Mu_m = 10.0 MU = 1.0 N = FacetNormal(mesh) IterType = 'Full' params = [kappa, Mu_m, MU] n = FacetNormal(mesh) u0, p0, b0, r0, Laplacian, Advection, gradPres, CurlCurl, gradR, NS_Couple, M_Couple = ExactSol.MHD3D( 7, 1) MO.PrintStr("Seting up initial guess matricies", 2, "=", "\n\n", "\n") BCtime = time.time() BC = MHDsetup.BoundaryIndices(mesh) MO.StrTimePrint("BC index function, time: ", time.time() - BCtime) Hiptmairtol = 1e-6 HiptmairMatrices = PrecondSetup.MagneticSetup(mesh, Magnetic, Lagrange, b0, r0, Hiptmairtol, params) F_NS = -MU * Laplacian + Advection + gradPres - kappa * NS_Couple if kappa == 0.0: F_M = Mu_m * CurlCurl + gradR - kappa * M_Couple else: F_M = Mu_m * kappa * CurlCurl + gradR - kappa * M_Couple MO.PrintStr("Setting up MHD initial guess", 5, "+", "\n\n", "\n\n") u_k, p_k = HartmanChannel.Stokes(Velocity, Pressure, F_NS, u0, 1, params, mesh) b_k, r_k = HartmanChannel.Maxwell(Magnetic, Lagrange, F_M, b0, r0, params, mesh, HiptmairMatrices, Hiptmairtol)
def foo(): m = 6 errL2u = np.zeros((m - 1, 1)) errH1u = np.zeros((m - 1, 1)) errL2p = np.zeros((m - 1, 1)) errL2b = np.zeros((m - 1, 1)) errCurlb = np.zeros((m - 1, 1)) errL2r = np.zeros((m - 1, 1)) errH1r = np.zeros((m - 1, 1)) l2uorder = np.zeros((m - 1, 1)) H1uorder = np.zeros((m - 1, 1)) l2porder = np.zeros((m - 1, 1)) l2border = np.zeros((m - 1, 1)) Curlborder = np.zeros((m - 1, 1)) l2rorder = np.zeros((m - 1, 1)) H1rorder = np.zeros((m - 1, 1)) NN = np.zeros((m - 1, 1)) DoF = np.zeros((m - 1, 1)) Velocitydim = np.zeros((m - 1, 1)) Magneticdim = np.zeros((m - 1, 1)) Pressuredim = np.zeros((m - 1, 1)) Lagrangedim = np.zeros((m - 1, 1)) Wdim = np.zeros((m - 1, 1)) iterations = np.zeros((m - 1, 1)) SolTime = np.zeros((m - 1, 1)) udiv = np.zeros((m - 1, 1)) MU = np.zeros((m - 1, 1)) level = np.zeros((m - 1, 1)) NSave = np.zeros((m - 1, 1)) Mave = np.zeros((m - 1, 1)) TotalTime = np.zeros((m - 1, 1)) nn = 2 dim = 2 ShowResultPlots = 'yes' split = 'Linear' MU[0] = 1e0 for xx in xrange(1, m): print xx level[xx - 1] = xx + 0 nn = 2**(level[xx - 1]) # Create mesh and define function space nn = int(nn) NN[xx - 1] = nn / 2 # parameters["form_compiler"]["quadrature_degree"] = 6 # parameters = CP.ParameterSetup() mesh = UnitCubeMesh(nn, nn, nn) order = 1 parameters['reorder_dofs_serial'] = False Velocity = VectorFunctionSpace( mesh, "CG", order) + VectorFunctionSpace(mesh, "B", 4) Pressure = FunctionSpace(mesh, "CG", order) Magnetic = FunctionSpace(mesh, "N1curl", order) Lagrange = FunctionSpace(mesh, "CG", order) W = MixedFunctionSpace([Velocity, Pressure, Magnetic, Lagrange]) # W = Velocity*Pressure*Magnetic*Lagrange Velocitydim[xx - 1] = Velocity.dim() Pressuredim[xx - 1] = Pressure.dim() Magneticdim[xx - 1] = Magnetic.dim() Lagrangedim[xx - 1] = Lagrange.dim() Wdim[xx - 1] = W.dim() print "\n\nW: ", Wdim[xx - 1], "Velocity: ", Velocitydim[ xx - 1], "Pressure: ", Pressuredim[xx - 1], "Magnetic: ", Magneticdim[ xx - 1], "Lagrange: ", Lagrangedim[xx - 1], "\n\n" dim = [Velocity.dim(), Pressure.dim(), Magnetic.dim(), Lagrange.dim()] def boundary(x, on_boundary): return on_boundary u0, p0, b0, r0, Laplacian, Advection, gradPres, CurlCurl, gradR, NS_Couple, M_Couple = ExactSol.MHD3D( 4, 1) bcu = DirichletBC(Velocity, u0, boundary) bcb = DirichletBC(Magnetic, b0, boundary) bcr = DirichletBC(Lagrange, r0, boundary) # bc = [u0,p0,b0,r0] bcs = [bcu, bcb, bcr] FSpaces = [Velocity, Pressure, Magnetic, Lagrange] (u, b, p, r) = TrialFunctions(W) (v, c, q, s) = TestFunctions(W) kappa = 1.0 Mu_m = 10.0 MU = 1.0 / 1 IterType = 'Full' Split = "No" Saddle = "No" Stokes = "No" SetupType = 'python-class' F_NS = -MU * Laplacian + Advection + gradPres - kappa * NS_Couple if kappa == 0: F_M = Mu_m * CurlCurl + gradR - kappa * M_Couple else: F_M = Mu_m * kappa * CurlCurl + gradR - kappa * M_Couple params = [kappa, Mu_m, MU] MO.PrintStr("Seting up initial guess matricies", 2, "=", "\n\n", "\n") BCtime = time.time() BC = MHDsetup.BoundaryIndices(mesh) MO.StrTimePrint("BC index function, time: ", time.time() - BCtime) Hiptmairtol = 1e-5 HiptmairMatrices = PrecondSetup.MagneticSetup(Magnetic, Lagrange, b0, r0, Hiptmairtol, params) MO.PrintStr("Setting up MHD initial guess", 5, "+", "\n\n", "\n\n") u_k, p_k, b_k, r_k = common.InitialGuess(FSpaces, [u0, p0, b0, r0], [F_NS, F_M], params, HiptmairMatrices, 1e-10, Neumann=Expression( ("0", "0")), options="New") b_t = TrialFunction(Velocity) c_t = TestFunction(Velocity) ones = Function(Pressure) ones.vector()[:] = (0 * ones.vector().array() + 1) # pConst = - assemble(p_k*dx)/assemble(ones*dx) p_k.vector()[:] += -assemble(p_k * dx) / assemble(ones * dx) x = Iter.u_prev(u_k, p_k, b_k, r_k) KSPlinearfluids, MatrixLinearFluids = PrecondSetup.FluidLinearSetup( Pressure, MU) kspFp, Fp = PrecondSetup.FluidNonLinearSetup(Pressure, MU, u_k) #plot(b_k) ns, maxwell, CoupleTerm, Lmaxwell, Lns = forms.MHD2D( mesh, W, F_M, F_NS, u_k, b_k, params, IterType, "CG", Saddle, Stokes) RHSform = forms.PicardRHS(mesh, W, u_k, p_k, b_k, r_k, params, "CG", Saddle, Stokes) bcu = DirichletBC(W.sub(0), Expression(("0.0", "0.0", "0.0")), boundary) bcb = DirichletBC(W.sub(2), Expression(("0.0", "0.0", "0.0")), boundary) bcr = DirichletBC(W.sub(3), Expression(("0.0")), boundary) bcs = [bcu, bcb, bcr] parameters['linear_algebra_backend'] = 'uBLAS' eps = 1.0 # error measure ||u-u_k|| tol = 1.0E-4 # tolerance iter = 0 # iteration counter maxiter = 10 # max no of iterations allowed SolutionTime = 0 outer = 0 # parameters['linear_algebra_backend'] = 'uBLAS' # FSpaces = [Velocity,Magnetic,Pressure,Lagrange] if IterType == "CD": MO.PrintStr("Setting up PETSc " + SetupType, 2, "=", "\n", "\n") Alin = MHDsetup.Assemble(W, ns, maxwell, CoupleTerm, Lns, Lmaxwell, RHSform, bcs + BC, "Linear", IterType) Fnlin, b = MHDsetup.Assemble(W, ns, maxwell, CoupleTerm, Lns, Lmaxwell, RHSform, bcs + BC, "NonLinear", IterType) A = Fnlin + Alin A, b = MHDsetup.SystemAssemble(FSpaces, A, b, SetupType, IterType) u = b.duplicate() u_is = PETSc.IS().createGeneral(range(Velocity.dim())) NS_is = PETSc.IS().createGeneral(range(Velocity.dim() + Pressure.dim())) M_is = PETSc.IS().createGeneral( range(Velocity.dim() + Pressure.dim(), W.dim())) OuterTol = 1e-5 InnerTol = 1e-5 NSits = 0 Mits = 0 TotalStart = time.time() SolutionTime = 0 while eps > tol and iter < maxiter: iter += 1 MO.PrintStr("Iter " + str(iter), 7, "=", "\n\n", "\n\n") AssembleTime = time.time() if IterType == "CD": MO.StrTimePrint("MHD CD RHS assemble, time: ", time.time() - AssembleTime) b = MHDsetup.Assemble(W, ns, maxwell, CoupleTerm, Lns, Lmaxwell, RHSform, bcs + BC, "CD", IterType) else: MO.PrintStr("Setting up PETSc " + SetupType, 2, "=", "\n", "\n") if Split == "Yes": if iter == 1: Alin = MHDsetup.Assemble(W, ns, maxwell, CoupleTerm, Lns, Lmaxwell, RHSform, bcs + BC, "Linear", IterType) Fnlin, b = MHDsetup.Assemble(W, ns, maxwell, CoupleTerm, Lns, Lmaxwell, RHSform, bcs + BC, "NonLinear", IterType) A = Fnlin + Alin A, b = MHDsetup.SystemAssemble(FSpaces, A, b, SetupType, IterType) u = b.duplicate() else: Fnline, b = MHDsetup.Assemble(W, ns, maxwell, CoupleTerm, Lns, Lmaxwell, RHSform, bcs + BC, "NonLinear", IterType) A = Fnlin + Alin A, b = MHDsetup.SystemAssemble(FSpaces, A, b, SetupType, IterType) else: AA, bb = assemble_system(maxwell + ns + CoupleTerm, (Lmaxwell + Lns) - RHSform, bcs) A, b = CP.Assemble(AA, bb) # if iter == 1: MO.StrTimePrint("MHD total assemble, time: ", time.time() - AssembleTime) u = b.duplicate() kspFp, Fp = PrecondSetup.FluidNonLinearSetup(Pressure, MU, u_k) print "Inititial guess norm: ", u.norm( PETSc.NormType.NORM_INFINITY) #A,Q if IterType == 'Full': n = FacetNormal(mesh) mat = as_matrix([[ b_k[2] * b_k[2] + b[1] * b[1], -b_k[1] * b_k[0], -b_k[0] * b_k[2] ], [ -b_k[1] * b_k[0], b_k[0] * b_k[0] + b_k[2] * b_k[2], -b_k[2] * b_k[1] ], [ -b_k[0] * b_k[2], -b_k[1] * b_k[2], b_k[0] * b_k[0] + b_k[1] * b_k[1] ]]) a = params[2] * inner(grad(b_t), grad(c_t)) * dx( W.mesh()) + inner((grad(b_t) * u_k), c_t) * dx(W.mesh( )) + (1. / 2) * div(u_k) * inner(c_t, b_t) * dx( W.mesh()) - (1. / 2) * inner(u_k, n) * inner( c_t, b_t) * ds(W.mesh()) + kappa / Mu_m * inner( mat * b_t, c_t) * dx(W.mesh()) ShiftedMass = assemble(a) bcu.apply(ShiftedMass) ShiftedMass = CP.Assemble(ShiftedMass) kspF = NSprecondSetup.LSCKSPnonlinear(ShiftedMass) else: F = A.getSubMatrix(u_is, u_is) kspF = NSprecondSetup.LSCKSPnonlinear(F) stime = time.time() u, mits, nsits = S.solve(A, b, u, params, W, 'Directclase', IterType, OuterTol, InnerTol, HiptmairMatrices, Hiptmairtol, KSPlinearfluids, Fp, kspF) Soltime = time.time() - stime MO.StrTimePrint("MHD solve, time: ", Soltime) Mits += mits NSits += nsits SolutionTime += Soltime u1, p1, b1, r1, eps = Iter.PicardToleranceDecouple( u, x, FSpaces, dim, "2", iter) p1.vector()[:] += -assemble(p1 * dx) / assemble(ones * dx) u_k.assign(u1) p_k.assign(p1) b_k.assign(b1) r_k.assign(r1) uOld = np.concatenate((u_k.vector().array(), p_k.vector().array(), b_k.vector().array(), r_k.vector().array()), axis=0) x = IO.arrayToVec(uOld) XX = np.concatenate((u_k.vector().array(), p_k.vector().array(), b_k.vector().array(), r_k.vector().array()), axis=0) SolTime[xx - 1] = SolutionTime / iter NSave[xx - 1] = (float(NSits) / iter) Mave[xx - 1] = (float(Mits) / iter) iterations[xx - 1] = iter TotalTime[xx - 1] = time.time() - TotalStart # dim = [Velocity.dim(), Pressure.dim(), Magnetic.dim(),Lagrange.dim()] # # ExactSolution = [u0,p0,b0,r0] # errL2u[xx-1], errH1u[xx-1], errL2p[xx-1], errL2b[xx-1], errCurlb[xx-1], errL2r[xx-1], errH1r[xx-1] = Iter.Errors(XX,mesh,FSpaces,ExactSolution,order,dim, "DG") # # if xx > 1: # l2uorder[xx-1] = np.abs(np.log2(errL2u[xx-2]/errL2u[xx-1])) # H1uorder[xx-1] = np.abs(np.log2(errH1u[xx-2]/errH1u[xx-1])) # # l2porder[xx-1] = np.abs(np.log2(errL2p[xx-2]/errL2p[xx-1])) # # l2border[xx-1] = np.abs(np.log2(errL2b[xx-2]/errL2b[xx-1])) # Curlborder[xx-1] = np.abs(np.log2(errCurlb[xx-2]/errCurlb[xx-1])) # # l2rorder[xx-1] = np.abs(np.log2(errL2r[xx-2]/errL2r[xx-1])) # H1rorder[xx-1] = np.abs(np.log2(errH1r[xx-2]/errH1r[xx-1])) # # # # # import pandas as pd # # # # LatexTitles = ["l","DoFu","Dofp","V-L2","L2-order","V-H1","H1-order","P-L2","PL2-order"] # LatexValues = np.concatenate((level,Velocitydim,Pressuredim,errL2u,l2uorder,errH1u,H1uorder,errL2p,l2porder), axis=1) # LatexTable = pd.DataFrame(LatexValues, columns = LatexTitles) # pd.set_option('precision',3) # LatexTable = MO.PandasFormat(LatexTable,"V-L2","%2.4e") # LatexTable = MO.PandasFormat(LatexTable,'V-H1',"%2.4e") # LatexTable = MO.PandasFormat(LatexTable,"H1-order","%1.2f") # LatexTable = MO.PandasFormat(LatexTable,'L2-order',"%1.2f") # LatexTable = MO.PandasFormat(LatexTable,"P-L2","%2.4e") # LatexTable = MO.PandasFormat(LatexTable,'PL2-order',"%1.2f") # print LatexTable # # # print "\n\n Magnetic convergence" # MagneticTitles = ["l","B DoF","R DoF","B-L2","L2-order","B-Curl","HCurl-order"] # MagneticValues = np.concatenate((level,Magneticdim,Lagrangedim,errL2b,l2border,errCurlb,Curlborder),axis=1) # MagneticTable= pd.DataFrame(MagneticValues, columns = MagneticTitles) # pd.set_option('precision',3) # MagneticTable = MO.PandasFormat(MagneticTable,"B-Curl","%2.4e") # MagneticTable = MO.PandasFormat(MagneticTable,'B-L2',"%2.4e") # MagneticTable = MO.PandasFormat(MagneticTable,"L2-order","%1.2f") # MagneticTable = MO.PandasFormat(MagneticTable,'HCurl-order',"%1.2f") # print MagneticTable import pandas as pd print "\n\n Iteration table" if IterType == "Full": IterTitles = [ "l", "DoF", "AV solve Time", "Total picard time", "picard iterations", "Av Outer its", "Av Inner its", ] else: IterTitles = [ "l", "DoF", "AV solve Time", "Total picard time", "picard iterations", "Av NS iters", "Av M iters" ] IterValues = np.concatenate( (level, Wdim, SolTime, TotalTime, iterations, Mave, NSave), axis=1) IterTable = pd.DataFrame(IterValues, columns=IterTitles) if IterType == "Full": IterTable = MO.PandasFormat(IterTable, 'Av Outer its', "%2.1f") IterTable = MO.PandasFormat(IterTable, 'Av Inner its', "%2.1f") else: IterTable = MO.PandasFormat(IterTable, 'Av NS iters', "%2.1f") IterTable = MO.PandasFormat(IterTable, 'Av M iters', "%2.1f") print IterTable print " \n Outer Tol: ", OuterTol, "Inner Tol: ", InnerTol tableName = "3d_nu=" + str(MU) + "_nu_m=" + str(Mu_m) + "_kappa=" + str( kappa) + ".tex" IterTable.to_latex(tableName) # # # if (ShowResultPlots == 'yes'): # plot(u_k) # plot(interpolate(u0,Velocity)) # # plot(p_k) # # plot(interpolate(p0,Pressure)) # # plot(b_k) # plot(interpolate(b0,Magnetic)) # # plot(r_k) # plot(interpolate(r0,Lagrange)) # # interactive() interactive()
def foo(): m = 6 mm = 5 errL2u = np.zeros((m - 1, 1)) errH1u = np.zeros((m - 1, 1)) errL2p = np.zeros((m - 1, 1)) errL2b = np.zeros((m - 1, 1)) errCurlb = np.zeros((m - 1, 1)) errL2r = np.zeros((m - 1, 1)) errH1r = np.zeros((m - 1, 1)) l2uorder = np.zeros((m - 1, 1)) H1uorder = np.zeros((m - 1, 1)) l2porder = np.zeros((m - 1, 1)) l2border = np.zeros((m - 1, 1)) Curlborder = np.zeros((m - 1, 1)) l2rorder = np.zeros((m - 1, 1)) H1rorder = np.zeros((m - 1, 1)) NN = np.zeros((m - 1, 1)) DoF = np.zeros((m - 1, 1)) Velocitydim = np.zeros((m - 1, 1)) Magneticdim = np.zeros((m - 1, 1)) Pressuredim = np.zeros((m - 1, 1)) Lagrangedim = np.zeros((m - 1, 1)) Wdim = np.zeros((m - 1, 1)) iterations = np.zeros((m - 1, 3 * (mm - 1))) SolTime = np.zeros((m - 1, 1)) udiv = np.zeros((m - 1, 1)) MU = np.zeros((m - 1, 1)) level = np.zeros((m - 1, 1)) NSave = np.zeros((m - 1, 1)) Mave = np.zeros((m - 1, 1)) TotalTime = np.zeros((m - 1, 1)) KappaSave = np.zeros((mm - 1, 1)) nn = 2 dim = 2 ShowResultPlots = 'yes' split = 'Linear' qq = -1 MU[0] = 1e0 MU = 0.0001 qq = -1 for yy in xrange(1, mm): MU = MU * 10 KappaSave[yy - 1] = MU IterTypes = ['Full', 'MD', 'CD'] for kk in range(len(IterTypes)): qq += 1 for xx in xrange(1, m): print xx level[xx - 1] = xx + 2 nn = 2**(level[xx - 1]) # Create mesh and define function space nn = int(nn) NN[xx - 1] = nn / 2 # parameters["form_compiler"]["quadrature_degree"] = 6 # parameters = CP.ParameterSetup() mesh = UnitSquareMesh(nn, nn) order = 1 parameters['reorder_dofs_serial'] = False Velocity = VectorFunctionSpace(mesh, "CG", order + 1) Pressure = FunctionSpace(mesh, "CG", order) Magnetic = FunctionSpace(mesh, "N1curl", order) Lagrange = FunctionSpace(mesh, "CG", order) W = MixedFunctionSpace( [Velocity, Pressure, Magnetic, Lagrange]) # W = Velocity*Pressure*Magnetic*Lagrange Velocitydim[xx - 1] = Velocity.dim() Pressuredim[xx - 1] = Pressure.dim() Magneticdim[xx - 1] = Magnetic.dim() Lagrangedim[xx - 1] = Lagrange.dim() Wdim[xx - 1] = W.dim() print "\n\nW: ", Wdim[xx - 1], "Velocity: ", Velocitydim[ xx - 1], "Pressure: ", Pressuredim[ xx - 1], "Magnetic: ", Magneticdim[ xx - 1], "Lagrange: ", Lagrangedim[xx - 1], "\n\n" dim = [ Velocity.dim(), Pressure.dim(), Magnetic.dim(), Lagrange.dim() ] def boundary(x, on_boundary): return on_boundary u0, p0, b0, r0, Laplacian, Advection, gradPres, CurlCurl, gradR, NS_Couple, M_Couple = ExactSol.MHD2D( 4, 1) bcu = DirichletBC(W.sub(0), u0, boundary) bcb = DirichletBC(W.sub(2), b0, boundary) bcr = DirichletBC(W.sub(3), r0, boundary) # bc = [u0,p0,b0,r0] bcs = [bcu, bcb, bcr] FSpaces = [Velocity, Pressure, Magnetic, Lagrange] (u, b, p, r) = TrialFunctions(W) (v, c, q, s) = TestFunctions(W) Mu_m = 1e1 kappa = 1 IterType = IterTypes[kk] Split = "No" Saddle = "No" Stokes = "No" F_NS = -MU * Laplacian + Advection + gradPres - kappa * NS_Couple if kappa == 0: F_M = Mu_m * CurlCurl + gradR - kappa * M_Couple else: F_M = Mu_m * kappa * CurlCurl + gradR - kappa * M_Couple params = [kappa, Mu_m, MU] # MO.PrintStr("Preconditioning MHD setup",5,"+","\n\n","\n\n") Hiptmairtol = 1e-5 HiptmairMatrices = PrecondSetup.MagneticSetup( Magnetic, Lagrange, b0, r0, Hiptmairtol, params) MO.PrintStr("Setting up MHD initial guess", 5, "+", "\n\n", "\n\n") u_k, p_k, b_k, r_k = common.InitialGuess(FSpaces, [u0, p0, b0, r0], [F_NS, F_M], params, HiptmairMatrices, 1e-6, Neumann=Expression( ("0", "0")), options="New", FS="DG") #plot(p_k, interactive = True) b_t = TrialFunction(Velocity) c_t = TestFunction(Velocity) #print assemble(inner(b,c)*dx).array().shape #print mat #ShiftedMass = assemble(inner(mat*b,c)*dx) #as_vector([inner(b,c)[0]*b_k[0],inner(b,c)[1]*(-b_k[1])]) ones = Function(Pressure) ones.vector()[:] = (0 * ones.vector().array() + 1) # pConst = - assemble(p_k*dx)/assemble(ones*dx) p_k.vector()[:] += -assemble(p_k * dx) / assemble(ones * dx) x = Iter.u_prev(u_k, p_k, b_k, r_k) KSPlinearfluids, MatrixLinearFluids = PrecondSetup.FluidLinearSetup( Pressure, MU) kspFp, Fp = PrecondSetup.FluidNonLinearSetup(Pressure, MU, u_k) #plot(b_k) ns, maxwell, CoupleTerm, Lmaxwell, Lns = forms.MHD2D( mesh, W, F_M, F_NS, u_k, b_k, params, IterType, "DG", Saddle, Stokes) RHSform = forms.PicardRHS(mesh, W, u_k, p_k, b_k, r_k, params, "DG", Saddle, Stokes) bcu = DirichletBC(Velocity, Expression(("0.0", "0.0")), boundary) bcb = DirichletBC(Magnetic, Expression(("0.0", "0.0")), boundary) bcr = DirichletBC(Lagrange, Expression(("0.0")), boundary) bcs = [bcu, bcb, bcr] parameters['linear_algebra_backend'] = 'uBLAS' SetupType = 'Matrix' BC = MHDsetup.BoundaryIndices(mesh) eps = 1.0 # error measure ||u-u_k|| tol = 1.0E-4 # tolerance iter = 0 # iteration counter maxiter = 20 # max no of iterations allowed SolutionTime = 0 outer = 0 # parameters['linear_algebra_backend'] = 'uBLAS' # FSpaces = [Velocity,Magnetic,Pressure,Lagrange] if IterType == "CD": MO.PrintStr("Setting up PETSc " + SetupType, 2, "=", "\n", "\n") Alin = MHDsetup.Assemble(W, ns, maxwell, CoupleTerm, Lns, Lmaxwell, RHSform, bcs + BC, "Linear", IterType) Fnlin, b = MHDsetup.Assemble(W, ns, maxwell, CoupleTerm, Lns, Lmaxwell, RHSform, bcs + BC, "NonLinear", IterType) A = Fnlin + Alin A, b = MHDsetup.SystemAssemble(FSpaces, A, b, SetupType, IterType) u = b.duplicate() u_is = PETSc.IS().createGeneral(range(Velocity.dim())) NS_is = PETSc.IS().createGeneral( range(Velocity.dim() + Pressure.dim())) M_is = PETSc.IS().createGeneral( range(Velocity.dim() + Pressure.dim(), W.dim())) OuterTol = 1e-5 InnerTol = 1e-5 NSits = 0 Mits = 0 TotalStart = time.time() SolutionTime = 0 while eps > tol and iter < maxiter: iter += 1 MO.PrintStr("Iter " + str(iter), 7, "=", "\n\n", "\n\n") AssembleTime = time.time() if IterType == "CD": MO.StrTimePrint("MHD CD RHS assemble, time: ", time.time() - AssembleTime) b = MHDsetup.Assemble(W, ns, maxwell, CoupleTerm, Lns, Lmaxwell, RHSform, bcs + BC, "CD", IterType) else: MO.PrintStr("Setting up PETSc " + SetupType, 2, "=", "\n", "\n") AA, bb = assemble_system(maxwell + ns + CoupleTerm, (Lmaxwell + Lns) - RHSform, bcs) A, b = CP.Assemble(AA, bb) # if iter == 1: MO.StrTimePrint("MHD total assemble, time: ", time.time() - AssembleTime) kspFp, Fp = PrecondSetup.FluidNonLinearSetup( Pressure, MU, u_k) u = b.duplicate() print "Inititial guess norm: ", u.norm() if u.norm() > 1e50: iter = 10000 break #A,Q kspF = 0 stime = time.time() u, mits, nsits = S.solve(A, b, u, params, W, 'Direct', IterType, OuterTol, InnerTol, HiptmairMatrices, Hiptmairtol, KSPlinearfluids, Fp, kspF) Soltime = time.time() - stime Mits += mits NSits += nsits SolutionTime += Soltime u1, p1, b1, r1, eps = Iter.PicardToleranceDecouple( u, x, FSpaces, dim, "2", iter) p1.vector()[:] += -assemble(p1 * dx) / assemble(ones * dx) u_k.assign(u1) p_k.assign(p1) b_k.assign(b1) r_k.assign(r1) uOld = np.concatenate( (u_k.vector().array(), p_k.vector().array(), b_k.vector().array(), r_k.vector().array()), axis=0) x = IO.arrayToVec(uOld) XX = np.concatenate( (u_k.vector().array(), p_k.vector().array(), b_k.vector().array(), r_k.vector().array()), axis=0) iterations[xx - 1, qq] = iter dim = [ Velocity.dim(), Pressure.dim(), Magnetic.dim(), Lagrange.dim() ] # # ExactSolution = [u0,p0,b0,r0] # errL2u[xx-1], errH1u[xx-1], errL2p[xx-1], errL2b[xx-1], errCurlb[xx-1], errL2r[xx-1], errH1r[xx-1] = Iter.Errors(XX,mesh,FSpaces,ExactSolution,order,dim, "DG") # # if xx > 1: # l2uorder[xx-1] = np.abs(np.log2(errL2u[xx-2]/errL2u[xx-1])) # H1uorder[xx-1] = np.abs(np.log2(errH1u[xx-2]/errH1u[xx-1])) # # l2porder[xx-1] = np.abs(np.log2(errL2p[xx-2]/errL2p[xx-1])) # # l2border[xx-1] = np.abs(np.log2(errL2b[xx-2]/errL2b[xx-1])) # Curlborder[xx-1] = np.abs(np.log2(errCurlb[xx-2]/errCurlb[xx-1])) # # l2rorder[xx-1] = np.abs(np.log2(errL2r[xx-2]/errL2r[xx-1])) # H1rorder[xx-1] = np.abs(np.log2(errH1r[xx-2]/errH1r[xx-1])) # # # # # import pandas as pd # # # # LatexTitles = ["l","DoFu","Dofp","V-L2","L2-order","V-H1","H1-order","P-L2","PL2-order"] # LatexValues = np.concatenate((level,Velocitydim,Pressuredim,errL2u,l2uorder,errH1u,H1uorder,errL2p,l2porder), axis=1) # LatexTable = pd.DataFrame(LatexValues, columns = LatexTitles) # pd.set_option('precision',3) # LatexTable = MO.PandasFormat(LatexTable,"V-L2","%2.4e") # LatexTable = MO.PandasFormat(LatexTable,'V-H1',"%2.4e") # LatexTable = MO.PandasFormat(LatexTable,"H1-order","%1.2f") # LatexTable = MO.PandasFormat(LatexTable,'L2-order',"%1.2f") # LatexTable = MO.PandasFormat(LatexTable,"P-L2","%2.4e") # LatexTable = MO.PandasFormat(LatexTable,'PL2-order',"%1.2f") # print LatexTable # # # print "\n\n Magnetic convergence" # MagneticTitles = ["l","B DoF","R DoF","B-L2","L2-order","B-Curl","HCurl-order"] # MagneticValues = np.concatenate((level,Magneticdim,Lagrangedim,errL2b,l2border,errCurlb,Curlborder),axis=1) # MagneticTable= pd.DataFrame(MagneticValues, columns = MagneticTitles) # pd.set_option('precision',3) # MagneticTable = MO.PandasFormat(MagneticTable,"B-Curl","%2.4e") # MagneticTable = MO.PandasFormat(MagneticTable,'B-L2',"%2.4e") # MagneticTable = MO.PandasFormat(MagneticTable,"L2-order","%1.2f") # MagneticTable = MO.PandasFormat(MagneticTable,'HCurl-order',"%1.2f") # print MagneticTable # import pandas as pd print iterations.shape[1] iter = ["P", "MD", "CD"] IterTitles = ["l", "DoF"] for i in range(iterations.shape[1] / 3): IterTitles += iter print IterTitles IterValues = np.concatenate((level, Wdim, iterations), axis=1) IterTable = pd.DataFrame(IterValues, columns=IterTitles) print IterTable.to_latex() print " \n Outer Tol: ", OuterTol, "Inner Tol: ", InnerTol print KappaSave # # # if (ShowResultPlots == 'yes'): # plot(u_k) # plot(interpolate(u0,Velocity)) # # plot(p_k) # # plot(interpolate(p0,Pressure)) # # plot(b_k) # plot(interpolate(b0,Magnetic)) # # plot(r_k) # plot(interpolate(r0,Lagrange)) # # interactive() interactive()
OptDB = PETSc.Options() ksp.max_it = 1000 # OptDB['pc_factor_shift_amount'] = 1 # OptDB['pc_factor_mat_ordering_type'] = 'rcm' # OptDB['pc_factor_mat_solver_package'] = 'mumps' ksp.setFromOptions() x = r toc() ksp.solve(b, x) time = toc() print time MO.StrTimePrint("Solve time",time) SolutionTime = SolutionTime +time outerit += ksp.its print "==============", ksp.its # r = bb.duplicate() # A.MUlt(x, r) # r.aypx(-1, bb) # rnorm = r.norm() # PETSc.Sys.Print('error norm = %g' % rnorm,comm=PETSc.COMM_WORLD) uu = IO.vecToArray(x) UU = uu[0:Vdim[xx-1][0]] # time = time+toc() u1 = Function(V) u1.vector()[:] = UU
b = interpolate(b_in(), MagneticE) r = interpolate(r0, LagrangeE) ErrorB = Function(Magnetic) ErrorR = Function(Lagrange) ErrorB = b - b_k ErrorR = r - r_k print b_k.vector().array() print b.vector().array() tic() errL2b[xx - 1] = sqrt(abs(assemble(inner(ErrorB, ErrorB) * dx))) MO.StrTimePrint("Magnetic L2 error, time: ", toc()) tic() errCurlb[xx - 1] = sqrt( abs(assemble(inner(curl(ErrorB), curl(ErrorB)) * dx))) MO.StrTimePrint("Magnetic Curl error, time: ", toc()) tic() errL2r[xx - 1] = sqrt(abs(assemble(inner(ErrorR, ErrorR) * dx))) MO.StrTimePrint("Multiplier L2 error, time: ", toc()) tic() errH1r[xx - 1] = sqrt(abs(assemble(inner(grad(ErrorR), grad(ErrorR)) * dx))) MO.StrTimePrint("Multiplier H1 error, time: ", toc()) import pandas as pd print "\n\n Magnetic convergence" MagneticTitles = [