show_details)
520     return out
521    
522     def solve_precB(self,v):
523     """
524     applies preconditioner for for M{BA^{-1}B^*} to M{Bv}
525     with accuracy L{self.getSubProblemTolerance()} (overwrite).
526    
527     @param v: velocity increment
528     @return: M{p=P(Bv)} where M{P^{-1}} is an approximation of M{BA^{-1}B^*}
529     @note: boundary conditions on p are zero.
530     """
531     self.__pde_prec.setValue(Y=-util.div(v))
532 gross 1414 self.__pde_prec.setTolerance(self.getSubProblemTolerance())
533 gross 2251 return self.__pde_prec.getSolution(verbose=self.show_details)

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