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# $Id$ |
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"""General test environment to test the solvers for scalar and vector equations |
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test parameters are |
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numDim = spatial dimension |
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totalNumElem = number of func in each direction |
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problem = solveScalar,solveVector |
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|
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solver_method = true/false |
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len_x0 = length of the domain in x0 direction (number of func in x0 is round(totalNumElem*len_x0) ) |
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alpha = a parameter of the PDE (not well defined yet) |
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|
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""" |
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from esys.escript import * |
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from esys.linearPDEs import * |
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import esys.finley as pdelib |
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|
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from numarray import * |
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|
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# these values are currently fixed: |
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len_x0=1. |
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alpha=0.1 |
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|
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#############################################################################################################3 |
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def solveVector(numDim, totalNumElem, len_x0, alpha, solver_method): |
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print "Vector solver:" |
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recDim=array([len_x0,1.,1.]) |
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# Define Computational Domain |
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numElem=int((totalNumElem/(len_x0*1.))**(1./numDim)) |
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elemDim = array([int(len_x0*numElem), numElem, numElem],Int) |
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|
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# Set Mesh |
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if (numDim == 2): |
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mesh = pdelib.Rectangle(elemDim[0], elemDim[1], 2, \ |
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l0 = len_x0, l1 = 1.) |
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totElem=elemDim[0]*elemDim[1] |
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elif (numDim == 3): |
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mesh = pdelib.Brick(elemDim[0], elemDim[1], elemDim[2], 2, \ |
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l0 = len_x0, l1 = 1., l2 = 1.) |
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totElem=elemDim[0]*elemDim[1]*elemDim[2] |
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|
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print " length of domain: ",recDim[:numDim] |
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print " requested elements: ",totalNumElem |
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print " num elements: ",totElem |
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# Set Mesh Descriptors |
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meshDim = mesh.getDim() |
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contfunc = ContinuousFunction(mesh) |
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func = Function(mesh) |
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x = contfunc.getX() |
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|
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# Set Boundary Mask / pdelib Template "q" Parameter Vector |
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bndryMask = Vector(value = 0, what = contfunc) |
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for i in range(meshDim): |
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bndryMask += (x[i].whereZero() + (x[i]-recDim[i]).whereZero()) \ |
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* ones((numDim,)) |
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|
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# Set True Solution / pdelib Template "r" Parameter Vector |
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u = Vector(value = 0, what = contfunc) |
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for i in range(meshDim): |
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for j in range(meshDim - 1): |
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u[i] += x[(i + j + 1) % meshDim]**2 |
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# Set pdelib Template "A" Parameter Tensor |
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A = Tensor4(value = 0, what = func) |
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for i in range(meshDim): |
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for j in range(meshDim): |
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A[i,i,j,j] += 1. |
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A[i,j,j,i] += alpha |
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A[i,j,i,j] += alpha |
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|
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# Build the pdelib System Matrix and RHS |
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mypde=LinearPDE(mesh) |
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mypde.setValue(A = A, Y = - 2 * alpha * (meshDim - 1)*ones(meshDim), q = bndryMask, r = u) |
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mypde.setSolverMethod(solver_method) |
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# Solve for Approximate Solution |
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u_approx = mypde.getSolution(iter_max=10000) |
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|
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# Report Results |
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error=Lsup(u - u_approx)/Lsup(u) |
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print " error L^sup Norm : ", error |
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print " residual L^sup Norm : ", Lsup(mypde.getResidual(u_approx)) |
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|
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return error |
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|
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################################################################################################################# |
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def solveScalar(numDim, totalNumElem, len_x0, alpha, solver_method): |
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print "Scalar solver:" |
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recDim=array([len_x0,1.,1.]) |
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# Define Computational Domain |
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numElem=int((totalNumElem/(len_x0*1.))**(1./numDim)) |
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elemDim = array([int(len_x0*numElem), numElem, numElem],Int) |
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# Set Mesh |
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if (numDim == 2): |
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mesh = pdelib.Rectangle(elemDim[0], elemDim[1], 2, \ |
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l0 = len_x0, l1 = 1.) |
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totElem=elemDim[0]*elemDim[1] |
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elif (numDim == 3): |
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mesh = pdelib.Brick(elemDim[0], elemDim[1], elemDim[2], 2, \ |
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l0 = len_x0, l1 = 1., l2 = 1.) |
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totElem=elemDim[0]*elemDim[1]*elemDim[2] |
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print " length of domain: ",recDim[:numDim] |
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print " requested elements: ",totalNumElem |
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print " num elements: ",totElem |
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|
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# Set Mesh Descriptors |
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meshDim = mesh.getDim() |
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contfunc = ContinuousFunction(mesh) |
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func = Function(mesh) |
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x = contfunc.getX() |
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|
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# Set Boundary Mask / pdelib Template "q" Parameter Vector |
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bndryMask = Scalar(value = 0, what = contfunc) |
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for i in range(meshDim): |
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bndryMask += (x[i].whereZero() + (x[i]-recDim[i]).whereZero()) * 1.0 |
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|
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# Set True Solution / pdelib Template "r" Parameter Vector |
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u = Scalar(value = 0, what = contfunc) |
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for j in range(meshDim): |
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u += x[j] * x[j] |
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# Build the pdelib System Matrix and RHS |
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mypde=LinearPDE(mesh) |
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mypde.setValue(A = identity(numDim), D = alpha, Y = alpha * u - 2 * meshDim, q = bndryMask, r = u) |
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mypde.setSolverMethod(solver_method) |
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# Solve for Approximate Solution |
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u_approx = mypde.getSolution(iter_max=10000) |
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|
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# Report Results |
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error=Lsup(u - u_approx)/Lsup(u) |
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print " error L^sup Norm : ", error |
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print " residual L^sup Norm : ", Lsup(mypde.getResidual(u_approx)) |
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return error |
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####################################################################################### |
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print "Test is started:" |
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print "----------------" |
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error=0. |
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for numDim in [2,3]: |
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for totalNumElem in [100, 200, 400, 800, 1600, 3200, 6400, 12800, 25600, 51200, 102400]: |
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for problem in [solveScalar,solveVector]: |
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# for solver_method in [ LinearPDE.PRES20, LinearPDE.PCG, LinearPDE.DIRECT, LinearPDE.BICGSTAB]: |
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for solver_method in [ LinearPDE.PRES20, LinearPDE.PCG, LinearPDE.BICGSTAB]: |
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error=max([problem(numDim, totalNumElem, len_x0, alpha, solver_method),error]) |
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print "----------------" |
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print "maximum error over all tests is ",error |
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print "----------------" |
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