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# $Id$ |
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|
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# Test for the AdvectivePDE class |
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# |
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# for a single equation the test problem is |
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# |
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# -(K_{ij}u_{,j})_{,i} - (w_i u)_{,i} + v_j u_{,j} =0 |
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# |
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# + constraints on the surface |
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# |
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# for system of two equation the test problem is |
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# |
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# -(K_{milj}u_{l,j})_{,i} - (w_{mil} u_l)_{,i} + v_{mlj} u_{l,j} =0 |
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# |
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# + constraints on the surface |
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# |
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# K,w and v are constant (we will set v=0 or w=0) |
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# |
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# the test solution is u(x)=e^{z_i*x_i} and u_l(x)=e^{z_{li}*x_i} |
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# |
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# an easy caculation shows that |
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# |
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# z_i*K_{ij}*z_j=(v_i-w_i)*z_i and z_{li}*K_{milj}*z_{lj}=(v_{mjl}-w_{mlj})*z_{lj} |
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# |
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# obviously one can choose: v_i-w_i=K_{ji}z_j and v_{mjl}-w_{mlj}=z_{li}*K_{milj} (no summation over l) |
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# |
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|
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from esys.escript import * |
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from esys.linearPDEs import AdvectivePDE,LinearPDE |
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from esys import finley |
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from random import random |
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|
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def printError(u,u_ex): |
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if u.getRank()==0: |
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out=" error = %e range = [%e:%e] [%e:%e]"%(Lsup(u-u_ex)/Lsup(u_ex),sup(u),inf(u),sup(u_ex),inf(u_ex)) |
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else: |
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out="\n" |
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for i in range(u.getShape()[0]): |
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out+=" %d error = %e range = [%e:%e] [%e:%e]\n"%(i,Lsup(u[i]-u_ex[i])/Lsup(u_ex[i]),sup(u[i]),inf(u[i]),sup(u_ex[i]),inf(u_ex[i])) |
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return out |
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|
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|
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def makeRandomFloats(n,val_low=0.,val_up=1.): |
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out=[] |
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for i in range(n): |
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out.append((val_up-val_low)*random()+val_low) |
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return out |
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|
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def makeRandomFloatMatrix(m,n,val_low=0.,val_up=1.): |
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out=[] |
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for i in range(m): |
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out.append(makeRandomFloats(n,val_low,val_up)) |
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return out |
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|
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def makeRandomFloatTensor(l,k,m,n,val_low=0.,val_up=1.): |
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out=[] |
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for j in range(l): |
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out2=[] |
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for i in range(k): out2.append(makeRandomFloatMatrix(m,n,val_low,val_up)) |
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out.append(out2) |
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return out |
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|
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ne=20 |
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# for d in [2,3]: |
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for d in [3]: |
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# create domain: |
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if d==2: |
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mydomain=finley.Rectangle(ne,ne,1) |
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x=mydomain.getX() |
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msk=x[0].whereZero()+(x[0]-1.).whereZero()+x[1].whereZero()+(x[1]-1.).whereZero() |
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else: |
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mydomain=finley.Brick(ne,ne,ne,1) |
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x=mydomain.getX() |
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msk=x[0].whereZero()+(x[0]-1.).whereZero()+x[1].whereZero()+(x[1]-1.).whereZero()+x[2].whereZero()+(x[2]-1.).whereZero() |
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print "@ generated %d-dimension mesh with %d elements in each direction"%(d,ne) |
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# for ncomp in [1,2]: |
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for ncomp in [2]: |
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if ncomp==1: |
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maskf=1. |
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Z=makeRandomFloats(d,-1.,0.) |
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K_sup=makeRandomFloatMatrix(d,d,-1.,1.) |
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K=numarray.identity(d)*1. |
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else: |
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maskf=numarray.ones(ncomp) |
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Z=makeRandomFloatMatrix(ncomp,d,-1.,0.) |
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K_sup=makeRandomFloatTensor(ncomp,d,ncomp,d,-1.,1.) |
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K=numarray.zeros([ncomp,d,ncomp,d])*0. |
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for i in range(ncomp): |
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K[i,:,i,:]=numarray.identity(d)*1. |
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K_sup=numarray.array(K_sup) |
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Z=numarray.array(Z) |
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Z/=length(Z) |
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if ncomp==1: |
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Zx=Z[0]*x[0] |
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for j in range(1,d): |
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Zx+=Z[j]*x[j] |
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else: |
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Zx=x[0]*Z[:,0] |
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for j in range(1,d): |
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Zx+=x[j]*Z[:,j] |
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K+=0.02*K_sup/length(K_sup) |
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K/=length(K) |
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if ncomp==1: |
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U=numarray.matrixmultiply(numarray.transpose(K),Z) |
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else: |
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U=numarray.zeros([ncomp,d,ncomp])*1. |
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for m in range(ncomp): |
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for l in range(ncomp): |
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for j in range(d): |
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for i in range(d): |
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U[m,j,l]+=K[m,i,l,j]*Z[l,i] |
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|
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# create domain: |
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mypde=AdvectivePDE(mydomain) |
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# mypde.setSolverMethod(mypde.DIRECT) |
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mypde.setValue(q=msk*maskf,A=K) |
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mypde.checkSymmetry() |
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# run Peclet |
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for Pe in [0.001,1.,1.,10.,100,1000.,10000.,100000.,1000000.,10000000.]: |
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peclet=Pe*length(U)/2./length(K)/ne |
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print "@@@ Peclet Number :",peclet |
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u_ex=exp(Pe*Zx) |
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mypde.setValue(r=u_ex) |
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# mypde.setValue(B=Data(),C=Pe*U) |
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# u=mypde.getSolution() |
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# print "@@@@ C=U: Pe = ",peclet,printError(u,u_ex) |
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mypde.setValue(C=Data(),B=-Pe*U) |
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u=mypde.getSolution() |
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print "@@@@ B=-U: Pe = ",peclet,printError(u,u_ex) |
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