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# $Id$ |
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from esys.escript import * |
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from esys.linearPDEs import Poisson |
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import esys.finley as finley |
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ne_list=[10,15,22,33,50,75] |
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height_list=[0.25,0.5,1.] |
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def getDomain(dim,ne,height): |
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if dim==2: |
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ne1=int(ne*height+0.5) |
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mydomain=finley.Rectangle(n0=ne,n1=ne1,l1=height,order=2) |
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totne=ne1*ne |
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else: |
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ne2=int(ne*height+0.5) |
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mydomain=finley.Brick(n0=ne,n1=ne,n2=ne2,l2=height,order=2) |
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totne=ne2*ne*ne |
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print "%d -dimensional domain generated."%dim |
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print "height of the domain is ",height |
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print "total number of elements is ",totne |
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return mydomain |
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def Solve1(mydomain,height): |
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print "Fully constraint solution" |
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l=[1.,1.,1.] |
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l[mydomain.getDim()-1]=height |
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cf=ContinuousFunction(mydomain) |
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x=cf.getX() |
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#construct exact solution: |
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u_ex=Scalar(1.,cf) |
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for i in range(mydomain.getDim()): |
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u_ex*=x[i]*(x[i]-l[i]) |
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#construct mask: |
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msk=Scalar(0.,cf) |
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for i in range(mydomain.getDim()): |
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msk+=x[i].whereZero()+(x[i]-l[i]).whereZero() |
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#construct right hand side |
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f=Scalar(0,cf) |
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for i in range(mydomain.getDim()): |
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f_p=Scalar(1,cf) |
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for j in range(mydomain.getDim()): |
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if i==j: |
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f_p*=-2. |
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else: |
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f_p*=x[j]*(x[j]-l[j]) |
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f+=f_p |
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mypde=Poisson(mydomain) |
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mypde.setValue(f=f,q=msk) |
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u=mypde.getSolution() |
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error=Lsup(u-u_ex)/Lsup(u_ex) |
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print "error = ",error |
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return error |
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def Solve2(mydomain,height): |
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print "Partially constraint solution" |
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l=[1.,1.,1.] |
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l[mydomain.getDim()-1]=height |
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print l |
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cf=ContinuousFunction(mydomain) |
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x=cf.getX() |
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#construct exact solution: |
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u_ex=Scalar(1.,cf) |
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for i in range(mydomain.getDim()): |
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u_ex*=x[i]*(2*l[i]-x[i]) |
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#construct mask: |
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msk=Scalar(0.,cf) |
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for i in range(mydomain.getDim()): |
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msk+=x[i].whereZero() |
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#construct right hand side |
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f=Scalar(0,cf) |
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for i in range(mydomain.getDim()): |
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f_p=Scalar(1,cf) |
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for j in range(mydomain.getDim()): |
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if i==j: |
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f_p*=2. |
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else: |
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f_p*=x[j]*(2*l[j]-x[j]) |
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f+=f_p |
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mypde=Poisson(mydomain) |
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mypde.setValue(f=f,q=msk) |
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u=mypde.getSolution() |
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error=Lsup(u-u_ex)/Lsup(u_ex) |
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print "error = ",error |
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return error |
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error=0 |
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for ne in ne_list: |
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for dim in [2,3]: |
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for height in height_list: |
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print "***************************************************************" |
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mydomain= getDomain(dim,ne,height) |
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print "---------------------------------------------------------------" |
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error=max(error,Solve1(mydomain,height)) |
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print "---------------------------------------------------------------" |
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error=max(error,Solve2(mydomain,height)) |
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print "***************************************************************" |
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print "***************************************************************" |
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print "maximum error: ",error |
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print "***************************************************************" |
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