/[escript]/trunk/escript/py_src/pdetools.py
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revision 720 by gross, Thu Apr 27 10:16:05 2006 UTC revision 1122 by gross, Tue May 1 03:21:04 2007 UTC
# Line 7  Currently includes: Line 7  Currently includes:
7      - Projector - to project a discontinuous      - Projector - to project a discontinuous
8      - Locator - to trace values in data objects at a certain location      - Locator - to trace values in data objects at a certain location
9      - TimeIntegrationManager - to handel extraplotion in time      - TimeIntegrationManager - to handel extraplotion in time
10        - SaddlePointProblem - solver for Saddle point problems using the inexact uszawa scheme
11    
12  @var __author__: name of author  @var __author__: name of author
13  @var __copyright__: copyrights  @var __copyright__: copyrights
# Line 131  class Projector: Line 132  class Projector:
132      self.__pde.setValue(D = 1.)      self.__pde.setValue(D = 1.)
133      return      return
134    
   def __del__(self):  
     return  
   
135    def __call__(self, input_data):    def __call__(self, input_data):
136      """      """
137      Projects input_data onto a continuous function      Projects input_data onto a continuous function
# Line 141  class Projector: Line 139  class Projector:
139      @param input_data: The input_data to be projected.      @param input_data: The input_data to be projected.
140      """      """
141      out=escript.Data(0.,input_data.getShape(),self.__pde.getFunctionSpaceForSolution())      out=escript.Data(0.,input_data.getShape(),self.__pde.getFunctionSpaceForSolution())
142        self.__pde.setValue(Y = escript.Data(), Y_reduced = escript.Data())
143      if input_data.getRank()==0:      if input_data.getRank()==0:
144          self.__pde.setValue(Y = input_data)          self.__pde.setValue(Y = input_data)
145          out=self.__pde.getSolution()          out=self.__pde.getSolution()
# Line 296  class Locator: Line 295  class Locator:
295         Initializes a Locator to access values in Data objects on the Doamin         Initializes a Locator to access values in Data objects on the Doamin
296         or FunctionSpace where for the sample point which         or FunctionSpace where for the sample point which
297         closest to the given point x.         closest to the given point x.
298    
299           @param where: function space
300           @type where: L{escript.FunctionSpace}
301           @param x: coefficient of the solution.
302           @type x: L{numarray.NumArray} or C{list} of L{numarray.NumArray}
303         """         """
304         if isinstance(where,escript.FunctionSpace):         if isinstance(where,escript.FunctionSpace):
305            self.__function_space=where            self.__function_space=where
306         else:         else:
307            self.__function_space=escript.ContinuousFunction(where)            self.__function_space=escript.ContinuousFunction(where)
308         self.__id=util.length(self.__function_space.getX()-x[:self.__function_space.getDim()]).mindp()         if isinstance(x, list):
309               self.__id=[]
310               for p in x:
311                  self.__id.append(util.length(self.__function_space.getX()-p[:self.__function_space.getDim()]).minGlobalDataPoint())
312           else:
313               self.__id=util.length(self.__function_space.getX()-x[:self.__function_space.getDim()]).minGlobalDataPoint()
314    
315       def __str__(self):       def __str__(self):
316         """         """
317         Returns the coordinates of the Locator as a string.         Returns the coordinates of the Locator as a string.
318         """         """
319         return "<Locator %s>"%str(self.getX())         x=self.getX()
320           if instance(x,list):
321              out="["
322              first=True
323              for xx in x:
324                if not first:
325                    out+=","
326                else:
327                    first=False
328                out+=str(xx)
329              out+="]>"
330           else:
331              out=str(x)
332           return out
333    
334         def getX(self):
335            """
336        Returns the exact coordinates of the Locator.
337        """
338            return self(self.getFunctionSpace().getX())
339    
340       def getFunctionSpace(self):       def getFunctionSpace(self):
341          """          """
# Line 315  class Locator: Line 343  class Locator:
343      """      """
344          return self.__function_space          return self.__function_space
345    
346       def getId(self):       def getId(self,item=None):
347          """          """
348      Returns the identifier of the location.      Returns the identifier of the location.
349      """      """
350          return self.__id          if item == None:
351               return self.__id
352            else:
353               if isinstance(self.__id,list):
354                  return self.__id[item]
355               else:
356                  return self.__id
357    
      def getX(self):  
         """  
     Returns the exact coordinates of the Locator.  
     """  
         return self(self.getFunctionSpace().getX())  
358    
359       def __call__(self,data):       def __call__(self,data):
360          """          """
# Line 341  class Locator: Line 370  class Locator:
370      """      """
371          if isinstance(data,escript.Data):          if isinstance(data,escript.Data):
372             if data.getFunctionSpace()==self.getFunctionSpace():             if data.getFunctionSpace()==self.getFunctionSpace():
373               out=data.convertToNumArrayFromDPNo(self.getId()[0],self.getId()[1])               dat=data
374             else:             else:
375               out=data.interpolate(self.getFunctionSpace()).convertToNumArrayFromDPNo(self.getId()[0],self.getId()[1])               dat=data.interpolate(self.getFunctionSpace())
376             if data.getRank()==0:             id=self.getId()
377                return out[0]             r=data.getRank()
378               if isinstance(id,list):
379                   out=[]
380                   for i in id:
381                      o=data.getValueOfGlobalDataPoint(*i)
382                      if data.getRank()==0:
383                         out.append(o[0])
384                      else:
385                         out.append(o)
386                   return out
387             else:             else:
388                return out               out=data.getValueOfGlobalDataPoint(*id)
389                 if data.getRank()==0:
390                    return out[0]
391                 else:
392                    return out
393          else:          else:
394             return data             return data
395    
396    class SaddlePointProblem(object):
397       """
398       This implements a solver for a saddlepoint problem
399    
400       M{f(u,p)=0}
401       M{g(u)=0}
402    
403       for u and p. The problem is solved with an inexact Uszawa scheme for p:
404    
405       M{Q_f (u^{k+1}-u^{k}) = - f(u^{k},p^{k})}
406       M{Q_g (p^{k+1}-p^{k}) =   g(u^{k+1})}
407    
408       where Q_f is an approximation of the Jacobiean A_f of f with respect to u  and Q_f is an approximation of
409       A_g A_f^{-1} A_g with A_g is the jacobiean of g with respect to p. As a the construction of a 'proper'
410       Q_g can be difficult, non-linear conjugate gradient method is applied to solve for p, so Q_g plays
411       in fact the role of a preconditioner.
412       """
413       def __init__(self,verbose=False,*args):
414           """
415           initializes the problem
416    
417           @param verbose: switches on the printing out some information
418           @type verbose: C{bool}
419           @note: this method may be overwritten by a particular saddle point problem
420           """
421           if not isinstance(verbose,bool):
422                raise TypeError("verbose needs to be of type bool.")
423           self.__verbose=verbose
424           self.relaxation=1.
425    
426       def trace(self,text):
427           """
428           prints text if verbose has been set
429    
430           @param text: a text message
431           @type text: C{str}
432           """
433           if self.__verbose: print "%s: %s"%(str(self),text)
434    
435       def solve_f(self,u,p,tol=1.e-8):
436           """
437           solves
438    
439           A_f du = f(u,p)
440    
441           with tolerance C{tol} and return du. A_f is Jacobiean of f with respect to u.
442    
443           @param u: current approximation of u
444           @type u: L{escript.Data}
445           @param p: current approximation of p
446           @type p: L{escript.Data}
447           @param tol: tolerance expected for du
448           @type tol: C{float}
449           @return: increment du
450           @rtype: L{escript.Data}
451           @note: this method has to be overwritten by a particular saddle point problem
452           """
453           pass
454    
455       def solve_g(self,u,tol=1.e-8):
456           """
457           solves
458    
459           Q_g dp = g(u)
460    
461           with Q_g is a preconditioner for A_g A_f^{-1} A_g with  A_g is the jacobiean of g with respect to p.
462    
463           @param u: current approximation of u
464           @type u: L{escript.Data}
465           @param tol: tolerance expected for dp
466           @type tol: C{float}
467           @return: increment dp
468           @rtype: L{escript.Data}
469           @note: this method has to be overwritten by a particular saddle point problem
470           """
471           pass
472    
473       def inner(self,p0,p1):
474           """
475           inner product of p0 and p1 approximating p. Typically this returns integrate(p0*p1)
476           @return: inner product of p0 and p1
477           @rtype: C{float}
478           """
479           pass
480    
481       subiter_max=3
482       def solve(self,u0,p0,tolerance=1.e-6,tolerance_u=None,iter_max=100,accepted_reduction=0.995,relaxation=None):
483            """
484            runs the solver
485    
486            @param u0: initial guess for C{u}
487            @type u0: L{esys.escript.Data}
488            @param p0: initial guess for C{p}
489            @type p0: L{esys.escript.Data}
490            @param tolerance: tolerance for relative error in C{u} and C{p}
491            @type tolerance: positive C{float}
492            @param tolerance_u: tolerance for relative error in C{u} if different from C{tolerance}
493            @type tolerance_u: positive C{float}
494            @param iter_max: maximum number of iteration steps.
495            @type iter_max: C{int}
496            @param accepted_reduction: if the norm  g cannot be reduced by C{accepted_reduction} backtracking to adapt the
497                                       relaxation factor. If C{accepted_reduction=None} no backtracking is used.
498            @type accepted_reduction: positive C{float} or C{None}
499            @param relaxation: initial relaxation factor. If C{relaxation==None}, the last relaxation factor is used.
500            @type relaxation: C{float} or C{None}
501            """
502            tol=1.e-2
503            if tolerance_u==None: tolerance_u=tolerance
504            if not relaxation==None: self.relaxation=relaxation
505            if accepted_reduction ==None:
506                  angle_limit=0.
507            elif accepted_reduction>=1.:
508                  angle_limit=0.
509            else:
510                  angle_limit=util.sqrt(1-accepted_reduction**2)
511            self.iter=0
512            u=u0
513            p=p0
514            #
515            #   initialize things:
516            #
517            converged=False
518            #
519            #  start loop:
520            #
521            #  initial search direction is g
522            #
523            while not converged :
524                if self.iter>iter_max:
525                    raise ArithmeticError("no convergence after %s steps."%self.iter)
526                f_new=self.solve_f(u,p,tol)
527                norm_f_new = util.Lsup(f_new)
528                u_new=u-f_new
529                g_new=self.solve_g(u_new,tol)
530                self.iter+=1
531                norm_g_new = util.sqrt(self.inner(g_new,g_new))
532                if norm_f_new==0. and norm_g_new==0.: return u, p
533                if self.iter>1 and not accepted_reduction==None:
534                   #
535                   #   did we manage to reduce the norm of G? I
536                   #   if not we start a backtracking procedure
537                   #
538                   # print "new/old norm = ",norm_g_new, norm_g, norm_g_new/norm_g
539                   if norm_g_new > accepted_reduction * norm_g:
540                      sub_iter=0
541                      s=self.relaxation
542                      d=g
543                      g_last=g
544                      self.trace("    start substepping: f = %s, g = %s, relaxation = %s."%(norm_f_new, norm_g_new, s))
545                      while sub_iter < self.subiter_max and  norm_g_new > accepted_reduction * norm_g:
546                         dg= g_new-g_last
547                         norm_dg=abs(util.sqrt(self.inner(dg,dg))/self.relaxation)
548                         rad=self.inner(g_new,dg)/self.relaxation
549                         # print "   ",sub_iter,": rad, norm_dg:",abs(rad), norm_dg*norm_g_new * angle_limit
550                         # print "   ",sub_iter,": rad, norm_dg:",rad, norm_dg, norm_g_new, norm_g
551                         if abs(rad) < norm_dg*norm_g_new * angle_limit:
552                             if sub_iter>0: self.trace("    no further improvements expected from backtracking.")
553                             break
554                         r=self.relaxation
555                         self.relaxation= - rad/norm_dg**2
556                         s+=self.relaxation
557                         #####
558                         # a=g_new+self.relaxation*dg/r
559                         # print "predicted new norm = ",util.sqrt(self.inner(a,a)),util.sqrt(self.inner(g_new,g_new)), self.relaxation
560                         #####
561                         g_last=g_new
562                         p+=self.relaxation*d
563                         f_new=self.solve_f(u,p,tol)
564                         u_new=u-f_new
565                         g_new=self.solve_g(u_new,tol)
566                         self.iter+=1
567                         norm_f_new = util.Lsup(f_new)
568                         norm_g_new = util.sqrt(self.inner(g_new,g_new))
569                         # print "   ",sub_iter," new g norm",norm_g_new
570                         self.trace("    %s th sub-step: f = %s, g = %s, relaxation = %s."%(sub_iter, norm_f_new, norm_g_new, s))
571                         #
572                         #   can we expect reduction of g?
573                         #
574                         # u_last=u_new
575                         sub_iter+=1
576                      self.relaxation=s
577                #
578                #  check for convergence:
579                #
580                norm_u_new = util.Lsup(u_new)
581                p_new=p+self.relaxation*g_new
582                norm_p_new = util.sqrt(self.inner(p_new,p_new))
583                self.trace("%s th step: f/u = %s, g/p = %s, relaxation = %s."%(self.iter,norm_f_new/norm_u_new, norm_g_new/norm_p_new, self.relaxation))
584    
585                if self.iter>1:
586                   dg2=g_new-g
587                   df2=f_new-f
588                   norm_dg2=util.sqrt(self.inner(dg2,dg2))
589                   norm_df2=util.Lsup(df2)
590                   # print norm_g_new, norm_g, norm_dg, norm_p, tolerance
591                   tol_eq_g=tolerance*norm_dg2/(norm_g*abs(self.relaxation))*norm_p_new
592                   tol_eq_f=tolerance_u*norm_df2/norm_f*norm_u_new
593                   if norm_g_new <= tol_eq_g and norm_f_new <= tol_eq_f:
594                       converged=True
595                f, norm_f, u, norm_u, g, norm_g, p, norm_p = f_new, norm_f_new, u_new, norm_u_new, g_new, norm_g_new, p_new, norm_p_new
596            self.trace("convergence after %s steps."%self.iter)
597            return u,p
598    #   def solve(self,u0,p0,tolerance=1.e-6,iter_max=10,self.relaxation=1.):
599    #      tol=1.e-2
600    #      iter=0
601    #      converged=False
602    #      u=u0*1.
603    #      p=p0*1.
604    #      while not converged and iter<iter_max:
605    #          du=self.solve_f(u,p,tol)
606    #          u-=du
607    #          norm_du=util.Lsup(du)
608    #          norm_u=util.Lsup(u)
609    #        
610    #          dp=self.relaxation*self.solve_g(u,tol)
611    #          p+=dp
612    #          norm_dp=util.sqrt(self.inner(dp,dp))
613    #          norm_p=util.sqrt(self.inner(p,p))
614    #          print iter,"-th step rel. errror u,p= (%s,%s) (%s,%s)(%s,%s)"%(norm_du,norm_dp,norm_du/norm_u,norm_dp/norm_p,norm_u,norm_p)
615    #          iter+=1
616    #
617    #          converged = (norm_du <= tolerance*norm_u) and  (norm_dp <= tolerance*norm_p)
618    #      if converged:
619    #          print "convergence after %s steps."%iter
620    #      else:
621    #          raise ArithmeticError("no convergence after %s steps."%iter)
622    #
623    #      return u,p
624              
625  # vim: expandtab shiftwidth=4:  # vim: expandtab shiftwidth=4:

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