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Revision 3885 - (show annotations)
Wed Apr 4 22:12:26 2012 UTC (7 years, 4 months ago) by gross
Original Path: trunk/escript/py_src/flows.py
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some fix in AMG
1 # -*- 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 # 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 #
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
24
25 :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 """
32
33 __author__="Lutz Gross, l.gross@uq.edu.au"
34
35 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 self.l=util.vol(self.domain)**(1./self.domain.getDim()) # length scale
100
101 elif self.solver == self.SMOOTH:
102 self.__pde_v=LinearPDESystem(domain)
103 self.__pde_v.setSymmetryOn()
104 if self.useReduced: self.__pde_v.setReducedOrderOn()
105 if self.verbose: print("DarcyFlow: flux smoothing is used.")
106 self.w=0
107
108 self.__f=escript.Scalar(0,self.__pde_p.getFunctionSpaceForCoefficient("X"))
109 self.__g=escript.Vector(0,self.__pde_p.getFunctionSpaceForCoefficient("Y"))
110 self.location_of_fixed_pressure = escript.Scalar(0, self.__pde_p.getFunctionSpaceForCoefficient("q"))
111 self.location_of_fixed_flux = escript.Vector(0, self.__pde_p.getFunctionSpaceForCoefficient("q"))
112 self.perm_scale=1.
113
114
115 def setValue(self,f=None, g=None, location_of_fixed_pressure=None, location_of_fixed_flux=None, permeability=None):
116 """
117 assigns values to model parameters
118
119 :param f: volumetic sources/sinks
120 :type f: scalar value on the domain (e.g. `escript.Data`)
121 :param g: flux sources/sinks
122 :type g: vector values on the domain (e.g. `escript.Data`)
123 :param location_of_fixed_pressure: mask for locations where pressure is fixed
124 :type location_of_fixed_pressure: scalar value on the domain (e.g. `escript.Data`)
125 :param location_of_fixed_flux: mask for locations where flux is fixed.
126 :type location_of_fixed_flux: vector values on the domain (e.g. `escript.Data`)
127 :param permeability: permeability tensor. If scalar ``s`` is given the tensor with ``s`` on the main diagonal is used.
128 :type permeability: scalar or symmetric tensor values on the domain (e.g. `escript.Data`)
129
130 :note: the values of parameters which are not set by calling ``setValue`` are not altered.
131 :note: at any point on the boundary of the domain the pressure
132 (``location_of_fixed_pressure`` >0) or the normal component of the
133 flux (``location_of_fixed_flux[i]>0``) if direction of the normal
134 is along the *x_i* axis.
135
136 """
137 if location_of_fixed_pressure!=None:
138 self.location_of_fixed_pressure=util.wherePositive(location_of_fixed_pressure)
139 self.__pde_p.setValue(q=self.location_of_fixed_pressure)
140 if location_of_fixed_flux!=None:
141 self.location_of_fixed_flux=util.wherePositive(location_of_fixed_flux)
142 if not self.__pde_v == None: self.__pde_v.setValue(q=self.location_of_fixed_flux)
143
144 if permeability!=None:
145
146 perm=util.interpolate(permeability,self.__pde_p.getFunctionSpaceForCoefficient("A"))
147 self.perm_scale=util.Lsup(util.length(perm))
148 if self.verbose: print(("DarcyFlow: permeability scaling factor = %e."%self.perm_scale))
149 perm=perm*(1./self.perm_scale)
150
151 if perm.getRank()==0:
152
153 perm_inv=(1./perm)
154 perm_inv=perm_inv*util.kronecker(self.domain.getDim())
155 perm=perm*util.kronecker(self.domain.getDim())
156
157
158 elif perm.getRank()==2:
159 perm_inv=util.inverse(perm)
160 else:
161 raise ValueError("illegal rank of permeability.")
162
163 self.__permeability=perm
164 self.__permeability_inv=perm_inv
165
166 #====================
167 self.__pde_p.setValue(A=self.__permeability)
168 if self.solver == self.EVAL:
169 pass # no extra work required
170 elif self.solver == self.POST:
171 k=util.kronecker(self.domain.getDim())
172 self.omega = self.w*util.length(perm_inv)*self.l*self.domain.getSize()
173 #self.__pde_v.setValue(D=self.__permeability_inv, A=self.omega*util.outer(k,k))
174 self.__pde_v.setValue(D=self.__permeability_inv, A_reduced=self.omega*util.outer(k,k))
175 elif self.solver == self.SMOOTH:
176 self.__pde_v.setValue(D=self.__permeability_inv)
177
178 if g != None:
179 g=util.interpolate(g, self.__pde_p.getFunctionSpaceForCoefficient("Y"))
180 if g.isEmpty():
181 g=Vector(0,self.__pde_p.getFunctionSpaceForCoefficient("Y"))
182 else:
183 if not g.getShape()==(self.domain.getDim(),): raise ValueError("illegal shape of g")
184 self.__g=g
185 if f !=None:
186 f=util.interpolate(f, self.__pde_p.getFunctionSpaceForCoefficient("Y"))
187 if f.isEmpty():
188 f=Scalar(0,self.__pde_p.getFunctionSpaceForCoefficient("Y"))
189 else:
190 if f.getRank()>0: raise ValueError("illegal rank of f.")
191 self.__f=f
192
193 def getSolverOptionsFlux(self):
194 """
195 Returns the solver options used to solve the flux problems
196 :return: `SolverOptions`
197 """
198 if self.__pde_v == None:
199 return None
200 else:
201 return self.__pde_v.getSolverOptions()
202
203 def setSolverOptionsFlux(self, options=None):
204 """
205 Sets the solver options used to solve the flux problems
206 If ``options`` is not present, the options are reset to default
207 :param options: `SolverOptions`
208 """
209 if not self.__pde_v == None:
210 self.__pde_v.setSolverOptions(options)
211
212 def getSolverOptionsPressure(self):
213 """
214 Returns the solver options used to solve the pressure problems
215 :return: `SolverOptions`
216 """
217 return self.__pde_p.getSolverOptions()
218
219 def setSolverOptionsPressure(self, options=None):
220 """
221 Sets the solver options used to solve the pressure problems
222 If ``options`` is not present, the options are reset to default
223
224 :param options: `SolverOptions`
225 :note: if the adaption of subtolerance is choosen, the tolerance set by ``options`` will be overwritten before the solver is called.
226 """
227 return self.__pde_p.setSolverOptions(options)
228
229 def solve(self, u0, p0):
230 """
231 solves the problem.
232
233 :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.
234 :type u0: vector value on the domain (e.g. `escript.Data`).
235 :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.
236 :type p0: scalar value on the domain (e.g. `escript.Data`).
237 :return: flux and pressure
238 :rtype: ``tuple`` of `escript.Data`.
239
240 """
241 self.__pde_p.setValue(X=self.__g * 1./self.perm_scale,
242 Y=self.__f * 1./self.perm_scale,
243 y= - util.inner(self.domain.getNormal(),u0 * self.location_of_fixed_flux * 1./self.perm_scale ),
244 r=p0)
245 p=self.__pde_p.getSolution()
246 u = self.getFlux(p, u0)
247 return u,p
248
249 def getFlux(self,p, u0=None):
250 """
251 returns the flux for a given pressure ``p`` where the flux is equal to ``u0``
252 on locations where ``location_of_fixed_flux`` is positive (see `setValue`).
253 Notice that ``g`` is used, see `setValue`.
254
255 :param p: pressure.
256 :type p: scalar value on the domain (e.g. `escript.Data`).
257 :param u0: flux on the locations of the domain marked be ``location_of_fixed_flux``.
258 :type u0: vector values on the domain (e.g. `escript.Data`) or ``None``
259 :return: flux
260 :rtype: `escript.Data`
261 """
262 if self.solver == self.EVAL:
263 u = self.__g-self.perm_scale * util.tensor_mult(self.__permeability,util.grad(p))
264 elif self.solver == self.POST or self.solver == self.SMOOTH:
265 self.__pde_v.setValue(Y=util.tensor_mult(self.__permeability_inv,self.__g * 1./self.perm_scale)-util.grad(p))
266 if u0 == None:
267 self.__pde_v.setValue(r=escript.Data())
268 else:
269 if not isinstance(u0, escript.Data) : u0 = escript.Vector(u0, escript.Solution(self.domain))
270 self.__pde_v.setValue(r=1./self.perm_scale * u0)
271 u= self.__pde_v.getSolution() * self.perm_scale
272 return u
273
274 class StokesProblemCartesian(HomogeneousSaddlePointProblem):
275 """
276 solves
277
278 -(eta*(u_{i,j}+u_{j,i}))_j + p_i = f_i-stress_{ij,j}
279 u_{i,i}=0
280
281 u=0 where fixed_u_mask>0
282 eta*(u_{i,j}+u_{j,i})*n_j-p*n_i=surface_stress +stress_{ij}n_j
283
284 if surface_stress is not given 0 is assumed.
285
286 typical usage:
287
288 sp=StokesProblemCartesian(domain)
289 sp.setTolerance()
290 sp.initialize(...)
291 v,p=sp.solve(v0,p0)
292 sp.setStokesEquation(...) # new values for some parameters
293 v1,p1=sp.solve(v,p)
294 """
295 def __init__(self,domain,**kwargs):
296 """
297 initialize the Stokes Problem
298
299 The approximation spaces used for velocity (=Solution(domain)) and pressure (=ReducedSolution(domain)) must be
300 LBB complient, for instance using quadratic and linear approximation on the same element or using linear approximation
301 with macro elements for the pressure.
302
303 :param domain: domain of the problem.
304 :type domain: `Domain`
305 """
306 HomogeneousSaddlePointProblem.__init__(self,**kwargs)
307 self.domain=domain
308 self.__pde_v=LinearPDE(domain,numEquations=self.domain.getDim(),numSolutions=self.domain.getDim())
309 self.__pde_v.setSymmetryOn()
310
311 self.__pde_prec=LinearPDE(domain)
312 self.__pde_prec.setReducedOrderOn()
313 self.__pde_prec.setSymmetryOn()
314
315 self.__pde_proj=LinearPDE(domain)
316 self.__pde_proj.setReducedOrderOn()
317 self.__pde_proj.setValue(D=1)
318 self.__pde_proj.setSymmetryOn()
319
320 def getSolverOptionsVelocity(self):
321 """
322 returns the solver options used solve the equation for velocity.
323
324 :rtype: `SolverOptions`
325 """
326 return self.__pde_v.getSolverOptions()
327 def setSolverOptionsVelocity(self, options=None):
328 """
329 set the solver options for solving the equation for velocity.
330
331 :param options: new solver options
332 :type options: `SolverOptions`
333 """
334 self.__pde_v.setSolverOptions(options)
335 def getSolverOptionsPressure(self):
336 """
337 returns the solver options used solve the equation for pressure.
338 :rtype: `SolverOptions`
339 """
340 return self.__pde_prec.getSolverOptions()
341 def setSolverOptionsPressure(self, options=None):
342 """
343 set the solver options for solving the equation for pressure.
344 :param options: new solver options
345 :type options: `SolverOptions`
346 """
347 self.__pde_prec.setSolverOptions(options)
348
349 def setSolverOptionsDiv(self, options=None):
350 """
351 set the solver options for solving the equation to project the divergence of
352 the velocity onto the function space of presure.
353
354 :param options: new solver options
355 :type options: `SolverOptions`
356 """
357 self.__pde_proj.setSolverOptions(options)
358 def getSolverOptionsDiv(self):
359 """
360 returns the solver options for solving the equation to project the divergence of
361 the velocity onto the function space of presure.
362
363 :rtype: `SolverOptions`
364 """
365 return self.__pde_proj.getSolverOptions()
366
367 def updateStokesEquation(self, v, p):
368 """
369 updates the Stokes equation to consider dependencies from ``v`` and ``p``
370 :note: This method can be overwritten by a subclass. Use `setStokesEquation` to set new values to model parameters.
371 """
372 pass
373 def setStokesEquation(self, f=None,fixed_u_mask=None,eta=None,surface_stress=None,stress=None, restoration_factor=None):
374 """
375 assigns new values to the model parameters.
376
377 :param f: external force
378 :type f: `Vector` object in `FunctionSpace` `Function` or similar
379 :param fixed_u_mask: mask of locations with fixed velocity.
380 :type fixed_u_mask: `Vector` object on `FunctionSpace` `Solution` or similar
381 :param eta: viscosity
382 :type eta: `Scalar` object on `FunctionSpace` `Function` or similar
383 :param surface_stress: normal surface stress
384 :type surface_stress: `Vector` object on `FunctionSpace` `FunctionOnBoundary` or similar
385 :param stress: initial stress
386 :type stress: `Tensor` object on `FunctionSpace` `Function` or similar
387 """
388 if eta !=None:
389 k=util.kronecker(self.domain.getDim())
390 kk=util.outer(k,k)
391 self.eta=util.interpolate(eta, escript.Function(self.domain))
392 self.__pde_prec.setValue(D=1/self.eta)
393 self.__pde_v.setValue(A=self.eta*(util.swap_axes(kk,0,3)+util.swap_axes(kk,1,3)))
394 if restoration_factor!=None:
395 n=self.domain.getNormal()
396 self.__pde_v.setValue(d=restoration_factor*util.outer(n,n))
397 if fixed_u_mask!=None:
398 self.__pde_v.setValue(q=fixed_u_mask)
399 if f!=None: self.__f=f
400 if surface_stress!=None: self.__surface_stress=surface_stress
401 if stress!=None: self.__stress=stress
402
403 def initialize(self,f=escript.Data(),fixed_u_mask=escript.Data(),eta=1,surface_stress=escript.Data(),stress=escript.Data(), restoration_factor=0):
404 """
405 assigns values to the model parameters
406
407 :param f: external force
408 :type f: `Vector` object in `FunctionSpace` `Function` or similar
409 :param fixed_u_mask: mask of locations with fixed velocity.
410 :type fixed_u_mask: `Vector` object on `FunctionSpace` `Solution` or similar
411 :param eta: viscosity
412 :type eta: `Scalar` object on `FunctionSpace` `Function` or similar
413 :param surface_stress: normal surface stress
414 :type surface_stress: `Vector` object on `FunctionSpace` `FunctionOnBoundary` or similar
415 :param stress: initial stress
416 :type stress: `Tensor` object on `FunctionSpace` `Function` or similar
417 """
418 self.setStokesEquation(f,fixed_u_mask, eta, surface_stress, stress, restoration_factor)
419
420 def Bv(self,v,tol):
421 """
422 returns inner product of element p and div(v)
423
424 :param v: a residual
425 :return: inner product of element p and div(v)
426 :rtype: ``float``
427 """
428 self.__pde_proj.setValue(Y=-util.div(v))
429 self.getSolverOptionsDiv().setTolerance(tol)
430 self.getSolverOptionsDiv().setAbsoluteTolerance(0.)
431 out=self.__pde_proj.getSolution()
432 return out
433
434 def inner_pBv(self,p,Bv):
435 """
436 returns inner product of element p and Bv=-div(v)
437
438 :param p: a pressure increment
439 :param Bv: a residual
440 :return: inner product of element p and Bv=-div(v)
441 :rtype: ``float``
442 """
443 return util.integrate(util.interpolate(p,escript.Function(self.domain))*util.interpolate(Bv, escript.Function(self.domain)))
444
445 def inner_p(self,p0,p1):
446 """
447 Returns inner product of p0 and p1
448
449 :param p0: a pressure
450 :param p1: a pressure
451 :return: inner product of p0 and p1
452 :rtype: ``float``
453 """
454 s0=util.interpolate(p0, escript.Function(self.domain))
455 s1=util.interpolate(p1, escript.Function(self.domain))
456 return util.integrate(s0*s1)
457
458 def norm_v(self,v):
459 """
460 returns the norm of v
461
462 :param v: a velovity
463 :return: norm of v
464 :rtype: non-negative ``float``
465 """
466 return util.sqrt(util.integrate(util.length(util.grad(v))**2))
467
468
469 def getDV(self, p, v, tol):
470 """
471 return the value for v for a given p
472
473 :param p: a pressure
474 :param v: a initial guess for the value v to return.
475 :return: dv given as *Adv=(f-Av-B^*p)*
476 """
477 self.updateStokesEquation(v,p)
478 self.__pde_v.setValue(Y=self.__f, y=self.__surface_stress)
479 self.getSolverOptionsVelocity().setTolerance(tol)
480 self.getSolverOptionsVelocity().setAbsoluteTolerance(0.)
481 if self.__stress.isEmpty():
482 self.__pde_v.setValue(X=p*util.kronecker(self.domain)-2*self.eta*util.symmetric(util.grad(v)))
483 else:
484 self.__pde_v.setValue(X=self.__stress+p*util.kronecker(self.domain)-2*self.eta*util.symmetric(util.grad(v)))
485 out=self.__pde_v.getSolution()
486 return out
487
488 def norm_Bv(self,Bv):
489 """
490 Returns Bv (overwrite).
491
492 :rtype: equal to the type of p
493 :note: boundary conditions on p should be zero!
494 """
495 return util.sqrt(util.integrate(util.interpolate(Bv, escript.Function(self.domain))**2))
496
497 def solve_AinvBt(self,p, tol):
498 """
499 Solves *Av=B^*p* with accuracy `tol`
500
501 :param p: a pressure increment
502 :return: the solution of *Av=B^*p*
503 :note: boundary conditions on v should be zero!
504 """
505 self.__pde_v.setValue(Y=escript.Data(), y=escript.Data(), X=-p*util.kronecker(self.domain))
506 out=self.__pde_v.getSolution()
507 return out
508
509 def solve_prec(self,Bv, tol):
510 """
511 applies preconditioner for for *BA^{-1}B^** to *Bv*
512 with accuracy `self.getSubProblemTolerance()`
513
514 :param Bv: velocity increment
515 :return: *p=P(Bv)* where *P^{-1}* is an approximation of *BA^{-1}B^ * )*
516 :note: boundary conditions on p are zero.
517 """
518 self.__pde_prec.setValue(Y=Bv)
519 self.getSolverOptionsPressure().setTolerance(tol)
520 self.getSolverOptionsPressure().setAbsoluteTolerance(0.)
521 out=self.__pde_prec.getSolution()
522 return out

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