# Diff of /trunk/escript/py_src/flows.py

revision 2624 by gross, Thu Aug 20 06:24:00 2009 UTC revision 2625 by jfenwick, Fri Aug 21 06:30:25 2009 UTC
# Line 21  __url__="https://launchpad.net/escript-f Line 21  __url__="https://launchpad.net/escript-f
21  """  """
22  Some models for flow  Some models for flow
23
24  @var __author__: name of author  :var __author__: name of author
26  @var __license__: licence agreement  :var __license__: licence agreement
27  @var __url__: url entry point on documentation  :var __url__: url entry point on documentation
28  @var __version__: version  :var __version__: version
29  @var __date__: date of the version  :var __date__: date of the version
30  """  """
31
32  __author__="Lutz Gross, l.gross@uq.edu.au"  __author__="Lutz Gross, l.gross@uq.edu.au"
# Line 40  class DarcyFlow(object): Line 40  class DarcyFlow(object):
40      """      """
41      solves the problem      solves the problem
42
43      M{u_i+k_{ij}*p_{,j} = g_i}      *u_i+k_{ij}*p_{,j} = g_i*
44      M{u_{i,i} = f}      *u_{i,i} = f*
45
46      where M{p} represents the pressure and M{u} the Darcy flux. M{k} represents the permeability,      where *p* represents the pressure and *u* the Darcy flux. *k* represents the permeability,
47
48      @note: The problem is solved in a least squares formulation.      :note: The problem is solved in a least squares formulation.
49      """      """
50
51      def __init__(self, domain, weight=None, useReduced=False, adaptSubTolerance=True):      def __init__(self, domain, weight=None, useReduced=False, adaptSubTolerance=True):
52          """          """
53          initializes the Darcy flux problem          initializes the Darcy flux problem
54          @param domain: domain of the problem          :param domain: domain of the problem
55          @type domain: L{Domain}          :type domain: `Domain`
56      @param useReduced: uses reduced oreder on flux and pressure      :param useReduced: uses reduced oreder on flux and pressure
57      @type useReduced: C{bool}      :type useReduced: ``bool``
58      @param adaptSubTolerance: switches on automatic subtolerance selection      :param adaptSubTolerance: switches on automatic subtolerance selection
59      @type adaptSubTolerance: C{bool}          :type adaptSubTolerance: ``bool``
60          """          """
61          self.domain=domain          self.domain=domain
62          if weight == None:          if weight == None:
# Line 83  class DarcyFlow(object): Line 83  class DarcyFlow(object):
83      """      """
84      Returns the solver options used to solve the flux problems      Returns the solver options used to solve the flux problems
85
86      M{(I+D^*D)u=F}      *(I+D^*D)u=F*
87
88      @return: L{SolverOptions}      :return: `SolverOptions`
89      """      """
90      return self.__pde_v.getSolverOptions()      return self.__pde_v.getSolverOptions()
91      def setSolverOptionsFlux(self, options=None):      def setSolverOptionsFlux(self, options=None):
92      """      """
93      Sets the solver options used to solve the flux problems      Sets the solver options used to solve the flux problems
94
95      M{(I+D^*D)u=F}      *(I+D^*D)u=F*
96
97      If C{options} is not present, the options are reset to default      If ``options`` is not present, the options are reset to default
98      @param options: L{SolverOptions}      :param options: `SolverOptions`
99      @note: if the adaption of subtolerance is choosen, the tolerance set by C{options} will be overwritten before the solver is called.      :note: if the adaption of subtolerance is choosen, the tolerance set by ``options`` will be overwritten before the solver is called.
100      """      """
101      return self.__pde_v.setSolverOptions(options)      return self.__pde_v.setSolverOptions(options)
102      def getSolverOptionsPressure(self):      def getSolverOptionsPressure(self):
103      """      """
104      Returns the solver options used to solve the pressure problems      Returns the solver options used to solve the pressure problems
105
106      M{(Q^*Q)p=Q^*G}      *(Q^*Q)p=Q^*G*
107
108      @return: L{SolverOptions}      :return: `SolverOptions`
109      """      """
110      return self.__pde_p.getSolverOptions()      return self.__pde_p.getSolverOptions()
111      def setSolverOptionsPressure(self, options=None):      def setSolverOptionsPressure(self, options=None):
112      """      """
113      Sets the solver options used to solve the pressure problems      Sets the solver options used to solve the pressure problems
114
115      M{(Q^*Q)p=Q^*G}      *(Q^*Q)p=Q^*G*
116
117      If C{options} is not present, the options are reset to default      If ``options`` is not present, the options are reset to default
118      @param options: L{SolverOptions}      :param options: `SolverOptions`
119      @note: if the adaption of subtolerance is choosen, the tolerance set by C{options} will be overwritten before the solver is called.      :note: if the adaption of subtolerance is choosen, the tolerance set by ``options`` will be overwritten before the solver is called.
120      """      """
121      return self.__pde_p.setSolverOptions(options)      return self.__pde_p.setSolverOptions(options)
122
# Line 124  class DarcyFlow(object): Line 124  class DarcyFlow(object):
124          """          """
125          assigns values to model parameters          assigns values to model parameters
126
127          @param f: volumetic sources/sinks          :param f: volumetic sources/sinks
128          @type f: scalar value on the domain (e.g. L{Data})          :type f: scalar value on the domain (e.g. `Data`)
129          @param g: flux sources/sinks          :param g: flux sources/sinks
130          @type g: vector values on the domain (e.g. L{Data})          :type g: vector values on the domain (e.g. `Data`)
131          @param location_of_fixed_pressure: mask for locations where pressure is fixed          :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. L{Data})          :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.          :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. L{Data})          :type location_of_fixed_flux: vector values on the domain (e.g. `Data`)
135          @param permeability: permeability tensor. If scalar C{s} is given the tensor with          :param permeability: permeability tensor. If scalar ``s`` is given the tensor with
136                               C{s} on the main diagonal is used. If vector C{v} is given the tensor with                               ``s`` on the main diagonal is used. If vector ``v`` is given the tensor with
137                               C{v} on the main diagonal is used.                               ``v`` on the main diagonal is used.
138          @type permeability: scalar, vector or tensor values on the domain (e.g. L{Data})          :type permeability: scalar, vector or tensor values on the domain (e.g. `Data`)
139
140          @note: the values of parameters which are not set by calling C{setValue} are not altered.          :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 (C{location_of_fixed_pressure} >0)          :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 (C{location_of_fixed_flux[i]>0} if direction of the normal                 or the normal component of the flux (``location_of_fixed_flux[i]>0`` if direction of the normal
143                 is along the M{x_i} axis.                 is along the *x_i* axis.
144          """          """
145          if f !=None:          if f !=None:
146             f=util.interpolate(f, self.__pde_v.getFunctionSpaceForCoefficient("X"))             f=util.interpolate(f, self.__pde_v.getFunctionSpaceForCoefficient("X"))
# Line 177  class DarcyFlow(object): Line 177  class DarcyFlow(object):
177
178      def setTolerance(self,rtol=1e-4):      def setTolerance(self,rtol=1e-4):
179          """          """
180          sets the relative tolerance C{rtol} used to terminate the solution process. The iteration is terminated if          sets the relative tolerance ``rtol`` used to terminate the solution process. The iteration is terminated if
181
182          M{|g-v-Qp| <= atol + rtol * min( max( |g-v|, |Qp| ), max( |v|, |g-Qp| ) ) }          *|g-v-Qp| <= atol + rtol * min( max( |g-v|, |Qp| ), max( |v|, |g-Qp| ) )*
183
184          where C{atol} is an absolut tolerance (see L{setAbsoluteTolerance}), M{|f|^2 = integrate(length(f)^2)} and M{(Qp)_i=k_{ij}p_{,j}} for the permeability M{k_{ij}}.          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
186          @param rtol: relative tolerance for the pressure          :param rtol: relative tolerance for the pressure
187          @type rtol: non-negative C{float}          :type rtol: non-negative ``float``
188          """          """
189          if rtol<0:          if rtol<0:
190              raise ValueError,"Relative tolerance needs to be non-negative."              raise ValueError,"Relative tolerance needs to be non-negative."
# Line 193  class DarcyFlow(object): Line 193  class DarcyFlow(object):
193          """          """
194          returns the relative tolerance          returns the relative tolerance
195
196          @return: current relative tolerance          :return: current relative tolerance
197          @rtype: C{float}          :rtype: ``float``
198          """          """
199          return self.__rtol          return self.__rtol
200
201      def setAbsoluteTolerance(self,atol=0.):      def setAbsoluteTolerance(self,atol=0.):
202          """          """
203          sets the absolute tolerance C{atol} used to terminate the solution process. The iteration is terminated if          sets the absolute tolerance ``atol`` used to terminate the solution process. The iteration is terminated if
204
205          M{|g-v-Qp| <= atol + rtol * min( max( |g-v|, |Qp| ), max( |v|, |g-Qp| ) ) }          *|g-v-Qp| <= atol + rtol * min( max( |g-v|, |Qp| ), max( |v|, |g-Qp| ) )*
206
207          where C{rtol} is an absolut tolerance (see L{setTolerance}), M{|f|^2 = integrate(length(f)^2)} and M{(Qp)_i=k_{ij}p_{,j}} for the permeability M{k_{ij}}.          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
209          @param atol: absolute tolerance for the pressure          :param atol: absolute tolerance for the pressure
210          @type atol: non-negative C{float}          :type atol: non-negative ``float``
211          """          """
212          if atol<0:          if atol<0:
213              raise ValueError,"Absolute tolerance needs to be non-negative."              raise ValueError,"Absolute tolerance needs to be non-negative."
# Line 216  class DarcyFlow(object): Line 216  class DarcyFlow(object):
216         """         """
217         returns the absolute tolerance         returns the absolute tolerance
218
219         @return: current absolute tolerance         :return: current absolute tolerance
220         @rtype: C{float}         :rtype: ``float``
221         """         """
222         return self.__atol         return self.__atol
223      def getSubProblemTolerance(self):      def getSubProblemTolerance(self):
224      """      """
225      Returns a suitable subtolerance      Returns a suitable subtolerance
226      @type: C{float}      @type: ``float``
227      """      """
228      return max(util.EPSILON**(0.75),self.getTolerance()**2)      return max(util.EPSILON**(0.75),self.getTolerance()**2)
229      def setSubProblemTolerance(self):      def setSubProblemTolerance(self):
# Line 244  class DarcyFlow(object): Line 244  class DarcyFlow(object):
244
245           The iteration is terminated if the residual norm is less then self.getTolerance().           The iteration is terminated if the residual norm is less then self.getTolerance().
246
247           @param u0: initial guess for the flux. At locations in the domain marked by C{location_of_fixed_flux} the value of C{u0} is kept unchanged.           :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. L{Data}).           :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 C{location_of_fixed_pressure} the value of C{p0} is kept unchanged.           :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. L{Data}).           :type p0: scalar value on the domain (e.g. `Data`).
251           @param verbose: if set some information on iteration progress are printed           :param verbose: if set some information on iteration progress are printed
252           @type verbose: C{bool}           :type verbose: ``bool``
253           @return: flux and pressure           :return: flux and pressure
254           @rtype: C{tuple} of L{Data}.           :rtype: ``tuple`` of `Data`.
255
256           @note: The problem is solved as a least squares form           :note: The problem is solved as a least squares form
257
258           M{(I+D^*D)u+Qp=D^*f+g}           *(I+D^*D)u+Qp=D^*f+g*
259           M{Q^*u+Q^*Qp=Q^*g}           *Q^*u+Q^*Qp=Q^*g*
260
261           where M{D} is the M{div} operator and M{(Qp)_i=k_{ij}p_{,j}} for the permeability M{k_{ij}}.           where *D* is the *div* operator and *(Qp)_i=k_{ij}p_{,j}* for the permeability *k_{ij}*.
262           We eliminate the flux form the problem by setting           We eliminate the flux form the problem by setting
263
264           M{u=(I+D^*D)^{-1}(D^*f-g-Qp)} with u=u0 on location_of_fixed_flux           *u=(I+D^*D)^{-1}(D^*f-g-Qp)* with u=u0 on location_of_fixed_flux
265
266           form the first equation. Inserted into the second equation we get           form the first equation. Inserted into the second equation we get
267
268           M{Q^*(I-(I+D^*D)^{-1})Qp= Q^*(g-(I+D^*D)^{-1}(D^*f+g))} with p=p0  on location_of_fixed_pressure           *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
270           which is solved using the PCG method (precondition is M{Q^*Q}). In each iteration step           which is solved using the PCG method (precondition is *Q^*Q*). In each iteration step
271           PDEs with operator M{I+D^*D} and with M{Q^*Q} needs to be solved using a sub iteration scheme.           PDEs with operator *I+D^*D* and with *Q^*Q* needs to be solved using a sub iteration scheme.
272           """           """
273           self.verbose=verbose           self.verbose=verbose
274           rtol=self.getTolerance()           rtol=self.getTolerance()
# Line 336  class DarcyFlow(object): Line 336  class DarcyFlow(object):
336
337      def getFlux(self,p=None, fixed_flux=Data()):      def getFlux(self,p=None, fixed_flux=Data()):
338          """          """
339          returns the flux for a given pressure C{p} where the flux is equal to C{fixed_flux}          returns the flux for a given pressure ``p`` where the flux is equal to ``fixed_flux``
340          on locations where C{location_of_fixed_flux} is positive (see L{setValue}).          on locations where ``location_of_fixed_flux`` is positive (see `setValue`).
341          Note that C{g} and C{f} are used, see L{setValue}.          Note that ``g`` and ``f`` are used, see `setValue`.
342
343          @param p: pressure.          :param p: pressure.
344          @type p: scalar value on the domain (e.g. L{Data}).          :type p: scalar value on the domain (e.g. `Data`).
345          @param fixed_flux: flux on the locations of the domain marked be C{location_of_fixed_flux}.          :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. L{Data}).          :type fixed_flux: vector values on the domain (e.g. `Data`).
347          @param tol: relative tolerance to be used.          :return: flux
348          @type tol: positive C{float}.          :rtype: `Data`
349          @return: flux          :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          @rtype: L{Data}                 for the permeability *k_{ij}*
@note: the method uses the least squares solution M{u=(I+D^*D)^{-1}(D^*f-g-Qp)} where M{D} is the M{div} operator and M{(Qp)_i=k_{ij}p_{,j}}
for the permeability M{k_{ij}}
351          """          """
352      self.setSubProblemTolerance()      self.setSubProblemTolerance()
353          g=self.__g          g=self.__g
# Line 384  class StokesProblemCartesian(Homogeneous Line 382  class StokesProblemCartesian(Homogeneous
382           """           """
383           initialize the Stokes Problem           initialize the Stokes Problem
384
385           @param domain: domain of the problem. The approximation order needs to be two.           :param domain: domain of the problem. The approximation order needs to be two.
386           @type domain: L{Domain}           :type domain: `Domain`
387       @param adaptSubTolerance: If True the tolerance for subproblem is set automatically.       :param adaptSubTolerance: If True the tolerance for subproblem is set automatically.
388       @type adaptSubTolerance: C{bool}       :type adaptSubTolerance: ``bool``
389           @warning: The apprximation order needs to be two otherwise you may see oscilations in the pressure.           :warning: The apprximation order needs to be two otherwise you may see oscilations in the pressure.
390           """           """
392           self.domain=domain           self.domain=domain
# Line 409  class StokesProblemCartesian(Homogeneous Line 407  class StokesProblemCartesian(Homogeneous
407           """           """
408       returns the solver options used  solve the equation for velocity.       returns the solver options used  solve the equation for velocity.
409
410       @rtype: L{SolverOptions}       :rtype: `SolverOptions`
411       """       """
412       return self.__pde_u.getSolverOptions()       return self.__pde_u.getSolverOptions()
413       def setSolverOptionsVelocity(self, options=None):       def setSolverOptionsVelocity(self, options=None):
414           """           """
415       set the solver options for solving the equation for velocity.       set the solver options for solving the equation for velocity.
416
417       @param options: new solver  options       :param options: new solver  options
418       @type options: L{SolverOptions}       :type options: `SolverOptions`
419       """       """
420           self.__pde_u.setSolverOptions(options)           self.__pde_u.setSolverOptions(options)
421       def getSolverOptionsPressure(self):       def getSolverOptionsPressure(self):
422           """           """
423       returns the solver options used  solve the equation for pressure.       returns the solver options used  solve the equation for pressure.
424       @rtype: L{SolverOptions}       :rtype: `SolverOptions`
425       """       """
426       return self.__pde_prec.getSolverOptions()       return self.__pde_prec.getSolverOptions()
427       def setSolverOptionsPressure(self, options=None):       def setSolverOptionsPressure(self, options=None):
428           """           """
429       set the solver options for solving the equation for pressure.       set the solver options for solving the equation for pressure.
430       @param options: new solver  options       :param options: new solver  options
431       @type options: L{SolverOptions}       :type options: `SolverOptions`
432       """       """
433       self.__pde_prec.setSolverOptions(options)       self.__pde_prec.setSolverOptions(options)
434
# Line 439  class StokesProblemCartesian(Homogeneous Line 437  class StokesProblemCartesian(Homogeneous
437       set the solver options for solving the equation to project the divergence of       set the solver options for solving the equation to project the divergence of
438       the velocity onto the function space of presure.       the velocity onto the function space of presure.
439
440       @param options: new solver options       :param options: new solver options
441       @type options: L{SolverOptions}       :type options: `SolverOptions`
442       """       """
443       self.__pde_prec.setSolverOptions(options)       self.__pde_prec.setSolverOptions(options)
444       def getSolverOptionsDiv(self):       def getSolverOptionsDiv(self):
# Line 448  class StokesProblemCartesian(Homogeneous Line 446  class StokesProblemCartesian(Homogeneous
446       returns the solver options for solving the equation to project the divergence of       returns the solver options for solving the equation to project the divergence of
447       the velocity onto the function space of presure.       the velocity onto the function space of presure.
448
449       @rtype: L{SolverOptions}       :rtype: `SolverOptions`
450       """       """
451       return self.__pde_prec.getSolverOptions()       return self.__pde_prec.getSolverOptions()
452       def setSubProblemTolerance(self):       def setSubProblemTolerance(self):
# Line 469  class StokesProblemCartesian(Homogeneous Line 467  class StokesProblemCartesian(Homogeneous
467          """          """
468          assigns values to the model parameters          assigns values to the model parameters
469
470          @param f: external force          :param f: external force
471          @type f: L{Vector} object in L{FunctionSpace} L{Function} or similar          :type f: `Vector` object in `FunctionSpace` `Function` or similar
472          @param fixed_u_mask: mask of locations with fixed velocity.          :param fixed_u_mask: mask of locations with fixed velocity.
473          @type fixed_u_mask: L{Vector} object on L{FunctionSpace} L{Solution} or similar          :type fixed_u_mask: `Vector` object on `FunctionSpace` `Solution` or similar
474          @param eta: viscosity          :param eta: viscosity
475          @type eta: L{Scalar} object on L{FunctionSpace} L{Function} or similar          :type eta: `Scalar` object on `FunctionSpace` `Function` or similar
476          @param surface_stress: normal surface stress          :param surface_stress: normal surface stress
477          @type eta: L{Vector} object on L{FunctionSpace} L{FunctionOnBoundary} or similar          :type surface_stress: `Vector` object on `FunctionSpace` `FunctionOnBoundary` or similar
478          @param stress: initial stress          :param stress: initial stress
479      @type stress: L{Tensor} object on L{FunctionSpace} L{Function} or similar      :type stress: `Tensor` object on `FunctionSpace` `Function` or similar
480          @note: All values needs to be set.          :note: All values needs to be set.
481          """          """
482          self.eta=eta          self.eta=eta
483          A =self.__pde_u.createCoefficient("A")          A =self.__pde_u.createCoefficient("A")
# Line 499  class StokesProblemCartesian(Homogeneous Line 497  class StokesProblemCartesian(Homogeneous
497           """           """
498           returns inner product of element p and div(v)           returns inner product of element p and div(v)
499
500           @param p: a pressure increment           :param v: a residual
501           @param v: a residual           :return: inner product of element p and div(v)
502           @return: inner product of element p and div(v)           :rtype: ``float``
@rtype: C{float}
503           """           """
504           self.__pde_proj.setValue(Y=-util.div(v))           self.__pde_proj.setValue(Y=-util.div(v))
505           return self.__pde_proj.getSolution()           return self.__pde_proj.getSolution()
# Line 511  class StokesProblemCartesian(Homogeneous Line 508  class StokesProblemCartesian(Homogeneous
508           """           """
509           returns inner product of element p and Bv=-div(v)           returns inner product of element p and Bv=-div(v)
510
511           @param p: a pressure increment           :param p: a pressure increment
512           @param v: a residual           :param Bv: a residual
513           @return: inner product of element p and Bv=-div(v)           :return: inner product of element p and Bv=-div(v)
514           @rtype: C{float}           :rtype: ``float``
515           """           """
516           return util.integrate(util.interpolate(p,Function(self.domain))*util.interpolate(Bv,Function(self.domain)))           return util.integrate(util.interpolate(p,Function(self.domain))*util.interpolate(Bv,Function(self.domain)))
517
# Line 522  class StokesProblemCartesian(Homogeneous Line 519  class StokesProblemCartesian(Homogeneous
519           """           """
520           Returns inner product of p0 and p1           Returns inner product of p0 and p1
521
522           @param p0: a pressure           :param p0: a pressure
523           @param p1: a pressure           :param p1: a pressure
524           @return: inner product of p0 and p1           :return: inner product of p0 and p1
525           @rtype: C{float}           :rtype: ``float``
526           """           """
527           s0=util.interpolate(p0/self.eta,Function(self.domain))           s0=util.interpolate(p0/self.eta,Function(self.domain))
528           s1=util.interpolate(p1/self.eta,Function(self.domain))           s1=util.interpolate(p1/self.eta,Function(self.domain))
# Line 535  class StokesProblemCartesian(Homogeneous Line 532  class StokesProblemCartesian(Homogeneous
532           """           """
533           returns the norm of v           returns the norm of v
534
535           @param v: a velovity           :param v: a velovity
536           @return: norm of v           :return: norm of v
537           @rtype: non-negative C{float}           :rtype: non-negative ``float``
538           """           """
540
# Line 545  class StokesProblemCartesian(Homogeneous Line 542  class StokesProblemCartesian(Homogeneous
542           """           """
543           return the value for v for a given p (overwrite)           return the value for v for a given p (overwrite)
544
545           @param p: a pressure           :param p: a pressure
546           @param v0: a initial guess for the value v to return.           :param v0: a initial guess for the value v to return.
547           @return: v given as M{v= A^{-1} (f-B^*p)}           :return: v given as *v= A^{-1} (f-B^*p)*
548           """           """
549           self.__pde_u.setValue(Y=self.__f, y=self.__surface_stress, r=v0)           self.__pde_u.setValue(Y=self.__f, y=self.__surface_stress, r=v0)
550           if self.__stress.isEmpty():           if self.__stress.isEmpty():
# Line 561  class StokesProblemCartesian(Homogeneous Line 558  class StokesProblemCartesian(Homogeneous
558          """          """
559          Returns Bv (overwrite).          Returns Bv (overwrite).
560
561          @rtype: equal to the type of p          :rtype: equal to the type of p
562          @note: boundary conditions on p should be zero!          :note: boundary conditions on p should be zero!
563          """          """
564          return util.sqrt(util.integrate(util.interpolate(Bv,Function(self.domain))**2))          return util.sqrt(util.integrate(util.interpolate(Bv,Function(self.domain))**2))
565
566       def solve_AinvBt(self,p):       def solve_AinvBt(self,p):
567           """           """
568           Solves M{Av=B^*p} with accuracy L{self.getSubProblemTolerance()}           Solves *Av=B^*p* with accuracy `self.getSubProblemTolerance()`
569
570           @param p: a pressure increment           :param p: a pressure increment
571           @return: the solution of M{Av=B^*p}           :return: the solution of *Av=B^*p*
572           @note: boundary conditions on v should be zero!           :note: boundary conditions on v should be zero!
573           """           """
574           self.__pde_u.setValue(Y=Data(), y=Data(), r=Data(),X=-p*util.kronecker(self.domain))           self.__pde_u.setValue(Y=Data(), y=Data(), r=Data(),X=-p*util.kronecker(self.domain))
575           out=self.__pde_u.getSolution()           out=self.__pde_u.getSolution()
# Line 580  class StokesProblemCartesian(Homogeneous Line 577  class StokesProblemCartesian(Homogeneous
577
578       def solve_prec(self,Bv):       def solve_prec(self,Bv):
579           """           """
580           applies preconditioner for for M{BA^{-1}B^*} to M{Bv}           applies preconditioner for for *BA^{-1}B^** to *Bv*
581           with accuracy L{self.getSubProblemTolerance()}           with accuracy `self.getSubProblemTolerance()`
582
583           @param v: velocity increment           :param Bv: velocity increment
584           @return: M{p=P(Bv)} where M{P^{-1}} is an approximation of M{BA^{-1}B^*}           :return: *p=P(Bv)* where *P^{-1}* is an approximation of *BA^{-1}B^ * )*
585           @note: boundary conditions on p are zero.           :note: boundary conditions on p are zero.
586           """           """
587           self.__pde_prec.setValue(Y=Bv)           self.__pde_prec.setValue(Y=Bv)
588           return self.__pde_prec.getSolution()           return self.__pde_prec.getSolution()

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