/[escript]/trunk/escript/py_src/flows.py
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Revision 2625 - (hide annotations)
Fri Aug 21 06:30:25 2009 UTC (10 years, 1 month ago) by jfenwick
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Merging changes from new doco branch.
All docstrings are now in reStructured text.
A few email addresses have been fixes as well.
1 ksteube 1809 ########################################################
2 gross 1414 #
3 jfenwick 2548 # Copyright (c) 2003-2009 by University of Queensland
4 ksteube 1809 # 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 jfenwick 2549 __copyright__="""Copyright (c) 2003-2009 by University of Queensland
14 ksteube 1809 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 jfenwick 2625 :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 gross 1414 """
31    
32     __author__="Lutz Gross, l.gross@uq.edu.au"
33    
34     from escript import *
35     import util
36 gross 2474 from linearPDEs import LinearPDE, LinearPDESystem, LinearSinglePDE, SolverOptions
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 jfenwick 2625 *u_i+k_{ij}*p_{,j} = g_i*
44     *u_{i,i} = f*
45 gross 1659
46 jfenwick 2625 where *p* represents the pressure and *u* the Darcy flux. *k* represents the permeability,
47 gross 1659
48 jfenwick 2625 :note: The problem is solved in a least squares formulation.
49 gross 2100 """
50 gross 1659
51 gross 2474 def __init__(self, domain, weight=None, useReduced=False, adaptSubTolerance=True):
52 gross 2100 """
53 gross 2208 initializes the Darcy flux problem
54 jfenwick 2625 :param domain: domain of the problem
55     :type domain: `Domain`
56     :param useReduced: uses reduced oreder on flux and pressure
57     :type useReduced: ``bool``
58     :param adaptSubTolerance: switches on automatic subtolerance selection
59     :type adaptSubTolerance: ``bool``
60 gross 2100 """
61     self.domain=domain
62 gross 2351 if weight == None:
63 gross 2354 s=self.domain.getSize()
64     self.__l=(3.*util.longestEdge(self.domain)*s/util.sup(s))**2
65 gross 2486 # self.__l=(3.*util.longestEdge(self.domain))**2
66     # self.__l=(0.1*util.longestEdge(self.domain)*s/util.sup(s))**2
67 gross 2351 else:
68     self.__l=weight
69 gross 2100 self.__pde_v=LinearPDESystem(domain)
70 gross 2208 if useReduced: self.__pde_v.setReducedOrderOn()
71     self.__pde_v.setSymmetryOn()
72 gross 2267 self.__pde_v.setValue(D=util.kronecker(domain), A=self.__l*util.outer(util.kronecker(domain),util.kronecker(domain)))
73 gross 2100 self.__pde_p=LinearSinglePDE(domain)
74     self.__pde_p.setSymmetryOn()
75 gross 2208 if useReduced: self.__pde_p.setReducedOrderOn()
76 gross 2100 self.__f=Scalar(0,self.__pde_v.getFunctionSpaceForCoefficient("X"))
77     self.__g=Vector(0,self.__pde_v.getFunctionSpaceForCoefficient("Y"))
78 gross 2264 self.setTolerance()
79     self.setAbsoluteTolerance()
80 gross 2474 self.__adaptSubTolerance=adaptSubTolerance
81     self.verbose=False
82     def getSolverOptionsFlux(self):
83     """
84     Returns the solver options used to solve the flux problems
85    
86 jfenwick 2625 *(I+D^*D)u=F*
87 gross 2474
88 jfenwick 2625 :return: `SolverOptions`
89 gross 2474 """
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 jfenwick 2625 *(I+D^*D)u=F*
96 gross 2474
97 jfenwick 2625 If ``options`` is not present, the options are reset to default
98     :param options: `SolverOptions`
99     :note: if the adaption of subtolerance is choosen, the tolerance set by ``options`` will be overwritten before the solver is called.
100 gross 2474 """
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 jfenwick 2625 *(Q^*Q)p=Q^*G*
107 gross 2474
108 jfenwick 2625 :return: `SolverOptions`
109 gross 2474 """
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 jfenwick 2625 *(Q^*Q)p=Q^*G*
116 gross 2474
117 jfenwick 2625 If ``options`` is not present, the options are reset to default
118     :param options: `SolverOptions`
119     :note: if the adaption of subtolerance is choosen, the tolerance set by ``options`` will be overwritten before the solver is called.
120 gross 2474 """
121     return self.__pde_p.setSolverOptions(options)
122 gross 1659
123 gross 2100 def setValue(self,f=None, g=None, location_of_fixed_pressure=None, location_of_fixed_flux=None, permeability=None):
124     """
125 gross 2208 assigns values to model parameters
126 gross 1659
127 jfenwick 2625 :param f: volumetic sources/sinks
128     :type f: scalar value on the domain (e.g. `Data`)
129     :param g: flux sources/sinks
130     :type g: vector values on the domain (e.g. `Data`)
131     :param location_of_fixed_pressure: mask for locations where pressure is fixed
132     :type location_of_fixed_pressure: scalar value on the domain (e.g. `Data`)
133     :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. `Data`)
135     :param permeability: permeability tensor. If scalar ``s`` is given the tensor with
136     ``s`` on the main diagonal is used. If vector ``v`` is given the tensor with
137     ``v`` on the main diagonal is used.
138     :type permeability: scalar, vector or tensor values on the domain (e.g. `Data`)
139 gross 1659
140 jfenwick 2625 :note: the values of parameters which are not set by calling ``setValue`` are not altered.
141     :note: at any point on the boundary of the domain the pressure (``location_of_fixed_pressure`` >0)
142     or the normal component of the flux (``location_of_fixed_flux[i]>0`` if direction of the normal
143     is along the *x_i* axis.
144 gross 2100 """
145 gross 2264 if f !=None:
146 gross 2100 f=util.interpolate(f, self.__pde_v.getFunctionSpaceForCoefficient("X"))
147     if f.isEmpty():
148     f=Scalar(0,self.__pde_v.getFunctionSpaceForCoefficient("X"))
149     else:
150     if f.getRank()>0: raise ValueError,"illegal rank of f."
151 gross 2267 self.__f=f
152 gross 2264 if g !=None:
153 gross 2100 g=util.interpolate(g, self.__pde_p.getFunctionSpaceForCoefficient("Y"))
154     if g.isEmpty():
155     g=Vector(0,self.__pde_v.getFunctionSpaceForCoefficient("Y"))
156     else:
157     if not g.getShape()==(self.domain.getDim(),):
158     raise ValueError,"illegal shape of g"
159     self.__g=g
160 gross 1659
161 gross 2100 if location_of_fixed_pressure!=None: self.__pde_p.setValue(q=location_of_fixed_pressure)
162     if location_of_fixed_flux!=None: self.__pde_v.setValue(q=location_of_fixed_flux)
163 gross 1659
164 gross 2100 if permeability!=None:
165     perm=util.interpolate(permeability,self.__pde_p.getFunctionSpaceForCoefficient("A"))
166     if perm.getRank()==0:
167     perm=perm*util.kronecker(self.domain.getDim())
168     elif perm.getRank()==1:
169     perm, perm2=Tensor(0.,self.__pde_p.getFunctionSpaceForCoefficient("A")), perm
170     for i in range(self.domain.getDim()): perm[i,i]=perm2[i]
171     elif perm.getRank()==2:
172     pass
173     else:
174     raise ValueError,"illegal rank of permeability."
175     self.__permeability=perm
176     self.__pde_p.setValue(A=util.transposed_tensor_mult(self.__permeability,self.__permeability))
177 gross 1659
178 gross 2264 def setTolerance(self,rtol=1e-4):
179     """
180 jfenwick 2625 sets the relative tolerance ``rtol`` used to terminate the solution process. The iteration is terminated if
181 gross 1659
182 jfenwick 2625 *|g-v-Qp| <= atol + rtol * min( max( |g-v|, |Qp| ), max( |v|, |g-Qp| ) )*
183 gross 2264
184 jfenwick 2625 where ``atol`` is an absolut tolerance (see `setAbsoluteTolerance`), *|f|^2 = integrate(length(f)^2)* and *(Qp)_i=k_{ij}p_{,j}* for the permeability *k_{ij}*.
185 gross 2264
186 jfenwick 2625 :param rtol: relative tolerance for the pressure
187     :type rtol: non-negative ``float``
188 gross 2100 """
189 gross 2264 if rtol<0:
190     raise ValueError,"Relative tolerance needs to be non-negative."
191     self.__rtol=rtol
192     def getTolerance(self):
193 gross 2100 """
194 gross 2264 returns the relative tolerance
195 gross 1659
196 jfenwick 2625 :return: current relative tolerance
197     :rtype: ``float``
198 caltinay 2169 """
199 gross 2264 return self.__rtol
200 gross 1659
201 gross 2264 def setAbsoluteTolerance(self,atol=0.):
202 gross 2208 """
203 jfenwick 2625 sets the absolute tolerance ``atol`` used to terminate the solution process. The iteration is terminated if
204 gross 1659
205 jfenwick 2625 *|g-v-Qp| <= atol + rtol * min( max( |g-v|, |Qp| ), max( |v|, |g-Qp| ) )*
206 gross 2208
207 jfenwick 2625 where ``rtol`` is an absolut tolerance (see `setTolerance`), *|f|^2 = integrate(length(f)^2)* and *(Qp)_i=k_{ij}p_{,j}* for the permeability *k_{ij}*.
208 gross 2208
209 jfenwick 2625 :param atol: absolute tolerance for the pressure
210     :type atol: non-negative ``float``
211 gross 2264 """
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 jfenwick 2625 :return: current absolute tolerance
220     :rtype: ``float``
221 gross 2264 """
222     return self.__atol
223     def getSubProblemTolerance(self):
224 gross 2474 """
225     Returns a suitable subtolerance
226 jfenwick 2625 @type: ``float``
227 gross 2474 """
228     return max(util.EPSILON**(0.75),self.getTolerance()**2)
229     def setSubProblemTolerance(self):
230 gross 2264 """
231 gross 2474 Sets the relative tolerance to solve the subproblem(s) if subtolerance adaption is selected.
232 gross 2264 """
233 gross 2474 if self.__adaptSubTolerance:
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 gross 2208
241 gross 2474 def solve(self,u0,p0, max_iter=100, verbose=False, max_num_corrections=10):
242 gross 2264 """
243     solves the problem.
244 gross 1659
245 gross 2208 The iteration is terminated if the residual norm is less then self.getTolerance().
246 gross 1659
247 jfenwick 2625 :param u0: initial guess for the flux. At locations in the domain marked by ``location_of_fixed_flux`` the value of ``u0`` is kept unchanged.
248     :type u0: vector value on the domain (e.g. `Data`).
249     :param p0: initial guess for the pressure. At locations in the domain marked by ``location_of_fixed_pressure`` the value of ``p0`` is kept unchanged.
250     :type p0: scalar value on the domain (e.g. `Data`).
251     :param verbose: if set some information on iteration progress are printed
252     :type verbose: ``bool``
253     :return: flux and pressure
254     :rtype: ``tuple`` of `Data`.
255 gross 2264
256 jfenwick 2625 :note: The problem is solved as a least squares form
257 gross 2100
258 jfenwick 2625 *(I+D^*D)u+Qp=D^*f+g*
259     *Q^*u+Q^*Qp=Q^*g*
260 gross 2100
261 jfenwick 2625 where *D* is the *div* operator and *(Qp)_i=k_{ij}p_{,j}* for the permeability *k_{ij}*.
262 gross 2264 We eliminate the flux form the problem by setting
263 caltinay 2169
264 jfenwick 2625 *u=(I+D^*D)^{-1}(D^*f-g-Qp)* with u=u0 on location_of_fixed_flux
265 caltinay 2169
266 gross 2208 form the first equation. Inserted into the second equation we get
267 caltinay 2169
268 jfenwick 2625 *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 gross 2264
270 jfenwick 2625 which is solved using the PCG method (precondition is *Q^*Q*). In each iteration step
271     PDEs with operator *I+D^*D* and with *Q^*Q* needs to be solved using a sub iteration scheme.
272 gross 2208 """
273 gross 2386 self.verbose=verbose
274 gross 2264 rtol=self.getTolerance()
275     atol=self.getAbsoluteTolerance()
276 gross 2474 self.setSubProblemTolerance()
277    
278 gross 2264 num_corrections=0
279     converged=False
280     p=p0
281     norm_r=None
282     while not converged:
283 gross 2474 v=self.getFlux(p, fixed_flux=u0)
284 gross 2264 Qp=self.__Q(p)
285     norm_v=self.__L2(v)
286     norm_Qp=self.__L2(Qp)
287     if norm_v == 0.:
288     if norm_Qp == 0.:
289     return v,p
290     else:
291     fac=norm_Qp
292     else:
293     if norm_Qp == 0.:
294     fac=norm_v
295     else:
296     fac=2./(1./norm_v+1./norm_Qp)
297     ATOL=(atol+rtol*fac)
298     if self.verbose:
299     print "DarcyFlux: L2 norm of v = %e."%norm_v
300     print "DarcyFlux: L2 norm of k.grad(p) = %e."%norm_Qp
301 gross 2486 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 gross 2264 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 gross 2354 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 gross 2264 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):
316     return util.tensor_mult(self.__permeability,util.grad(p))
317    
318     def __Aprod(self,dp):
319 gross 2474 if self.getSolverOptionsFlux().isVerbose(): print "DarcyFlux: Applying operator"
320 gross 2264 Qdp=self.__Q(dp)
321     self.__pde_v.setValue(Y=-Qdp,X=Data(), r=Data())
322 gross 2474 du=self.__pde_v.getSolution()
323 gross 2370 # self.__pde_v.getOperator().saveMM("proj.mm")
324 gross 2264 return Qdp+du
325     def __inner_GMRES(self,r,s):
326     return util.integrate(util.inner(r,s))
327    
328 gross 2100 def __inner_PCG(self,p,r):
329 gross 2264 return util.integrate(util.inner(self.__Q(p), r))
330 gross 2100
331     def __Msolve_PCG(self,r):
332 gross 2474 if self.getSolverOptionsPressure().isVerbose(): print "DarcyFlux: Applying preconditioner"
333 gross 2264 self.__pde_p.setValue(X=util.transposed_tensor_mult(self.__permeability,r), Y=Data(), r=Data())
334 gross 2370 # self.__pde_p.getOperator().saveMM("prec.mm")
335 gross 2474 return self.__pde_p.getSolution()
336 gross 2100
337 gross 2474 def getFlux(self,p=None, fixed_flux=Data()):
338 gross 2264 """
339 jfenwick 2625 returns the flux for a given pressure ``p`` where the flux is equal to ``fixed_flux``
340     on locations where ``location_of_fixed_flux`` is positive (see `setValue`).
341     Note that ``g`` and ``f`` are used, see `setValue`.
342 gross 2264
343 jfenwick 2625 :param p: pressure.
344     :type p: scalar value on the domain (e.g. `Data`).
345     :param fixed_flux: flux on the locations of the domain marked be ``location_of_fixed_flux``.
346     :type fixed_flux: vector values on the domain (e.g. `Data`).
347     :return: flux
348     :rtype: `Data`
349     :note: the method uses the least squares solution *u=(I+D^*D)^{-1}(D^*f-g-Qp)* where *D* is the *div* operator and *(Qp)_i=k_{ij}p_{,j}*
350     for the permeability *k_{ij}*
351 gross 2264 """
352 gross 2474 self.setSubProblemTolerance()
353 gross 2264 g=self.__g
354     f=self.__f
355 gross 2267 self.__pde_v.setValue(X=self.__l*f*util.kronecker(self.domain), r=fixed_flux)
356 gross 2264 if p == None:
357     self.__pde_v.setValue(Y=g)
358     else:
359     self.__pde_v.setValue(Y=g-self.__Q(p))
360 gross 2474 return self.__pde_v.getSolution()
361 gross 2264
362 gross 1414 class StokesProblemCartesian(HomogeneousSaddlePointProblem):
363 gross 2251 """
364 gross 2264 solves
365 gross 1414
366 gross 2208 -(eta*(u_{i,j}+u_{j,i}))_j + p_i = f_i-stress_{ij,j}
367     u_{i,i}=0
368 gross 1414
369 gross 2208 u=0 where fixed_u_mask>0
370     eta*(u_{i,j}+u_{j,i})*n_j-p*n_i=surface_stress +stress_{ij}n_j
371 gross 1414
372 gross 2264 if surface_stress is not given 0 is assumed.
373 gross 1414
374 gross 2251 typical usage:
375 gross 1414
376 gross 2208 sp=StokesProblemCartesian(domain)
377     sp.setTolerance()
378     sp.initialize(...)
379     v,p=sp.solve(v0,p0)
380 gross 2251 """
381 gross 2474 def __init__(self,domain,adaptSubTolerance=True, **kwargs):
382 gross 2100 """
383 gross 2208 initialize the Stokes Problem
384 gross 2100
385 jfenwick 2625 :param domain: domain of the problem. The approximation order needs to be two.
386     :type domain: `Domain`
387     :param adaptSubTolerance: If True the tolerance for subproblem is set automatically.
388     :type adaptSubTolerance: ``bool``
389     :warning: The apprximation order needs to be two otherwise you may see oscilations in the pressure.
390 gross 2100 """
391 gross 2474 HomogeneousSaddlePointProblem.__init__(self,adaptSubTolerance=adaptSubTolerance,**kwargs)
392 gross 1414 self.domain=domain
393     self.vol=util.integrate(1.,Function(self.domain))
394     self.__pde_u=LinearPDE(domain,numEquations=self.domain.getDim(),numSolutions=self.domain.getDim())
395     self.__pde_u.setSymmetryOn()
396 gross 2474
397 gross 1414 self.__pde_prec=LinearPDE(domain)
398     self.__pde_prec.setReducedOrderOn()
399     self.__pde_prec.setSymmetryOn()
400    
401 gross 2415 self.__pde_proj=LinearPDE(domain)
402     self.__pde_proj.setReducedOrderOn()
403     self.__pde_proj.setValue(D=1)
404     self.__pde_proj.setSymmetryOn()
405    
406 gross 2474 def getSolverOptionsVelocity(self):
407     """
408     returns the solver options used solve the equation for velocity.
409    
410 jfenwick 2625 :rtype: `SolverOptions`
411 gross 2474 """
412     return self.__pde_u.getSolverOptions()
413     def setSolverOptionsVelocity(self, options=None):
414     """
415     set the solver options for solving the equation for velocity.
416    
417 jfenwick 2625 :param options: new solver options
418     :type options: `SolverOptions`
419 gross 2474 """
420     self.__pde_u.setSolverOptions(options)
421     def getSolverOptionsPressure(self):
422     """
423     returns the solver options used solve the equation for pressure.
424 jfenwick 2625 :rtype: `SolverOptions`
425 gross 2474 """
426     return self.__pde_prec.getSolverOptions()
427     def setSolverOptionsPressure(self, options=None):
428     """
429     set the solver options for solving the equation for pressure.
430 jfenwick 2625 :param options: new solver options
431     :type options: `SolverOptions`
432 gross 2474 """
433     self.__pde_prec.setSolverOptions(options)
434 gross 2415
435 gross 2474 def setSolverOptionsDiv(self, options=None):
436     """
437     set the solver options for solving the equation to project the divergence of
438     the velocity onto the function space of presure.
439    
440 jfenwick 2625 :param options: new solver options
441     :type options: `SolverOptions`
442 gross 2474 """
443     self.__pde_prec.setSolverOptions(options)
444     def getSolverOptionsDiv(self):
445     """
446     returns the solver options for solving the equation to project the divergence of
447     the velocity onto the function space of presure.
448    
449 jfenwick 2625 :rtype: `SolverOptions`
450 gross 2474 """
451     return self.__pde_prec.getSolverOptions()
452     def setSubProblemTolerance(self):
453     """
454     Updates the tolerance for subproblems
455     """
456     if self.adaptSubTolerance():
457     sub_tol=self.getSubProblemTolerance()
458     self.getSolverOptionsDiv().setTolerance(sub_tol)
459     self.getSolverOptionsDiv().setAbsoluteTolerance(0.)
460     self.getSolverOptionsPressure().setTolerance(sub_tol)
461     self.getSolverOptionsPressure().setAbsoluteTolerance(0.)
462     self.getSolverOptionsVelocity().setTolerance(sub_tol)
463     self.getSolverOptionsVelocity().setAbsoluteTolerance(0.)
464    
465    
466 gross 2620 def initialize(self,f=Data(),fixed_u_mask=Data(),eta=1,surface_stress=Data(),stress=Data(), restoration_factor=0):
467 gross 2208 """
468     assigns values to the model parameters
469 gross 2100
470 jfenwick 2625 :param f: external force
471     :type f: `Vector` object in `FunctionSpace` `Function` or similar
472     :param fixed_u_mask: mask of locations with fixed velocity.
473     :type fixed_u_mask: `Vector` object on `FunctionSpace` `Solution` or similar
474     :param eta: viscosity
475     :type eta: `Scalar` object on `FunctionSpace` `Function` or similar
476     :param surface_stress: normal surface stress
477     :type surface_stress: `Vector` object on `FunctionSpace` `FunctionOnBoundary` or similar
478     :param stress: initial stress
479     :type stress: `Tensor` object on `FunctionSpace` `Function` or similar
480     :note: All values needs to be set.
481 gross 2208 """
482     self.eta=eta
483     A =self.__pde_u.createCoefficient("A")
484     self.__pde_u.setValue(A=Data())
485     for i in range(self.domain.getDim()):
486     for j in range(self.domain.getDim()):
487 gross 2264 A[i,j,j,i] += 1.
488 gross 2208 A[i,j,i,j] += 1.
489 gross 2620 n=self.domain.getNormal()
490 gross 2264 self.__pde_prec.setValue(D=1/self.eta)
491 gross 2620 self.__pde_u.setValue(A=A*self.eta,q=fixed_u_mask, d=restoration_factor*util.outer(n,n))
492 gross 2251 self.__f=f
493     self.__surface_stress=surface_stress
494 gross 2208 self.__stress=stress
495 gross 1414
496 gross 2445 def Bv(self,v):
497 gross 2251 """
498     returns inner product of element p and div(v)
499 gross 1414
500 jfenwick 2625 :param v: a residual
501     :return: inner product of element p and div(v)
502     :rtype: ``float``
503 gross 2100 """
504 gross 2445 self.__pde_proj.setValue(Y=-util.div(v))
505     return self.__pde_proj.getSolution()
506 gross 2208
507 gross 2445 def inner_pBv(self,p,Bv):
508     """
509     returns inner product of element p and Bv=-div(v)
510    
511 jfenwick 2625 :param p: a pressure increment
512     :param Bv: a residual
513     :return: inner product of element p and Bv=-div(v)
514     :rtype: ``float``
515 gross 2445 """
516     return util.integrate(util.interpolate(p,Function(self.domain))*util.interpolate(Bv,Function(self.domain)))
517    
518 gross 2251 def inner_p(self,p0,p1):
519 gross 2100 """
520 gross 2251 Returns inner product of p0 and p1
521 gross 1414
522 jfenwick 2625 :param p0: a pressure
523     :param p1: a pressure
524     :return: inner product of p0 and p1
525     :rtype: ``float``
526 gross 2100 """
527     s0=util.interpolate(p0/self.eta,Function(self.domain))
528     s1=util.interpolate(p1/self.eta,Function(self.domain))
529     return util.integrate(s0*s1)
530 artak 1550
531 gross 2251 def norm_v(self,v):
532 gross 2100 """
533 gross 2251 returns the norm of v
534 gross 2208
535 jfenwick 2625 :param v: a velovity
536     :return: norm of v
537     :rtype: non-negative ``float``
538 gross 2100 """
539 gross 2251 return util.sqrt(util.integrate(util.length(util.grad(v))))
540 gross 2100
541 gross 2251 def getV(self, p, v0):
542 gross 1414 """
543 gross 2251 return the value for v for a given p (overwrite)
544    
545 jfenwick 2625 :param p: a pressure
546     :param v0: a initial guess for the value v to return.
547     :return: v given as *v= A^{-1} (f-B^*p)*
548 gross 1414 """
549 gross 2251 self.__pde_u.setValue(Y=self.__f, y=self.__surface_stress, r=v0)
550 gross 2100 if self.__stress.isEmpty():
551 gross 2251 self.__pde_u.setValue(X=p*util.kronecker(self.domain))
552 gross 2100 else:
553 gross 2251 self.__pde_u.setValue(X=self.__stress+p*util.kronecker(self.domain))
554 gross 2474 out=self.__pde_u.getSolution()
555 gross 2208 return out
556 gross 1414
557 gross 2445 def norm_Bv(self,Bv):
558 gross 2251 """
559     Returns Bv (overwrite).
560    
561 jfenwick 2625 :rtype: equal to the type of p
562     :note: boundary conditions on p should be zero!
563 gross 2251 """
564 gross 2445 return util.sqrt(util.integrate(util.interpolate(Bv,Function(self.domain))**2))
565 gross 2251
566     def solve_AinvBt(self,p):
567     """
568 jfenwick 2625 Solves *Av=B^*p* with accuracy `self.getSubProblemTolerance()`
569 gross 2251
570 jfenwick 2625 :param p: a pressure increment
571     :return: the solution of *Av=B^*p*
572     :note: boundary conditions on v should be zero!
573 gross 2251 """
574     self.__pde_u.setValue(Y=Data(), y=Data(), r=Data(),X=-p*util.kronecker(self.domain))
575 gross 2474 out=self.__pde_u.getSolution()
576 gross 2251 return out
577    
578 gross 2445 def solve_prec(self,Bv):
579 gross 2251 """
580 jfenwick 2625 applies preconditioner for for *BA^{-1}B^** to *Bv*
581     with accuracy `self.getSubProblemTolerance()`
582 gross 2251
583 jfenwick 2625 :param Bv: velocity increment
584     :return: *p=P(Bv)* where *P^{-1}* is an approximation of *BA^{-1}B^ * )*
585     :note: boundary conditions on p are zero.
586 gross 2251 """
587 gross 2445 self.__pde_prec.setValue(Y=Bv)
588 gross 2474 return self.__pde_prec.getSolution()

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