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# $Id$ |
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"""tests a variety of functions in connection with contact elements""" |
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from escript import * |
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from linearPDEs import LinearPDE |
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import finley |
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import math |
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numElements=4 |
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numEquations=2 |
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|
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seed=1 |
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rand_factor=sqrt(2.) |
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def randomNum(): |
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global seed |
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seed+=1 |
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s=rand_factor*seed |
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return s-int(s) |
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|
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|
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def mkMesh(dim,order,numElm,onElem): |
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if dim==2: |
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ms1=finley.Rectangle(numElm,numElm,order,l1=0.5,useElementsOnFace=onElem) |
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ms2=finley.Rectangle(numElm,numElm,order,l1=0.5,useElementsOnFace=onElem) |
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ms2.setX(ms2.getX()+[0,0.5]) |
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else: |
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ms1=finley.Brick(numElm,numElm,numElm,order,l2=0.5,useElementsOnFace=onElem) |
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ms2=finley.Brick(numElm,numElm,numElm,order,l2=0.5,useElementsOnFace=onElem) |
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ms2.setX(ms2.getX()+[0,0,0.5]) |
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return finley.JoinFaces([ms1,ms2]) |
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|
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|
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def mkCharateristicFunction(msh): |
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"""returns a scalar function on nodes which is -1 below and 1 above the fault""" |
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options = { |
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"verbose" : True, |
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"reordering" : NO_REORDERING, |
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"tolerance" : 1.E-13, |
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"final_residual" : 0., |
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"iterative" : True, |
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"iterative_method" : BICGSTAB, |
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"preconditioner" : JACOBI, |
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"iter_max" : 4000, |
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"iter" : 0, |
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"drop_tolerance" : 1.10, |
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"drop_storage" : 2. |
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} |
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e=Function(msh) |
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d=msh.getDim() |
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x=e.getX()[d-1] |
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mypde=LinearPDE(D=1,Y=(x-0.5).whatPositive()) |
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return 2*mypde.getSolution(**options)-1 |
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|
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max_error_text="" |
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max_error=0. |
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for dim in [2,3]: |
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for order in [1,2]: |
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for onElem in [False,True]: |
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if onElem: |
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onElem_text=",elements on face" |
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else: |
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onElem_text="" |
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case="Contact: %dD, order %d%s"%(dim,order,onElem_text) |
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print case |
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msh=mkMesh(dim,order,numElements,onElem) |
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c0=FunctionOnContact0(msh) |
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c1=FunctionOnContact1(msh) |
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n=ContinuousFunction(msh) |
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# |
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# check the normal on the fault 0: |
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# |
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refNormal=Vector(0,what=c0) |
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if dim==3: |
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refNormal.setTaggedValue(100,[0,0,1]) |
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else: |
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refNormal.setTaggedValue(10,[0,1]) |
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error_norm=Lsup(c0.getNormal()-refNormal) |
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text=" %s : error normals 0= %e"%(case,error_norm) |
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print "@@@ %s"%text |
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if error_norm>max_error: max_error_text,max_error=text,error_norm |
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# |
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# check the normal on the fault 1: |
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# |
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refNormal=Vector(0,what=c1) |
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if dim==3: |
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refNormal.setTaggedValue(100,[0,0,-1]) |
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else: |
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refNormal.setTaggedValue(10,[0,-1]) |
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error_norm=Lsup(c1.getNormal()-refNormal) |
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text=" %s : error normals 1= %e"%(case,error_norm) |
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print "@@@ %s"%text |
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if error_norm>max_error: max_error_text,max_error=text,error_norm |
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# |
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# integration on 0: |
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# |
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g=c0.getX()[dim-1]**2 |
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error_norm=abs(g.integrate()-0.25) |
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text=" %s : error integrate 0= %e"%(case,error_norm) |
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print "@@@ %s"%text |
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if error_norm>max_error: max_error_text,max_error=text,error_norm |
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# |
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# integration on 1: |
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# |
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g=c1.getX()[0]**2 |
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error_norm=abs(g.integrate()-1./3.) |
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text=" %s : error integrate 1= %e"%(case,error_norm) |
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print "@@@ %s"%text |
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if error_norm>max_error: max_error_text,max_error=text,error_norm |
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# |
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# gradient: |
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# |
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if onElem: |
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x=n.getX() |
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char=(x[dim-1]-0.5).whereNegative() |
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foo=2*x[dim-1]*char+(10*x[dim-1]-4)*(1-char) |
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|
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error_norm=Lsup(foo.grad(c0)[dim-1]-2) |
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text=" %s : error gradient on 0= %e"%(case,error_norm) |
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print "@@@ %s"%text |
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if error_norm>max_error: max_error_text,max_error=text,error_norm |
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|
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error_norm=Lsup(foo.grad(c1)[dim-1]-10) |
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text=" %s : error gradient on 1= %e"%(case,error_norm) |
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print "@@@ %s"%text |
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if error_norm>max_error: max_error_text,max_error=text,error_norm |
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|
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char=mkCharateristicFunction(msh) |
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for red in [False,True]: |
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if red: |
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case_red=",reduced" |
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else: |
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case_red="" |
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for ne in range(1,numEquations+1): |
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u_ex=Data(0,shape=(ne,),what=n) |
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for i in range(ne): |
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u_ex[i]=char*(i+1)*n.getX()[0] |
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u0=u_ex.interpolate(c0) |
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u1=u_ex.interpolate(c1) |
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if ne==1: |
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d=randomNum() |
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y=d*(u1-u0) |
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else: |
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d=Id(ne) |
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for i in range(ne): |
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for j in range(ne): |
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d[i,j]=randomNum() |
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y=Data(0,shape=(ne,),what=c0) |
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for i in range(ne): |
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for j in range(ne): |
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y[i]+=d[i,j]*(u1[j]-u0[j]) |
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mypde=linearPDE(d_contact=d,y_contact=y) |
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mypde.setReducedOrderForEquationsTo(red) |
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error_norm=Lsup(mypde.getResidual(u_ex))/Lsup(mypde.getRightHandSide()) |
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text=" %s%s, assembling %d equations: error = %e"%(case,case_red,ne,error_norm) |
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print "@@@ %s"%text |
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if error_norm>max_error: max_error_text,max_error=text,error_norm |
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|
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|
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print "maximal error for ",max_error_text |
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