/[escript]/trunk/escript/py_src/flows.py
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Revision 2719 - (hide annotations)
Wed Oct 14 06:38:03 2009 UTC (9 years, 11 months ago) by gross
File MIME type: text/x-python
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a new Stokes solver added
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 artak 2689 #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 gross 2264 num_corrections=0
278     converged=False
279     p=p0
280     norm_r=None
281     while not converged:
282 gross 2474 v=self.getFlux(p, fixed_flux=u0)
283 gross 2264 Qp=self.__Q(p)
284     norm_v=self.__L2(v)
285     norm_Qp=self.__L2(Qp)
286     if norm_v == 0.:
287     if norm_Qp == 0.:
288     return v,p
289     else:
290     fac=norm_Qp
291     else:
292     if norm_Qp == 0.:
293     fac=norm_v
294     else:
295     fac=2./(1./norm_v+1./norm_Qp)
296     ATOL=(atol+rtol*fac)
297     if self.verbose:
298     print "DarcyFlux: L2 norm of v = %e."%norm_v
299     print "DarcyFlux: L2 norm of k.grad(p) = %e."%norm_Qp
300 gross 2486 print "DarcyFlux: L2 defect u = %e."%(util.integrate(util.length(self.__g-util.interpolate(v,Function(self.domain))-Qp)**2)**(0.5),)
301     print "DarcyFlux: L2 defect div(v) = %e."%(util.integrate((self.__f-util.div(v))**2)**(0.5),)
302 gross 2264 print "DarcyFlux: absolute tolerance ATOL = %e."%ATOL
303     if norm_r == None or norm_r>ATOL:
304     if num_corrections>max_num_corrections:
305     raise ValueError,"maximum number of correction steps reached."
306 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)
307 gross 2264 num_corrections+=1
308     else:
309     converged=True
310     return v,p
311     def __L2(self,v):
312     return util.sqrt(util.integrate(util.length(util.interpolate(v,Function(self.domain)))**2))
313    
314     def __Q(self,p):
315     return util.tensor_mult(self.__permeability,util.grad(p))
316    
317     def __Aprod(self,dp):
318 gross 2474 if self.getSolverOptionsFlux().isVerbose(): print "DarcyFlux: Applying operator"
319 gross 2264 Qdp=self.__Q(dp)
320     self.__pde_v.setValue(Y=-Qdp,X=Data(), r=Data())
321 gross 2474 du=self.__pde_v.getSolution()
322 gross 2370 # self.__pde_v.getOperator().saveMM("proj.mm")
323 gross 2264 return Qdp+du
324     def __inner_GMRES(self,r,s):
325     return util.integrate(util.inner(r,s))
326    
327 gross 2100 def __inner_PCG(self,p,r):
328 gross 2264 return util.integrate(util.inner(self.__Q(p), r))
329 gross 2100
330     def __Msolve_PCG(self,r):
331 gross 2474 if self.getSolverOptionsPressure().isVerbose(): print "DarcyFlux: Applying preconditioner"
332 gross 2264 self.__pde_p.setValue(X=util.transposed_tensor_mult(self.__permeability,r), Y=Data(), r=Data())
333 gross 2370 # self.__pde_p.getOperator().saveMM("prec.mm")
334 gross 2474 return self.__pde_p.getSolution()
335 gross 2100
336 gross 2474 def getFlux(self,p=None, fixed_flux=Data()):
337 gross 2264 """
338 jfenwick 2625 returns the flux for a given pressure ``p`` where the flux is equal to ``fixed_flux``
339     on locations where ``location_of_fixed_flux`` is positive (see `setValue`).
340     Note that ``g`` and ``f`` are used, see `setValue`.
341 gross 2264
342 jfenwick 2625 :param p: pressure.
343     :type p: scalar value on the domain (e.g. `Data`).
344     :param fixed_flux: flux on the locations of the domain marked be ``location_of_fixed_flux``.
345     :type fixed_flux: vector values on the domain (e.g. `Data`).
346     :return: flux
347     :rtype: `Data`
348     :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}*
349     for the permeability *k_{ij}*
350 gross 2264 """
351 gross 2474 self.setSubProblemTolerance()
352 gross 2264 g=self.__g
353     f=self.__f
354 gross 2267 self.__pde_v.setValue(X=self.__l*f*util.kronecker(self.domain), r=fixed_flux)
355 gross 2264 if p == None:
356     self.__pde_v.setValue(Y=g)
357     else:
358     self.__pde_v.setValue(Y=g-self.__Q(p))
359 gross 2474 return self.__pde_v.getSolution()
360 gross 2264
361 gross 1414 class StokesProblemCartesian(HomogeneousSaddlePointProblem):
362 gross 2251 """
363 gross 2264 solves
364 gross 1414
365 gross 2208 -(eta*(u_{i,j}+u_{j,i}))_j + p_i = f_i-stress_{ij,j}
366     u_{i,i}=0
367 gross 1414
368 gross 2208 u=0 where fixed_u_mask>0
369     eta*(u_{i,j}+u_{j,i})*n_j-p*n_i=surface_stress +stress_{ij}n_j
370 gross 1414
371 gross 2264 if surface_stress is not given 0 is assumed.
372 gross 1414
373 gross 2251 typical usage:
374 gross 1414
375 gross 2208 sp=StokesProblemCartesian(domain)
376     sp.setTolerance()
377     sp.initialize(...)
378     v,p=sp.solve(v0,p0)
379 gross 2251 """
380 gross 2719 def __init__(self,domain,**kwargs):
381 gross 2100 """
382 gross 2208 initialize the Stokes Problem
383 gross 2100
384 jfenwick 2625 :param domain: domain of the problem. The approximation order needs to be two.
385     :type domain: `Domain`
386     :warning: The apprximation order needs to be two otherwise you may see oscilations in the pressure.
387 gross 2100 """
388 gross 2719 HomogeneousSaddlePointProblem.__init__(self,**kwargs)
389 gross 1414 self.domain=domain
390     self.__pde_u=LinearPDE(domain,numEquations=self.domain.getDim(),numSolutions=self.domain.getDim())
391     self.__pde_u.setSymmetryOn()
392 gross 2474
393 gross 1414 self.__pde_prec=LinearPDE(domain)
394     self.__pde_prec.setReducedOrderOn()
395     self.__pde_prec.setSymmetryOn()
396    
397 gross 2415 self.__pde_proj=LinearPDE(domain)
398     self.__pde_proj.setReducedOrderOn()
399     self.__pde_proj.setValue(D=1)
400     self.__pde_proj.setSymmetryOn()
401    
402 gross 2474 def getSolverOptionsVelocity(self):
403     """
404     returns the solver options used solve the equation for velocity.
405    
406 jfenwick 2625 :rtype: `SolverOptions`
407 gross 2474 """
408     return self.__pde_u.getSolverOptions()
409     def setSolverOptionsVelocity(self, options=None):
410     """
411     set the solver options for solving the equation for velocity.
412    
413 jfenwick 2625 :param options: new solver options
414     :type options: `SolverOptions`
415 gross 2474 """
416     self.__pde_u.setSolverOptions(options)
417     def getSolverOptionsPressure(self):
418     """
419     returns the solver options used solve the equation for pressure.
420 jfenwick 2625 :rtype: `SolverOptions`
421 gross 2474 """
422     return self.__pde_prec.getSolverOptions()
423     def setSolverOptionsPressure(self, options=None):
424     """
425     set the solver options for solving the equation for pressure.
426 jfenwick 2625 :param options: new solver options
427     :type options: `SolverOptions`
428 gross 2474 """
429     self.__pde_prec.setSolverOptions(options)
430 gross 2415
431 gross 2474 def setSolverOptionsDiv(self, options=None):
432     """
433     set the solver options for solving the equation to project the divergence of
434     the velocity onto the function space of presure.
435    
436 jfenwick 2625 :param options: new solver options
437     :type options: `SolverOptions`
438 gross 2474 """
439 artak 2689 self.__pde_proj.setSolverOptions(options)
440 gross 2474 def getSolverOptionsDiv(self):
441     """
442     returns the solver options for solving the equation to project the divergence of
443     the velocity onto the function space of presure.
444    
445 jfenwick 2625 :rtype: `SolverOptions`
446 gross 2474 """
447 artak 2689 return self.__pde_proj.getSolverOptions()
448 gross 2474
449 gross 2620 def initialize(self,f=Data(),fixed_u_mask=Data(),eta=1,surface_stress=Data(),stress=Data(), restoration_factor=0):
450 gross 2208 """
451     assigns values to the model parameters
452 gross 2100
453 jfenwick 2625 :param f: external force
454     :type f: `Vector` object in `FunctionSpace` `Function` or similar
455     :param fixed_u_mask: mask of locations with fixed velocity.
456     :type fixed_u_mask: `Vector` object on `FunctionSpace` `Solution` or similar
457     :param eta: viscosity
458     :type eta: `Scalar` object on `FunctionSpace` `Function` or similar
459     :param surface_stress: normal surface stress
460     :type surface_stress: `Vector` object on `FunctionSpace` `FunctionOnBoundary` or similar
461     :param stress: initial stress
462     :type stress: `Tensor` object on `FunctionSpace` `Function` or similar
463     :note: All values needs to be set.
464 gross 2208 """
465     self.eta=eta
466     A =self.__pde_u.createCoefficient("A")
467     self.__pde_u.setValue(A=Data())
468     for i in range(self.domain.getDim()):
469     for j in range(self.domain.getDim()):
470 gross 2264 A[i,j,j,i] += 1.
471 gross 2208 A[i,j,i,j] += 1.
472 gross 2620 n=self.domain.getNormal()
473 gross 2264 self.__pde_prec.setValue(D=1/self.eta)
474 gross 2620 self.__pde_u.setValue(A=A*self.eta,q=fixed_u_mask, d=restoration_factor*util.outer(n,n))
475 gross 2251 self.__f=f
476     self.__surface_stress=surface_stress
477 gross 2208 self.__stress=stress
478 gross 1414
479 gross 2719 def Bv(self,v,tol):
480 gross 2251 """
481     returns inner product of element p and div(v)
482 gross 1414
483 jfenwick 2625 :param v: a residual
484     :return: inner product of element p and div(v)
485     :rtype: ``float``
486 gross 2100 """
487 gross 2719 self.__pde_proj.setValue(Y=-util.div(v)) # -???
488     self.getSolverOptionsDiv().setTolerance(tol)
489     self.getSolverOptionsDiv().setAbsoluteTolerance(0.)
490     out=self.__pde_proj.getSolution()
491     return out
492 gross 2208
493 gross 2445 def inner_pBv(self,p,Bv):
494     """
495     returns inner product of element p and Bv=-div(v)
496    
497 jfenwick 2625 :param p: a pressure increment
498     :param Bv: a residual
499     :return: inner product of element p and Bv=-div(v)
500     :rtype: ``float``
501 gross 2445 """
502     return util.integrate(util.interpolate(p,Function(self.domain))*util.interpolate(Bv,Function(self.domain)))
503    
504 gross 2251 def inner_p(self,p0,p1):
505 gross 2100 """
506 gross 2251 Returns inner product of p0 and p1
507 gross 1414
508 jfenwick 2625 :param p0: a pressure
509     :param p1: a pressure
510     :return: inner product of p0 and p1
511     :rtype: ``float``
512 gross 2100 """
513 gross 2719 s0=util.interpolate(p0,Function(self.domain))
514     s1=util.interpolate(p1,Function(self.domain))
515 gross 2100 return util.integrate(s0*s1)
516 artak 1550
517 gross 2251 def norm_v(self,v):
518 gross 2100 """
519 gross 2251 returns the norm of v
520 gross 2208
521 jfenwick 2625 :param v: a velovity
522     :return: norm of v
523     :rtype: non-negative ``float``
524 gross 2100 """
525 gross 2719 return util.sqrt(util.integrate(util.length(util.grad(v))**2))
526 gross 2100
527 gross 2719 def getDV(self, p, v, tol):
528 gross 1414 """
529 gross 2251 return the value for v for a given p (overwrite)
530    
531 jfenwick 2625 :param p: a pressure
532 gross 2719 :param v: a initial guess for the value v to return.
533     :return: dv given as *Adv=(f-Av-B^*p)*
534 gross 1414 """
535 gross 2719 self.__pde_u.setValue(Y=self.__f, y=self.__surface_stress)
536     self.getSolverOptionsVelocity().setTolerance(tol)
537     self.getSolverOptionsVelocity().setAbsoluteTolerance(0.)
538 gross 2100 if self.__stress.isEmpty():
539 gross 2719 self.__pde_u.setValue(X=p*util.kronecker(self.domain)-2*self.eta*util.symmetric(util.grad(v)))
540 gross 2100 else:
541 gross 2719 self.__pde_u.setValue(X=self.__stress+p*util.kronecker(self.domain)-2*self.eta*util.symmetric(util.grad(v)))
542 gross 2474 out=self.__pde_u.getSolution()
543 gross 2208 return out
544 gross 1414
545 gross 2445 def norm_Bv(self,Bv):
546 gross 2251 """
547     Returns Bv (overwrite).
548    
549 jfenwick 2625 :rtype: equal to the type of p
550     :note: boundary conditions on p should be zero!
551 gross 2251 """
552 gross 2445 return util.sqrt(util.integrate(util.interpolate(Bv,Function(self.domain))**2))
553 gross 2251
554 gross 2719 def solve_AinvBt(self,p, tol):
555 gross 2251 """
556 gross 2719 Solves *Av=B^*p* with accuracy `tol`
557 gross 2251
558 jfenwick 2625 :param p: a pressure increment
559     :return: the solution of *Av=B^*p*
560     :note: boundary conditions on v should be zero!
561 gross 2251 """
562 gross 2719 self.__pde_u.setValue(Y=Data(), y=Data(), X=-p*util.kronecker(self.domain))
563 gross 2474 out=self.__pde_u.getSolution()
564 gross 2251 return out
565    
566 gross 2719 def solve_prec(self,Bv, tol):
567 gross 2251 """
568 jfenwick 2625 applies preconditioner for for *BA^{-1}B^** to *Bv*
569     with accuracy `self.getSubProblemTolerance()`
570 gross 2251
571 jfenwick 2625 :param Bv: velocity increment
572     :return: *p=P(Bv)* where *P^{-1}* is an approximation of *BA^{-1}B^ * )*
573     :note: boundary conditions on p are zero.
574 gross 2251 """
575 gross 2445 self.__pde_prec.setValue(Y=Bv)
576 gross 2719 self.getSolverOptionsPressure().setTolerance(tol)
577     self.getSolverOptionsPressure().setAbsoluteTolerance(0.)
578     out=self.__pde_prec.getSolution()
579     return out

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