/[escript]/trunk/escriptcore/py_src/flows.py
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revision 1519 by artak, Tue Apr 22 03:45:36 2008 UTC revision 3910 by gross, Thu Jun 14 00:45:03 2012 UTC
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1  # $Id:$  # -*- coding: utf-8 -*-
2    ########################################################
3  #  #
4  #######################################################  # Copyright (c) 2003-2010 by University of Queensland
5    # Earth Systems Science Computational Center (ESSCC)
6    # http://www.uq.edu.au/esscc
7  #  #
8  #       Copyright 2008 by University of Queensland  # Primary Business: Queensland, Australia
9  #  # Licensed under the Open Software License version 3.0
10  #                http://esscc.uq.edu.au  # http://www.opensource.org/licenses/osl-3.0.php
 #        Primary Business: Queensland, Australia  
 #  Licensed under the Open Software License version 3.0  
 #     http://www.opensource.org/licenses/osl-3.0.php  
 #  
 #######################################################  
11  #  #
12    ########################################################
13    
14    __copyright__="""Copyright (c) 2003-2010 by University of Queensland
15    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    __url__="https://launchpad.net/escript-finley"
21    
22  """  """
23  Some models for flow  Some models for flow
24    
25  @var __author__: name of author  :var __author__: name of author
26  @var __copyright__: copyrights  :var __copyright__: copyrights
27  @var __license__: licence agreement  :var __license__: licence agreement
28  @var __url__: url entry point on documentation  :var __url__: url entry point on documentation
29  @var __version__: version  :var __version__: version
30  @var __date__: date of the version  :var __date__: date of the version
31  """  """
32    
33  __author__="Lutz Gross, l.gross@uq.edu.au"  __author__="Lutz Gross, l.gross@uq.edu.au"
 __copyright__="""  Copyright (c) 2008 by ACcESS MNRF  
                     http://www.access.edu.au  
                 Primary Business: Queensland, Australia"""  
 __license__="""Licensed under the Open Software License version 3.0  
              http://www.opensource.org/licenses/osl-3.0.php"""  
 __url__="http://www.iservo.edu.au/esys"  
 __version__="$Revision:$"  
 __date__="$Date:$"  
   
 from escript import *  
 import util  
 from linearPDEs import LinearPDE  
 from pdetools import HomogeneousSaddlePointProblem  
34    
35  class StokesProblemCartesian(HomogeneousSaddlePointProblem):  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    
40    class DarcyFlow(object):
41       """
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       :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       """
54       EVAL="EVAL"
55       SIMPLE="EVAL"
56       POST="POST"
57       SMOOTH="SMOOTH"
58       def __init__(self, domain, useReduced=False, solver="POST", verbose=False, w=1.):
59          """
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          :param solver: solver method
66          :type solver: in [`DarcyFlow.EVAL`, `DarcyFlow.POST',  `DarcyFlow.SMOOTH' ]
67          :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          """
73          if not solver in [DarcyFlow.EVAL, DarcyFlow.POST,  DarcyFlow.SMOOTH ] :
74              raise ValueError("unknown solver %d."%solver)
75    
76          self.domain=domain
77          self.solver=solver
78          self.useReduced=useReduced
79          self.verbose=verbose
80          self.l=None
81          self.w=None
82        
83          self.__pde_p=LinearSinglePDE(domain)
84          self.__pde_p.setSymmetryOn()
85          if self.useReduced: self.__pde_p.setReducedOrderOn()
86    
87          if self.solver  == self.EVAL:
88             self.__pde_v=None
89             if self.verbose: print("DarcyFlow: simple solver is used.")
90    
91          elif self.solver  == self.POST:
92             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             self.__pde_v=LinearPDESystem(domain)
96             self.__pde_v.setSymmetryOn()
97             if self.useReduced: self.__pde_v.setReducedOrderOn()
98             self.w=w
99             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    
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             if self.verbose: print("DarcyFlow: flux smoothing is used.")
108             self.w=0
109    
110          self.__f=escript.Scalar(0,self.__pde_p.getFunctionSpaceForCoefficient("X"))
111          self.__g=escript.Vector(0,self.__pde_p.getFunctionSpaceForCoefficient("Y"))
112          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          self.location_of_fixed_pressure = escript.Scalar(0, self.__pde_p.getFunctionSpaceForCoefficient("q"))
117          self.location_of_fixed_flux = escript.Vector(0, self.__pde_p.getFunctionSpaceForCoefficient("q"))
118          self.perm_scale=1.
119        
120            
121       def setValue(self,f=None, g=None, location_of_fixed_pressure=None, location_of_fixed_flux=None, permeability=None):
122        """        """
123        solves        assigns values to model parameters
124    
125            -(eta*(u_{i,j}+u_{j,i}))_j - p_i = f_i        :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          :type permeability: scalar or symmetric tensor values on the domain (e.g. `escript.Data`)
135    
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          if location_of_fixed_pressure!=None:
144               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               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              if not self.__pde_v == None:
153                  self.__pde_v.setValue(q=self.location_of_fixed_flux)
154                
155          if permeability!=None:
156        
157             perm=util.interpolate(permeability,self.__pde_p.getFunctionSpaceForCoefficient("A"))
158             self.perm_scale=util.Lsup(util.length(perm))
159             if self.verbose: print(("DarcyFlow: permeability scaling factor = %e."%self.perm_scale))
160             perm=perm*(1./self.perm_scale)
161            
162             if perm.getRank()==0:
163    
164                perm_inv=(1./perm)
165                perm_inv=perm_inv*util.kronecker(self.domain.getDim())
166                perm=perm*util.kronecker(self.domain.getDim())
167            
168            
169             elif perm.getRank()==2:
170                perm_inv=util.inverse(perm)
171             else:
172                raise ValueError("illegal rank of permeability.")
173            
174             self.__permeability=perm
175             self.__permeability_inv=perm_inv
176        
177             #====================
178             self.__pde_p.setValue(A=self.__permeability)
179             if self.solver  == self.EVAL:
180                  pass # no extra work required
181             elif self.solver  == self.POST:
182                  k=util.kronecker(self.domain.getDim())
183                  self.omega = self.w*util.length(perm_inv)*self.l*self.domain.getSize()
184                  #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             elif self.solver  == self.SMOOTH:
187                self.__pde_v.setValue(D=self.__permeability_inv)
188    
189          if g != None:
190            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            self.__permeability_invXg=util.tensor_mult(self.__permeability_inv,self.__g * (1./self.perm_scale ))
197            self.__permeability_invXg_ref=util.integrate(self.__permeability_invXg)/util.vol(self.domain)
198          if f !=None:
199             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    
206       def getSolverOptionsFlux(self):
207          """
208          Returns the solver options used to solve the flux problems
209          :return: `SolverOptions`
210          """
211          if self.__pde_v == None:
212              return None
213          else:
214              return self.__pde_v.getSolverOptions()
215          
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          if not self.__pde_v == None:
223              self.__pde_v.setSolverOptions(options)
224        
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       def solve(self, u0, p0):
243          """
244          solves the problem.
245          
246          :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    
253          """
254          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                                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                                r=p0 - p0_hydrostatic)
265          pp=self.__pde_p.getSolution()
266          u = self._getFlux(pp, u0)
267          return u,pp + p0_hydrostatic
268          
269       def getFlux(self,p, u0=None):
270            """
271            returns the flux for a given pressure ``p`` where the flux is equal to ``u0``
272            on locations where ``location_of_fixed_flux`` is positive (see `setValue`).
273            Notice that ``g`` is used, see `setValue`.
274    
275            :param p: pressure.
276            :type p: scalar value on the domain (e.g. `escript.Data`).
277            :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            :return: flux
280            :rtype: `escript.Data`
281            """
282            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            if self.solver  == self.EVAL:
304               u = self.__g - util.tensor_mult(self.__permeability, self.perm_scale * (util.grad(pp) + self.__permeability_invXg_ref))
305            elif self.solver  == self.POST or self.solver  == self.SMOOTH:
306                self.__pde_v.setValue(Y= self.__permeability_invXg - (util.grad(pp) + self.__permeability_invXg_ref))
307                print
308                if u0 == None:
309                   self.__pde_v.setValue(r=escript.Data())
310                else:
311                   if not isinstance(u0, escript.Data) : u0 = escript.Vector(u0, escript.Solution(self.domain))
312                   self.__pde_v.setValue(r=1./self.perm_scale * u0)
313                u= self.__pde_v.getSolution() * self.perm_scale
314            return u
315          
316    class StokesProblemCartesian(HomogeneousSaddlePointProblem):
317         """
318         solves
319    
320              -(eta*(u_{i,j}+u_{j,i}))_j + p_i = f_i-stress_{ij,j}
321                  u_{i,i}=0                  u_{i,i}=0
322    
323            u=0 where  fixed_u_mask>0            u=0 where  fixed_u_mask>0
324            eta*(u_{i,j}+u_{j,i})*n_j=surface_stress            eta*(u_{i,j}+u_{j,i})*n_j-p*n_i=surface_stress +stress_{ij}n_j
325    
326        if surface_stress is not give 0 is assumed.       if surface_stress is not given 0 is assumed.
327    
328        typical usage:       typical usage:
329    
330              sp=StokesProblemCartesian(domain)              sp=StokesProblemCartesian(domain)
331              sp.setTolerance()              sp.setTolerance()
332              sp.initialize(...)              sp.initialize(...)
333              v,p=sp.solve(v0,p0)              v,p=sp.solve(v0,p0)
334        """              sp.setStokesEquation(...) # new values for some parameters
335        def __init__(self,domain,**kwargs):              v1,p1=sp.solve(v,p)
336         """
337         def __init__(self,domain,**kwargs):
338             """
339             initialize the Stokes Problem
340    
341             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             :type domain: `Domain`
347             """
348           HomogeneousSaddlePointProblem.__init__(self,**kwargs)           HomogeneousSaddlePointProblem.__init__(self,**kwargs)
349           self.domain=domain           self.domain=domain
350           self.vol=util.integrate(1.,Function(self.domain))           self.__pde_v=LinearPDE(domain,numEquations=self.domain.getDim(),numSolutions=self.domain.getDim())
351           self.__pde_u=LinearPDE(domain,numEquations=self.domain.getDim(),numSolutions=self.domain.getDim())           self.__pde_v.setSymmetryOn()
352           self.__pde_u.setSymmetryOn()      
          self.__pde_u.setSolverMethod(preconditioner=LinearPDE.ILU0)  
               
353           self.__pde_prec=LinearPDE(domain)           self.__pde_prec=LinearPDE(domain)
354           self.__pde_prec.setReducedOrderOn()           self.__pde_prec.setReducedOrderOn()
355           self.__pde_prec.setSymmetryOn()           self.__pde_prec.setSymmetryOn()
356    
357           self.__pde_proj=LinearPDE(domain)           self.__pde_proj=LinearPDE(domain)
358           self.__pde_proj.setReducedOrderOn()           self.__pde_proj.setReducedOrderOn()
359             self.__pde_proj.setValue(D=1)
360           self.__pde_proj.setSymmetryOn()           self.__pde_proj.setSymmetryOn()
          self.__pde_proj.setValue(D=1.)  
361    
362        def initialize(self,f=Data(),fixed_u_mask=Data(),eta=1,surface_stress=Data()):       def getSolverOptionsVelocity(self):
363          self.eta=eta           """
364          A =self.__pde_u.createCoefficientOfGeneralPDE("A")       returns the solver options used  solve the equation for velocity.
365      self.__pde_u.setValue(A=Data())      
366          for i in range(self.domain.getDim()):       :rtype: `SolverOptions`
367          for j in range(self.domain.getDim()):       """
368              A[i,j,j,i] += 1.           return self.__pde_v.getSolverOptions()
369              A[i,j,i,j] += 1.       def setSolverOptionsVelocity(self, options=None):
370      self.__pde_prec.setValue(D=1./self.eta)           """
371          self.__pde_u.setValue(A=A*self.eta,q=fixed_u_mask,Y=f,y=surface_stress)       set the solver options for solving the equation for velocity.
372        
373        def B(self,arg):       :param options: new solver  options
374           d=util.div(arg)       :type options: `SolverOptions`
375           self.__pde_proj.setValue(Y=d)       """
376           self.__pde_proj.setTolerance(self.getSubProblemTolerance())           self.__pde_v.setSolverOptions(options)
377           return self.__pde_proj.getSolution(verbose=self.show_details)       def getSolverOptionsPressure(self):
378             """
379        def inner(self,p0,p1):       returns the solver options used  solve the equation for pressure.
380           s0=util.interpolate(p0,Function(self.domain))       :rtype: `SolverOptions`
381           s1=util.interpolate(p1,Function(self.domain))       """
382             return self.__pde_prec.getSolverOptions()
383         def setSolverOptionsPressure(self, options=None):
384             """
385         set the solver options for solving the equation for pressure.
386         :param options: new solver  options
387         :type options: `SolverOptions`
388         """
389             self.__pde_prec.setSolverOptions(options)
390    
391         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         :param options: new solver options
397         :type options: `SolverOptions`
398         """
399             self.__pde_proj.setSolverOptions(options)
400         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         :rtype: `SolverOptions`
406         """
407             return self.__pde_proj.getSolverOptions()
408    
409         def updateStokesEquation(self, v, p):
410             """
411             updates the Stokes equation to consider dependencies from ``v`` and ``p``
412             :note: This method can be overwritten by a subclass. Use `setStokesEquation` to set new values to model parameters.
413             """
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                self.eta=util.interpolate(eta, escript.Function(self.domain))
434                self.__pde_prec.setValue(D=1/self.eta)
435                self.__pde_v.setValue(A=self.eta*(util.swap_axes(kk,0,3)+util.swap_axes(kk,1,3)))
436            if restoration_factor!=None:
437                n=self.domain.getNormal()
438                self.__pde_v.setValue(d=restoration_factor*util.outer(n,n))
439            if fixed_u_mask!=None:
440                self.__pde_v.setValue(q=fixed_u_mask)
441            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         def initialize(self,f=escript.Data(),fixed_u_mask=escript.Data(),eta=1,surface_stress=escript.Data(),stress=escript.Data(), restoration_factor=0):
446            """
447            assigns values to the model parameters
448    
449            :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            :type stress: `Tensor` object on `FunctionSpace` `Function` or similar
459            """
460            self.setStokesEquation(f,fixed_u_mask, eta, surface_stress, stress, restoration_factor)
461    
462         def Bv(self,v,tol):
463             """
464             returns inner product of element p and div(v)
465    
466             :param v: a residual
467             :return: inner product of element p and div(v)
468             :rtype: ``float``
469             """
470             self.__pde_proj.setValue(Y=-util.div(v))
471             self.getSolverOptionsDiv().setTolerance(tol)
472             self.getSolverOptionsDiv().setAbsoluteTolerance(0.)
473             out=self.__pde_proj.getSolution()
474             return out
475    
476         def inner_pBv(self,p,Bv):
477             """
478             returns inner product of element p and Bv=-div(v)
479    
480             :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             """
485             return util.integrate(util.interpolate(p,escript.Function(self.domain))*util.interpolate(Bv, escript.Function(self.domain)))
486    
487         def inner_p(self,p0,p1):
488             """
489             Returns inner product of p0 and p1
490    
491             :param p0: a pressure
492             :param p1: a pressure
493             :return: inner product of p0 and p1
494             :rtype: ``float``
495             """
496             s0=util.interpolate(p0, escript.Function(self.domain))
497             s1=util.interpolate(p1, escript.Function(self.domain))
498           return util.integrate(s0*s1)           return util.integrate(s0*s1)
499    
500        def getStress(self,u):       def norm_v(self,v):
501           mg=util.grad(u)           """
502           return 2.*self.eta*util.symmetric(mg)           returns the norm of v
503    
504        def solve_A(self,u,p):           :param v: a velovity
505           """           :return: norm of v
506           solves Av=f-Au-B^*p (v=0 on fixed_u_mask)           :rtype: non-negative ``float``
507           """           """
508           self.__pde_u.setTolerance(self.getSubProblemTolerance())           return util.sqrt(util.integrate(util.length(util.grad(v))**2))
509           self.__pde_u.setValue(X=-self.getStress(u)-p*util.kronecker(self.domain))  
510           return  self.__pde_u.getSolution(verbose=self.show_details)  
511         def getDV(self, p, v, tol):
512        def solve_prec(self,p):           """
513           self.__pde_prec.setTolerance(self.getSubProblemTolerance())           return the value for v for a given p
514           self.__pde_prec.setValue(Y=p)  
515           q=self.__pde_prec.getSolution(verbose=self.show_details)           :param p: a pressure
516           return q           :param v: a initial guess for the value v to return.
517        def stoppingcriterium(self,Bv,v,p):           :return: dv given as *Adv=(f-Av-B^*p)*
518            n_r=util.sqrt(self.inner(Bv,Bv))           """
519            n_v=util.Lsup(v)           self.updateStokesEquation(v,p)
520            if self.verbose: print "PCG step %s: L2(div(v)) = %s, Lsup(v)=%s"%(self.iter,n_r,n_v)           self.__pde_v.setValue(Y=self.__f, y=self.__surface_stress)
521            self.iter+=1           self.getSolverOptionsVelocity().setTolerance(tol)
522            if n_r <= self.vol**(1./2.-1./self.domain.getDim())*n_v*self.getTolerance():           self.getSolverOptionsVelocity().setAbsoluteTolerance(0.)
523                if self.verbose: print "PCG terminated after %s steps."%self.iter           if self.__stress.isEmpty():
524                return True              self.__pde_v.setValue(X=p*util.kronecker(self.domain)-2*self.eta*util.symmetric(util.grad(v)))
525            else:           else:
526                return False              self.__pde_v.setValue(X=self.__stress+p*util.kronecker(self.domain)-2*self.eta*util.symmetric(util.grad(v)))
527        def stoppingcriterium2(self,norm_r,norm_b,solver='GMRES',TOL=None):           out=self.__pde_v.getSolution()
528        if TOL==None:           return  out
529               TOL=self.getTolerance()  
530            if self.verbose: print "%s step %s: L2(r) = %s, L2(b)*TOL=%s"%(solver,self.iter,norm_r,norm_b*TOL)       def norm_Bv(self,Bv):
531            self.iter+=1          """
532                      Returns Bv (overwrite).
533            if norm_r <= norm_b*TOL:  
534                if self.verbose: print "%s terminated after %s steps."%(solver,self.iter)          :rtype: equal to the type of p
535                return True          :note: boundary conditions on p should be zero!
536            else:          """
537                return False          return util.sqrt(util.integrate(util.interpolate(Bv, escript.Function(self.domain))**2))
538    
539         def solve_AinvBt(self,p, tol):
540             """
541             Solves *Av=B^*p* with accuracy `tol`
542    
543             :param p: a pressure increment
544             :return: the solution of *Av=B^*p*
545             :note: boundary conditions on v should be zero!
546             """
547             self.__pde_v.setValue(Y=escript.Data(), y=escript.Data(), X=-p*util.kronecker(self.domain))
548             out=self.__pde_v.getSolution()
549             return  out
550    
551         def solve_prec(self,Bv, tol):
552             """
553             applies preconditioner for for *BA^{-1}B^** to *Bv*
554             with accuracy `self.getSubProblemTolerance()`
555    
556             :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             """
560             self.__pde_prec.setValue(Y=Bv)
561             self.getSolverOptionsPressure().setTolerance(tol)
562             self.getSolverOptionsPressure().setAbsoluteTolerance(0.)
563             out=self.__pde_prec.getSolution()
564             return out

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