/[escript]/trunk/escriptcore/py_src/flows.py
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Revision 3911 - (hide annotations)
Thu Jun 14 01:01:03 2012 UTC (7 years, 2 months ago) by jfenwick
Original Path: trunk/escript/py_src/flows.py
File MIME type: text/x-python
File size: 23938 byte(s)
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1 gross 3071 # -*- coding: utf-8 -*-
2 ksteube 1809 ########################################################
3 gross 1414 #
4 jfenwick 3911 # Copyright (c) 2003-2012 by University of Queensland
5 ksteube 1809 # Earth Systems Science Computational Center (ESSCC)
6     # http://www.uq.edu.au/esscc
7 gross 1414 #
8 ksteube 1809 # Primary Business: Queensland, Australia
9     # Licensed under the Open Software License version 3.0
10     # http://www.opensource.org/licenses/osl-3.0.php
11 gross 1414 #
12 ksteube 1809 ########################################################
13 gross 1414
14 jfenwick 3911 __copyright__="""Copyright (c) 2003-2012 by University of Queensland
15 ksteube 1809 Earth Systems Science Computational Center (ESSCC)
16     http://www.uq.edu.au/esscc
17     Primary Business: Queensland, Australia"""
18     __license__="""Licensed under the Open Software License version 3.0
19     http://www.opensource.org/licenses/osl-3.0.php"""
20 jfenwick 2344 __url__="https://launchpad.net/escript-finley"
21 ksteube 1809
22 gross 1414 """
23     Some models for flow
24    
25 jfenwick 2625 :var __author__: name of author
26     :var __copyright__: copyrights
27     :var __license__: licence agreement
28     :var __url__: url entry point on documentation
29     :var __version__: version
30     :var __date__: date of the version
31 gross 1414 """
32    
33     __author__="Lutz Gross, l.gross@uq.edu.au"
34    
35 jfenwick 3771 from . import escript
36     from . import util
37     from .linearPDEs import LinearPDE, LinearPDESystem, LinearSinglePDE, SolverOptions
38     from .pdetools import HomogeneousSaddlePointProblem,Projector, ArithmeticTuple, PCG, NegativeNorm, GMRES
39 gross 1414
40 gross 3502 class DarcyFlow(object):
41 gross 3499 """
42     solves the problem
43    
44     *u_i+k_{ij}*p_{,j} = g_i*
45     *u_{i,i} = f*
46    
47     where *p* represents the pressure and *u* the Darcy flux. *k* represents the permeability,
48    
49 gross 3569 :cvar EVAL: direct pressure gradient evaluation for flux
50     :cvar POST: global postprocessing of flux by solving the PDE *K_{ij} u_j + (w * K * l u_{k,k})_{,i}= - p_{,j} + K_{ij} g_j*
51     where *l* is the length scale, *K* is the inverse of the permeability tensor, and *w* is a positive weighting factor.
52     :cvar SMOOTH: global smoothing by solving the PDE *K_{ij} u_j= - p_{,j} + K_{ij} g_j*
53 gross 3499 """
54 gross 3569 EVAL="EVAL"
55     SIMPLE="EVAL"
56 gross 3502 POST="POST"
57 gross 3569 SMOOTH="SMOOTH"
58 gross 3630 def __init__(self, domain, useReduced=False, solver="POST", verbose=False, w=1.):
59 gross 3499 """
60     initializes the Darcy flux problem
61     :param domain: domain of the problem
62     :type domain: `Domain`
63     :param useReduced: uses reduced oreder on flux and pressure
64     :type useReduced: ``bool``
65 gross 3502 :param solver: solver method
66 gross 3569 :type solver: in [`DarcyFlow.EVAL`, `DarcyFlow.POST', `DarcyFlow.SMOOTH' ]
67 gross 3502 :param verbose: if ``True`` some information on the iteration progress are printed.
68     :type verbose: ``bool``
69     :param w: weighting factor for `DarcyFlow.POST` solver
70     :type w: ``float``
71    
72 gross 3499 """
73 gross 3569 if not solver in [DarcyFlow.EVAL, DarcyFlow.POST, DarcyFlow.SMOOTH ] :
74 jfenwick 3771 raise ValueError("unknown solver %d."%solver)
75 gross 3569
76 gross 3499 self.domain=domain
77 gross 3502 self.solver=solver
78 gross 3499 self.useReduced=useReduced
79 gross 3502 self.verbose=verbose
80 gross 3569 self.l=None
81     self.w=None
82    
83 gross 3502 self.__pde_p=LinearSinglePDE(domain)
84     self.__pde_p.setSymmetryOn()
85     if self.useReduced: self.__pde_p.setReducedOrderOn()
86 gross 3569
87     if self.solver == self.EVAL:
88     self.__pde_v=None
89 jfenwick 3852 if self.verbose: print("DarcyFlow: simple solver is used.")
90 gross 3569
91 gross 3502 elif self.solver == self.POST:
92 jfenwick 3852 if util.inf(w)<0.:
93     raise ValueError("Weighting factor must be non-negative.")
94     if self.verbose: print("DarcyFlow: global postprocessing of flux is used.")
95 gross 3569 self.__pde_v=LinearPDESystem(domain)
96     self.__pde_v.setSymmetryOn()
97     if self.useReduced: self.__pde_v.setReducedOrderOn()
98 jfenwick 3852 self.w=w
99 gross 3905 x=self.domain.getX()
100     self.l=min( [util.sup(x[i])-util.inf(x[i]) for i in xrange(self.domain.getDim()) ] )
101     #self.l=util.vol(self.domain)**(1./self.domain.getDim()) # length scale
102 gross 3569
103     elif self.solver == self.SMOOTH:
104     self.__pde_v=LinearPDESystem(domain)
105     self.__pde_v.setSymmetryOn()
106     if self.useReduced: self.__pde_v.setReducedOrderOn()
107 jfenwick 3852 if self.verbose: print("DarcyFlow: flux smoothing is used.")
108     self.w=0
109 gross 3569
110 gross 3502 self.__f=escript.Scalar(0,self.__pde_p.getFunctionSpaceForCoefficient("X"))
111 gross 3569 self.__g=escript.Vector(0,self.__pde_p.getFunctionSpaceForCoefficient("Y"))
112 gross 3909 self.__permeability_invXg=escript.Vector(0,self.__pde_p.getFunctionSpaceForCoefficient("Y"))
113     self.__permeability_invXg_ref=util.numpy.zeros((self.domain.getDim()),util.numpy.float64)
114     self.ref_point_id=None
115     self.ref_point=util.numpy.zeros((self.domain.getDim()),util.numpy.float64)
116 gross 3502 self.location_of_fixed_pressure = escript.Scalar(0, self.__pde_p.getFunctionSpaceForCoefficient("q"))
117 gross 3569 self.location_of_fixed_flux = escript.Vector(0, self.__pde_p.getFunctionSpaceForCoefficient("q"))
118 gross 3619 self.perm_scale=1.
119 gross 3502
120    
121 gross 3499 def setValue(self,f=None, g=None, location_of_fixed_pressure=None, location_of_fixed_flux=None, permeability=None):
122     """
123     assigns values to model parameters
124    
125     :param f: volumetic sources/sinks
126     :type f: scalar value on the domain (e.g. `escript.Data`)
127     :param g: flux sources/sinks
128     :type g: vector values on the domain (e.g. `escript.Data`)
129     :param location_of_fixed_pressure: mask for locations where pressure is fixed
130     :type location_of_fixed_pressure: scalar value on the domain (e.g. `escript.Data`)
131     :param location_of_fixed_flux: mask for locations where flux is fixed.
132     :type location_of_fixed_flux: vector values on the domain (e.g. `escript.Data`)
133     :param permeability: permeability tensor. If scalar ``s`` is given the tensor with ``s`` on the main diagonal is used.
134 gross 3502 :type permeability: scalar or symmetric tensor values on the domain (e.g. `escript.Data`)
135 gross 3499
136     :note: the values of parameters which are not set by calling ``setValue`` are not altered.
137     :note: at any point on the boundary of the domain the pressure
138     (``location_of_fixed_pressure`` >0) or the normal component of the
139     flux (``location_of_fixed_flux[i]>0``) if direction of the normal
140     is along the *x_i* axis.
141    
142     """
143 gross 3502 if location_of_fixed_pressure!=None:
144 gross 3909 self.location_of_fixed_pressure=util.wherePositive(util.interpolate(location_of_fixed_pressure, self.__pde_p.getFunctionSpaceForCoefficient("q")))
145     self.ref_point_id=self.location_of_fixed_pressure.maxGlobalDataPoint()
146     if not self.location_of_fixed_pressure.getTupleForGlobalDataPoint(*self.ref_point_id)[0] > 0: raise ValueError("pressure needs to be fixed at least one point.")
147     self.ref_point=self.__pde_p.getFunctionSpaceForCoefficient("q").getX().getTupleForGlobalDataPoint(*self.ref_point_id)
148     if self.verbose: print(("DarcyFlow: reference point at %s."%(self.ref_point,)))
149 gross 3502 self.__pde_p.setValue(q=self.location_of_fixed_pressure)
150     if location_of_fixed_flux!=None:
151     self.location_of_fixed_flux=util.wherePositive(location_of_fixed_flux)
152 gross 3910 if not self.__pde_v == None:
153     self.__pde_v.setValue(q=self.location_of_fixed_flux)
154 gross 3499
155     if permeability!=None:
156 gross 3502
157 jfenwick 3852 perm=util.interpolate(permeability,self.__pde_p.getFunctionSpaceForCoefficient("A"))
158 gross 3619 self.perm_scale=util.Lsup(util.length(perm))
159 jfenwick 3852 if self.verbose: print(("DarcyFlow: permeability scaling factor = %e."%self.perm_scale))
160 gross 3619 perm=perm*(1./self.perm_scale)
161 gross 3502
162 jfenwick 3852 if perm.getRank()==0:
163 gross 3569
164 jfenwick 3852 perm_inv=(1./perm)
165     perm_inv=perm_inv*util.kronecker(self.domain.getDim())
166     perm=perm*util.kronecker(self.domain.getDim())
167 gross 3502
168    
169 jfenwick 3852 elif perm.getRank()==2:
170     perm_inv=util.inverse(perm)
171     else:
172     raise ValueError("illegal rank of permeability.")
173 gross 3499
174 jfenwick 3852 self.__permeability=perm
175     self.__permeability_inv=perm_inv
176 gross 3502
177 gross 3569 #====================
178 jfenwick 3852 self.__pde_p.setValue(A=self.__permeability)
179 gross 3569 if self.solver == self.EVAL:
180     pass # no extra work required
181     elif self.solver == self.POST:
182 jfenwick 3852 k=util.kronecker(self.domain.getDim())
183     self.omega = self.w*util.length(perm_inv)*self.l*self.domain.getSize()
184 gross 3885 #self.__pde_v.setValue(D=self.__permeability_inv, A=self.omega*util.outer(k,k))
185     self.__pde_v.setValue(D=self.__permeability_inv, A_reduced=self.omega*util.outer(k,k))
186 gross 3569 elif self.solver == self.SMOOTH:
187 jfenwick 3852 self.__pde_v.setValue(D=self.__permeability_inv)
188 gross 3502
189 gross 3499 if g != None:
190 jfenwick 3852 g=util.interpolate(g, self.__pde_p.getFunctionSpaceForCoefficient("Y"))
191     if g.isEmpty():
192     g=Vector(0,self.__pde_p.getFunctionSpaceForCoefficient("Y"))
193     else:
194     if not g.getShape()==(self.domain.getDim(),): raise ValueError("illegal shape of g")
195     self.__g=g
196 gross 3910 self.__permeability_invXg=util.tensor_mult(self.__permeability_inv,self.__g * (1./self.perm_scale ))
197 gross 3909 self.__permeability_invXg_ref=util.integrate(self.__permeability_invXg)/util.vol(self.domain)
198 gross 3499 if f !=None:
199 jfenwick 3852 f=util.interpolate(f, self.__pde_p.getFunctionSpaceForCoefficient("Y"))
200     if f.isEmpty():
201     f=Scalar(0,self.__pde_p.getFunctionSpaceForCoefficient("Y"))
202     else:
203     if f.getRank()>0: raise ValueError("illegal rank of f.")
204     self.__f=f
205 gross 3569
206 gross 3071 def getSolverOptionsFlux(self):
207     """
208     Returns the solver options used to solve the flux problems
209     :return: `SolverOptions`
210     """
211 gross 3569 if self.__pde_v == None:
212     return None
213     else:
214     return self.__pde_v.getSolverOptions()
215 gross 3071
216     def setSolverOptionsFlux(self, options=None):
217     """
218     Sets the solver options used to solve the flux problems
219     If ``options`` is not present, the options are reset to default
220     :param options: `SolverOptions`
221     """
222 gross 3569 if not self.__pde_v == None:
223     self.__pde_v.setSolverOptions(options)
224 gross 3071
225     def getSolverOptionsPressure(self):
226     """
227     Returns the solver options used to solve the pressure problems
228     :return: `SolverOptions`
229     """
230     return self.__pde_p.getSolverOptions()
231    
232     def setSolverOptionsPressure(self, options=None):
233     """
234     Sets the solver options used to solve the pressure problems
235     If ``options`` is not present, the options are reset to default
236    
237     :param options: `SolverOptions`
238     :note: if the adaption of subtolerance is choosen, the tolerance set by ``options`` will be overwritten before the solver is called.
239     """
240     return self.__pde_p.setSolverOptions(options)
241    
242 gross 3569 def solve(self, u0, p0):
243 gross 3071 """
244 gross 3502 solves the problem.
245 gross 3071
246 gross 3502 :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.
247     :type u0: vector value on the domain (e.g. `escript.Data`).
248     :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.
249     :type p0: scalar value on the domain (e.g. `escript.Data`).
250     :return: flux and pressure
251     :rtype: ``tuple`` of `escript.Data`.
252 gross 2960
253 gross 3071 """
254 gross 3909 p0=util.interpolate(p0, self.__pde_p.getFunctionSpaceForCoefficient("q"))
255     if self.ref_point_id == None:
256     p_ref=0
257     else:
258     p_ref=p0.getTupleForGlobalDataPoint(*self.ref_point_id)[0]
259     p0_hydrostatic=p_ref+util.inner(self.__permeability_invXg_ref, self.__pde_p.getFunctionSpaceForCoefficient("q").getX() - self.ref_point)
260     g_2=self.__g - util.tensor_mult(self.__permeability, self.__permeability_invXg_ref * self.perm_scale)
261     self.__pde_p.setValue(X=g_2 * 1./self.perm_scale,
262 gross 3620 Y=self.__f * 1./self.perm_scale,
263     y= - util.inner(self.domain.getNormal(),u0 * self.location_of_fixed_flux * 1./self.perm_scale ),
264 gross 3909 r=p0 - p0_hydrostatic)
265     pp=self.__pde_p.getSolution()
266     u = self._getFlux(pp, u0)
267     return u,pp + p0_hydrostatic
268 gross 3502
269     def getFlux(self,p, u0=None):
270 gross 2100 """
271 gross 3502 returns the flux for a given pressure ``p`` where the flux is equal to ``u0``
272 jfenwick 2625 on locations where ``location_of_fixed_flux`` is positive (see `setValue`).
273 gross 3569 Notice that ``g`` is used, see `setValue`.
274 gross 2264
275 jfenwick 2625 :param p: pressure.
276 gross 3440 :type p: scalar value on the domain (e.g. `escript.Data`).
277 gross 3502 :param u0: flux on the locations of the domain marked be ``location_of_fixed_flux``.
278     :type u0: vector values on the domain (e.g. `escript.Data`) or ``None``
279 jfenwick 2625 :return: flux
280 gross 3440 :rtype: `escript.Data`
281 gross 2264 """
282 gross 3909 p=util.interpolate(p, self.__pde_p.getFunctionSpaceForCoefficient("q"))
283     if self.ref_point_id == None:
284     p_ref=0
285     else:
286     p_ref=p.getTupleForGlobalDataPoint(*self.ref_point_id)[0]
287     p_hydrostatic=p_ref+util.inner(self.__permeability_invXg_ref, self.__pde_p.getFunctionSpaceForCoefficient("q").getX() - self.ref_point)
288     return self._getFlux(p-p_hydrostatic, u0)
289    
290     def _getFlux(self,pp, u0=None):
291     """
292     returns the flux for a given pressure ``p`` where the flux is equal to ``u0``
293     on locations where ``location_of_fixed_flux`` is positive (see `setValue`).
294     Notice that ``g`` is used, see `setValue`.
295    
296     :param p: pressure.
297     :type p: scalar value on the domain (e.g. `escript.Data`).
298     :param u0: flux on the locations of the domain marked be ``location_of_fixed_flux``.
299     :type u0: vector values on the domain (e.g. `escript.Data`) or ``None``
300     :return: flux
301     :rtype: `escript.Data`
302     """
303 gross 3569 if self.solver == self.EVAL:
304 gross 3909 u = self.__g - util.tensor_mult(self.__permeability, self.perm_scale * (util.grad(pp) + self.__permeability_invXg_ref))
305 gross 3569 elif self.solver == self.POST or self.solver == self.SMOOTH:
306 gross 3909 self.__pde_v.setValue(Y= self.__permeability_invXg - (util.grad(pp) + self.__permeability_invXg_ref))
307 gross 3910 print
308 gross 3502 if u0 == None:
309 jfenwick 3852 self.__pde_v.setValue(r=escript.Data())
310     else:
311 gross 3630 if not isinstance(u0, escript.Data) : u0 = escript.Vector(u0, escript.Solution(self.domain))
312 jfenwick 3852 self.__pde_v.setValue(r=1./self.perm_scale * u0)
313 gross 3910 u= self.__pde_v.getSolution() * self.perm_scale
314 jfenwick 3852 return u
315 gross 3502
316 gross 1414 class StokesProblemCartesian(HomogeneousSaddlePointProblem):
317 gross 2251 """
318 gross 2264 solves
319 gross 1414
320 gross 2208 -(eta*(u_{i,j}+u_{j,i}))_j + p_i = f_i-stress_{ij,j}
321     u_{i,i}=0
322 gross 1414
323 gross 2208 u=0 where fixed_u_mask>0
324     eta*(u_{i,j}+u_{j,i})*n_j-p*n_i=surface_stress +stress_{ij}n_j
325 gross 1414
326 gross 2264 if surface_stress is not given 0 is assumed.
327 gross 1414
328 gross 2251 typical usage:
329 gross 1414
330 gross 2208 sp=StokesProblemCartesian(domain)
331     sp.setTolerance()
332     sp.initialize(...)
333     v,p=sp.solve(v0,p0)
334 gross 3582 sp.setStokesEquation(...) # new values for some parameters
335     v1,p1=sp.solve(v,p)
336 gross 2251 """
337 gross 2719 def __init__(self,domain,**kwargs):
338 gross 2100 """
339 gross 2208 initialize the Stokes Problem
340 gross 2100
341 gross 2793 The approximation spaces used for velocity (=Solution(domain)) and pressure (=ReducedSolution(domain)) must be
342     LBB complient, for instance using quadratic and linear approximation on the same element or using linear approximation
343     with macro elements for the pressure.
344    
345     :param domain: domain of the problem.
346 jfenwick 2625 :type domain: `Domain`
347 gross 2100 """
348 gross 2719 HomogeneousSaddlePointProblem.__init__(self,**kwargs)
349 gross 1414 self.domain=domain
350 gross 3502 self.__pde_v=LinearPDE(domain,numEquations=self.domain.getDim(),numSolutions=self.domain.getDim())
351     self.__pde_v.setSymmetryOn()
352 gross 2474
353 gross 1414 self.__pde_prec=LinearPDE(domain)
354     self.__pde_prec.setReducedOrderOn()
355     self.__pde_prec.setSymmetryOn()
356    
357 gross 2415 self.__pde_proj=LinearPDE(domain)
358     self.__pde_proj.setReducedOrderOn()
359 jfenwick 3852 self.__pde_proj.setValue(D=1)
360 gross 2415 self.__pde_proj.setSymmetryOn()
361    
362 gross 2474 def getSolverOptionsVelocity(self):
363     """
364     returns the solver options used solve the equation for velocity.
365    
366 jfenwick 2625 :rtype: `SolverOptions`
367 gross 2474 """
368 jfenwick 3852 return self.__pde_v.getSolverOptions()
369 gross 2474 def setSolverOptionsVelocity(self, options=None):
370     """
371     set the solver options for solving the equation for velocity.
372    
373 jfenwick 2625 :param options: new solver options
374     :type options: `SolverOptions`
375 gross 2474 """
376 gross 3502 self.__pde_v.setSolverOptions(options)
377 gross 2474 def getSolverOptionsPressure(self):
378     """
379     returns the solver options used solve the equation for pressure.
380 jfenwick 2625 :rtype: `SolverOptions`
381 gross 2474 """
382 jfenwick 3852 return self.__pde_prec.getSolverOptions()
383 gross 2474 def setSolverOptionsPressure(self, options=None):
384     """
385     set the solver options for solving the equation for pressure.
386 jfenwick 2625 :param options: new solver options
387     :type options: `SolverOptions`
388 gross 2474 """
389 jfenwick 3852 self.__pde_prec.setSolverOptions(options)
390 gross 2415
391 gross 2474 def setSolverOptionsDiv(self, options=None):
392     """
393     set the solver options for solving the equation to project the divergence of
394     the velocity onto the function space of presure.
395    
396 jfenwick 2625 :param options: new solver options
397     :type options: `SolverOptions`
398 gross 2474 """
399 jfenwick 3852 self.__pde_proj.setSolverOptions(options)
400 gross 2474 def getSolverOptionsDiv(self):
401     """
402     returns the solver options for solving the equation to project the divergence of
403     the velocity onto the function space of presure.
404    
405 jfenwick 2625 :rtype: `SolverOptions`
406 gross 2474 """
407 jfenwick 3852 return self.__pde_proj.getSolverOptions()
408 gross 2474
409 gross 2793 def updateStokesEquation(self, v, p):
410     """
411     updates the Stokes equation to consider dependencies from ``v`` and ``p``
412 gross 3582 :note: This method can be overwritten by a subclass. Use `setStokesEquation` to set new values to model parameters.
413 gross 2793 """
414     pass
415     def setStokesEquation(self, f=None,fixed_u_mask=None,eta=None,surface_stress=None,stress=None, restoration_factor=None):
416     """
417     assigns new values to the model parameters.
418    
419     :param f: external force
420     :type f: `Vector` object in `FunctionSpace` `Function` or similar
421     :param fixed_u_mask: mask of locations with fixed velocity.
422     :type fixed_u_mask: `Vector` object on `FunctionSpace` `Solution` or similar
423     :param eta: viscosity
424     :type eta: `Scalar` object on `FunctionSpace` `Function` or similar
425     :param surface_stress: normal surface stress
426     :type surface_stress: `Vector` object on `FunctionSpace` `FunctionOnBoundary` or similar
427     :param stress: initial stress
428     :type stress: `Tensor` object on `FunctionSpace` `Function` or similar
429     """
430     if eta !=None:
431     k=util.kronecker(self.domain.getDim())
432     kk=util.outer(k,k)
433 jfenwick 3432 self.eta=util.interpolate(eta, escript.Function(self.domain))
434 jfenwick 3852 self.__pde_prec.setValue(D=1/self.eta)
435 gross 3502 self.__pde_v.setValue(A=self.eta*(util.swap_axes(kk,0,3)+util.swap_axes(kk,1,3)))
436 gross 2793 if restoration_factor!=None:
437     n=self.domain.getNormal()
438 gross 3502 self.__pde_v.setValue(d=restoration_factor*util.outer(n,n))
439 gross 2793 if fixed_u_mask!=None:
440 gross 3502 self.__pde_v.setValue(q=fixed_u_mask)
441 gross 2793 if f!=None: self.__f=f
442     if surface_stress!=None: self.__surface_stress=surface_stress
443     if stress!=None: self.__stress=stress
444    
445 jfenwick 3432 def initialize(self,f=escript.Data(),fixed_u_mask=escript.Data(),eta=1,surface_stress=escript.Data(),stress=escript.Data(), restoration_factor=0):
446 gross 2208 """
447     assigns values to the model parameters
448 gross 2100
449 jfenwick 2625 :param f: external force
450     :type f: `Vector` object in `FunctionSpace` `Function` or similar
451     :param fixed_u_mask: mask of locations with fixed velocity.
452     :type fixed_u_mask: `Vector` object on `FunctionSpace` `Solution` or similar
453     :param eta: viscosity
454     :type eta: `Scalar` object on `FunctionSpace` `Function` or similar
455     :param surface_stress: normal surface stress
456     :type surface_stress: `Vector` object on `FunctionSpace` `FunctionOnBoundary` or similar
457     :param stress: initial stress
458 jfenwick 3852 :type stress: `Tensor` object on `FunctionSpace` `Function` or similar
459 gross 2208 """
460 gross 2793 self.setStokesEquation(f,fixed_u_mask, eta, surface_stress, stress, restoration_factor)
461 gross 1414
462 gross 2719 def Bv(self,v,tol):
463 gross 2251 """
464     returns inner product of element p and div(v)
465 gross 1414
466 jfenwick 2625 :param v: a residual
467     :return: inner product of element p and div(v)
468     :rtype: ``float``
469 gross 2100 """
470 gross 2793 self.__pde_proj.setValue(Y=-util.div(v))
471 jfenwick 3852 self.getSolverOptionsDiv().setTolerance(tol)
472     self.getSolverOptionsDiv().setAbsoluteTolerance(0.)
473 gross 2719 out=self.__pde_proj.getSolution()
474     return out
475 gross 2208
476 gross 2445 def inner_pBv(self,p,Bv):
477     """
478     returns inner product of element p and Bv=-div(v)
479    
480 jfenwick 2625 :param p: a pressure increment
481     :param Bv: a residual
482     :return: inner product of element p and Bv=-div(v)
483     :rtype: ``float``
484 gross 2445 """
485 jfenwick 3432 return util.integrate(util.interpolate(p,escript.Function(self.domain))*util.interpolate(Bv, escript.Function(self.domain)))
486 gross 2445
487 gross 2251 def inner_p(self,p0,p1):
488 gross 2100 """
489 gross 2251 Returns inner product of p0 and p1
490 gross 1414
491 jfenwick 2625 :param p0: a pressure
492     :param p1: a pressure
493     :return: inner product of p0 and p1
494     :rtype: ``float``
495 gross 2100 """
496 jfenwick 3432 s0=util.interpolate(p0, escript.Function(self.domain))
497     s1=util.interpolate(p1, escript.Function(self.domain))
498 gross 2100 return util.integrate(s0*s1)
499 artak 1550
500 gross 2251 def norm_v(self,v):
501 gross 2100 """
502 gross 2251 returns the norm of v
503 gross 2208
504 jfenwick 2625 :param v: a velovity
505     :return: norm of v
506     :rtype: non-negative ``float``
507 gross 2100 """
508 gross 2719 return util.sqrt(util.integrate(util.length(util.grad(v))**2))
509 gross 2100
510 gross 2793
511 gross 2719 def getDV(self, p, v, tol):
512 gross 1414 """
513 gross 3582 return the value for v for a given p
514 gross 2251
515 jfenwick 2625 :param p: a pressure
516 gross 2719 :param v: a initial guess for the value v to return.
517     :return: dv given as *Adv=(f-Av-B^*p)*
518 gross 1414 """
519 gross 2793 self.updateStokesEquation(v,p)
520 gross 3502 self.__pde_v.setValue(Y=self.__f, y=self.__surface_stress)
521 jfenwick 3852 self.getSolverOptionsVelocity().setTolerance(tol)
522     self.getSolverOptionsVelocity().setAbsoluteTolerance(0.)
523 gross 2100 if self.__stress.isEmpty():
524 gross 3502 self.__pde_v.setValue(X=p*util.kronecker(self.domain)-2*self.eta*util.symmetric(util.grad(v)))
525 gross 2100 else:
526 gross 3502 self.__pde_v.setValue(X=self.__stress+p*util.kronecker(self.domain)-2*self.eta*util.symmetric(util.grad(v)))
527     out=self.__pde_v.getSolution()
528 gross 2208 return out
529 gross 1414
530 gross 2445 def norm_Bv(self,Bv):
531 gross 2251 """
532     Returns Bv (overwrite).
533    
534 jfenwick 2625 :rtype: equal to the type of p
535     :note: boundary conditions on p should be zero!
536 gross 2251 """
537 jfenwick 3432 return util.sqrt(util.integrate(util.interpolate(Bv, escript.Function(self.domain))**2))
538 gross 2251
539 gross 2719 def solve_AinvBt(self,p, tol):
540 gross 2251 """
541 gross 2719 Solves *Av=B^*p* with accuracy `tol`
542 gross 2251
543 jfenwick 2625 :param p: a pressure increment
544     :return: the solution of *Av=B^*p*
545     :note: boundary conditions on v should be zero!
546 gross 2251 """
547 gross 3502 self.__pde_v.setValue(Y=escript.Data(), y=escript.Data(), X=-p*util.kronecker(self.domain))
548     out=self.__pde_v.getSolution()
549 gross 2251 return out
550    
551 gross 2719 def solve_prec(self,Bv, tol):
552 gross 2251 """
553 jfenwick 2625 applies preconditioner for for *BA^{-1}B^** to *Bv*
554     with accuracy `self.getSubProblemTolerance()`
555 gross 2251
556 jfenwick 2625 :param Bv: velocity increment
557     :return: *p=P(Bv)* where *P^{-1}* is an approximation of *BA^{-1}B^ * )*
558     :note: boundary conditions on p are zero.
559 gross 2251 """
560 gross 2445 self.__pde_prec.setValue(Y=Bv)
561 jfenwick 3852 self.getSolverOptionsPressure().setTolerance(tol)
562     self.getSolverOptionsPressure().setAbsoluteTolerance(0.)
563 gross 2719 out=self.__pde_prec.getSolution()
564     return out

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