VelPres = Velocitydim[xx-1][0] +Pressuredim[xx-1][0] params = [kappa,Mu_m,MU] u_k,p_k,b_k,r_k = common.InitialGuess(FSpaces,[u0,p0,b0,r0],[Laplacian+gradPres,F_M],params,Neumann=Expression(("0","0")),options ="New") x = Iter.u_prev(u_k,p_k,b_k,r_k) IterType = 'CD' ns,maxwell,CoupleTerm,Lmaxwell,Lns = forms.MHD2D(mesh, W,F_M,F_NS, u_k,b_k,params,IterType) parameters['linear_algebra_backend'] = 'uBLAS' RHSform = forms.PicardRHS(mesh, W, u_k, p_k, b_k, r_k, params) bcu = DirichletBC(W.sub(0),Expression(("0","0")), boundary) bcb = DirichletBC(W.sub(2),Expression(("0","0")), boundary) bcr = DirichletBC(W.sub(3),Expression(("0")), boundary) bcs = [bcu,bcb,bcr] eps = 1.0 # error measure ||u-u_k|| tol = 1.0E-5 # tolerance iter = 0 # iteration counter maxiter = 10 # max no of iterations allowed SolutionTime = 0 outer = 0 parameters['linear_algebra_backend'] = 'PETSc' p = forms.Preconditioner(mesh,W,u_k,params,IterType)
def foo(): m = 7 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 = 100.0 for yy in xrange(1, 5): MU = MU / 10 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) Pressure = FunctionSpace(mesh, "DG", order - 1) 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) #kappa = 1.0 kappa = 1.0 Mu_m = 1e1 IterType = 'MD' 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") RHSform = forms.PicardRHS(mesh, W, u_k, p_k, b_k, r_k, params, "DG") bcu = DirichletBC(W.sub(0), Expression(("0.0", "0.0")), boundary) bcb = DirichletBC(W.sub(2), Expression(("0.0", "0.0")), boundary) bcr = DirichletBC(W.sub(3), Expression(("0.0")), boundary) bcs = [bcu, bcb, bcr] eps = 1.0 # error measure ||u-u_k|| tol = 1.0E-4 # tolerance iter = 0 # iteration counter maxiter = 40 # max no of iterations allowed SolutionTime = 0 outer = 0 # parameters['linear_algebra_backend'] = 'uBLAS' # FSpaces = [Velocity,Magnetic,Pressure,Lagrange] if IterType == "CD": AA, bb = assemble_system(maxwell + ns, (Lmaxwell + Lns) - RHSform, bcs) A, b = CP.Assemble(AA, bb) # u = b.duplicate() # P = CP.Assemble(PP) 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") tic() if IterType == "CD": bb = assemble((Lmaxwell + Lns) - RHSform) for bc in bcs: bc.apply(bb) FF = AA.sparray()[0:dim[0], 0:dim[0]] A, b = CP.Assemble(AA, bb) # if iter == 1 if iter == 1: u = b.duplicate() F = A.getSubMatrix(u_is, u_is) kspF = NSprecondSetup.LSCKSPnonlinear(F) else: AA, bb = assemble_system(maxwell + ns + CoupleTerm, (Lmaxwell + Lns) - RHSform, bcs) A, b = CP.Assemble(AA, bb) # if iter == 1: if iter == 1: u = b.duplicate() print("{:40}").format("MHD assemble, time: "), " ==> ", ( "{:4f}").format( toc()), ("{:9}").format(" time: "), ("{:4}").format( time.strftime('%X %x %Z')[0:5]) kspFp, Fp = PrecondSetup.FluidNonLinearSetup(Pressure, MU, u_k) print "Inititial guess norm: ", u.norm() if iter > 3 and uNorm < u.norm(): iter = 100000 break uNorm = u.norm() #A,Q if IterType == 'Combined': n = FacetNormal(mesh) mat = as_matrix([[b_k[1] * b_k[1], -b_k[1] * b_k[0]], [-b_k[1] * b_k[0], b_k[0] * b_k[0]]]) F = A.getSubMatrix(u_is, u_is) 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) kspF = NSprecondSetup.LSCKSPnonlinear(F) 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, 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) 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 IterTable.to_latex('Tables/IterType=' + IterType + '_n=' + str(m) + '_mu=' + str(MU) + '_kappa=' + str(kappa) + '_mu_m=' + str(Mu_m) + '.tex') # # # 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()
ns, maxwell, CoupleTerm, Lmaxwell, Lns = forms.MHD2D(mesh, W, F_M, F_NS, u_k, b_k, params, IterType, "DG", SaddlePoint="Yes") RHSform = forms.PicardRHS(mesh, W, u_k, p_k, b_k, r_k, params, "DG", SaddlePoint="Yes") bcu = DirichletBC(W.sub(0), Expression(("0.0", "0.0", "0.0")), boundary) bcb = DirichletBC(W.sub(1), Expression(("0.0", "0.0", "0.0")), boundary) bcr = DirichletBC(W.sub(3), Expression(("0.0")), boundary) bcs = [bcu, bcb, bcr] eps = 1.0 # error measure ||u-u_k|| tol = 1.0E-4 # tolerance iter = 0 # iteration counter maxiter = 40 # max no of iterations allowed SolutionTime = 0
#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", Stokes = "Yes") RHSform = forms.PicardRHS(mesh, W, u_k, p_k, b_k, r_k, params,"DG",Stokes = "Yes") bcu = DirichletBC(W.sub(0),Expression(("0.0","0.0")), boundary) bcb = DirichletBC(W.sub(2),Expression(("0.0","0.0")), boundary) bcb2 = DirichletBC(Magnetic,Expression(("0.0","0.0")), boundary) bcr = DirichletBC(W.sub(3),Expression(("0.0")), boundary) bcs = [bcu,bcb,bcr] eps = 1.0 # error measure ||u-u_k|| tol = 1.0E-4 # tolerance iter = 0 # iteration counter maxiter = 40 # max no of iterations allowed SolutionTime = 0 outer = 0
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")), boundary) bcb = DirichletBC(W.sub(2),Expression(("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 = 20 # max no of iterations allowed SolutionTime = 0 outer = 0 # parameters['linear_algebra_backend'] = 'uBLAS'
def foo(): m = 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, 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 + 5 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 = 2 parameters['reorder_dofs_serial'] = False Velocity = VectorFunctionSpace(mesh, "CG", order) Pressure = FunctionSpace(mesh, "CG", order - 1) 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(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")), boundary) bcb = DirichletBC(W.sub(2), Expression(("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[1] * b_k[1], -b_k[1] * b_k[0]], [-b_k[1] * b_k[0], b_k[0] * b_k[0]]]) 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 # # # 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 = 2 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+9 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) Pressure = FunctionSpace(mesh, "DG", order-1) Magnetic = FunctionSpace(mesh, "N1curl", order) Lagrange = FunctionSpace(mesh, "CG", order) W = MixedFunctionSpace([Velocity,Magnetic, Pressure, 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(), Magnetic.dim(), Pressure.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(1),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) kappa = 1.0 Mu_m =1e1 MU = 1.0/1 HiptmairTol = 1e-4 CGtol = 1e-4 IterType = 'Full' 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") HiptmairMatrices = PrecondSetup.MagneticSetup(Magnetic, Lagrange, b0, r0, CGtol, 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,HiptmairTol,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,b_k,p_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", SaddlePoint = "Yes") RHSform = forms.PicardRHS(mesh, W, u_k, p_k, b_k, r_k, params,"DG",SaddlePoint = "Yes") bcu = DirichletBC(W.sub(0),Expression(("0.0","0.0")), boundary) bcb = DirichletBC(W.sub(1),Expression(("0.0","0.0")), boundary) bcr = DirichletBC(W.sub(3),Expression(("0.0")), boundary) bcs = [bcu,bcb,bcr] eps = 1.0 # error measure ||u-u_k|| tol = 1.0E-4 # tolerance iter = 0 # iteration counter maxiter = 40 # max no of iterations allowed SolutionTime = 0 outer = 0 # parameters['linear_algebra_backend'] = 'uBLAS' # FSpaces = [Velocity,Magnetic,Pressure,Lagrange] if IterType == "CD": AA, bb = assemble_system(maxwell+ns, (Lmaxwell + Lns) - RHSform, bcs) A,b = CP.Assemble(AA,bb) # u = b.duplicate() # P = CP.Assemble(PP) 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-3 NSits =0 Mits =0 TotalStart =time.time() SolutionTime = 0 kspMASS = PrecondSetup.Masstest(Lagrange, p0, CGtol) while eps > tol and iter < maxiter: iter += 1 MO.PrintStr("Iter "+str(iter),7,"=","\n\n","\n\n") tic() if IterType == "CD": bb = assemble((Lmaxwell + Lns) - RHSform) for bc in bcs: bc.apply(bb) FF = AA.sparray()[0:dim[0],0:dim[0]] A,b = CP.Assemble(AA,bb) # if iter == 1 if iter == 1: u = b.duplicate() F = A.getSubMatrix(u_is,u_is) kspF = NSprecondSetup.LSCKSPnonlinear(F) else: AA, bb = assemble_system(maxwell+ns+CoupleTerm, (Lmaxwell + Lns) - RHSform, bcs) A,b = CP.Assemble(AA,bb) del AA, bb n = FacetNormal(mesh) mat = as_matrix([[b_k[1]*b_k[1],-b_k[1]*b_k[0]],[-b_k[1]*b_k[0],b_k[0]*b_k[0]]]) 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) #MO.StoreMatrix(AA.sparray()[0:dim[0],0:dim[0]]+ShiftedMass.sparray(),"A") FF = CP.Assemble(ShiftedMass) kspF = NSprecondSetup.LSCKSPnonlinear(FF) # if iter == 1: if iter == 1: u = b.duplicate() print ("{:40}").format("MHD assemble, time: "), " ==> ",("{:4f}").format(toc()), ("{:9}").format(" time: "), ("{:4}").format(time.strftime('%X %x %Z')[0:5]) kspFp, Fp = PrecondSetup.FluidNonLinearSetup(Pressure, MU, u_k) print "Inititial guess norm: ", u.norm() ksp = PETSc.KSP() ksp.create(comm=PETSc.COMM_WORLD) pc = ksp.getPC() ksp.setType('gmres') pc.setType('python') pc.setType(PETSc.PC.Type.PYTHON) # FSpace = [Velocity,Magnetic,Pressure,Lagrange] reshist = {} def monitor(ksp, its, fgnorm): reshist[its] = fgnorm print its," OUTER:", fgnorm # ksp.setMonitor(monitor) ksp.max_it = 1000 FFSS = [Velocity,Magnetic,Pressure,Lagrange] pc.setPythonContext(MHDpreconditioner.InnerOuterMAGNETICapprox(FFSS,kspF,KSPlinearfluids[0],KSPlinearfluids[1],Fp, HiptmairMatrices[3],kspMASS, HiptmairMatrices[2], HiptmairMatrices[0], HiptmairMatrices[1], HiptmairMatrices[6],HiptmairTol,FF)) #pc.setPythonContext(MHDpreconditioner.InnerOuterMAGNETICapprox(FFSS,kspF,KSPlinearfluids[0], KSPlinearfluids[1],Fp, HiptmairMatrices[3], HiptmairMatrices[4], HiptmairMatrices[2], HiptmairMatrices[0], HiptmairMatrices[1], HiptmairMatrices[6],HiptmairTol,FF)) # OptDB = PETSc.Options() # OptDB['pc_factor_mat_solver_package'] = "mumps" # OptDB['pc_factor_mat_ordering_type'] = "rcm" # ksp.setFromOptions() scale = b.norm() b = b/scale ksp.setOperators(A,A) stime = time.time() ksp.solve(b,u) Soltime = time.time()- stime NSits += ksp.its # Mits +=dodim print ("{:40}").format("MHD solve, time: "), " ==> ",("{:4f}").format(Soltime), ("{:9}").format(" time: "), ("{:4}").format(time.strftime('%X %x %Z')[0:5]) u = u*scale SolutionTime = SolutionTime +Soltime MO.PrintStr("Number of iterations ="+str(ksp.its),60,"+","\n\n","\n\n") u1, p1, b1, r1, eps= Iter.PicardToleranceDecouple(u,x,FSpaces,dim,"2",iter, SaddlePoint = "Yes") 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(),b_k.vector().array(),p_k.vector().array(),r_k.vector().array()), axis=0) x = IO.arrayToVec(uOld) ksp.destroy() kspF.destroy() kspFp.destroy() A.destroy() del HiptmairMatrices, KSPlinearfluids kspMASS.destroy() 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 print SolTime 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,NSave,Mave),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.to_latex() print " \n Outer Tol: ",OuterTol, "Inner Tol: ", InnerTol # # # if (ShowResultPlots == 'yes'): # plot(u_k) # plot(interpolate(ue,Velocity)) # plot(p_k) # plot(interpolate(pe,Pressure)) # plot(b_k) # plot(interpolate(be,Magnetic)) # plot(r_k) # plot(interpolate(re,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()