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+ 10 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 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, 1e-5, 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,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 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]]]) 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) #MO.StoreMatrix(AA.sparray()[0:dim[0],0:dim[0]]+ShiftedMass.sparray(),"A") kspF = NSprecondSetup.LSCKSPnonlinear(F) # 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() solver = 'Schur' if solver == 'Schur': FF = CP.Assemble(ShiftedMass) kspF = NSprecondSetup.LSCKSPnonlinear(FF) ksp = PETSc.KSP() ksp.create(comm=PETSc.COMM_WORLD) pc = ksp.getPC() ksp.setType('fgmres') 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], HiptmairMatrices[4], HiptmairMatrices[2], HiptmairMatrices[0], HiptmairMatrices[1], HiptmairMatrices[6],1e-5,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) del A stime = time.time() ksp.solve(b,u) Soltime = time.time()- stime NSits += ksp.its Mits += ksp.its # Mits +=dodim u = u*scale SolutionTime = SolutionTime +Soltime MO.PrintStr("Number iterations ="+str(ksp.its),60,"+","\n\n","\n\n") MO.PrintStr("Time: "+str(Soltime),60,"+","\n\n","\n\n") else: kspOuter = PETSc.KSP() kspOuter.create(comm=PETSc.COMM_WORLD) FFSS = [Velocity,Magnetic,Pressure,Lagrange] kspOuter.setType('fgmres') kspOuter.setOperators(A,A) pcOuter = kspOuter.getPC() pcOuter.setType(PETSc.PC.Type.KSP) kspInner = pcOuter.getKSP() kspInner.setType('gmres') pcInner = kspInner.getPC() # FSpace = [Velocity,Magnetic,Pressure,Lagrange] reshist = {} def monitor(ksp, its, fgnorm): reshist[its] = fgnorm print its," OUTER:", fgnorm kspOuter.setMonitor(monitor) kspOuter.max_it = 500 kspInner.max_it = 100 kspOuter.setTolerances(OuterTol) kspInner.setTolerances(InnerTol) pcInner.setType('python') pcInner.setPythonContext(MHDpreconditioner.InnerOuter(A,FFSS,kspF, KSPlinearfluids[0], KSPlinearfluids[1],Fp, HiptmairMatrices[3], HiptmairMatrices[4], HiptmairMatrices[2], HiptmairMatrices[0], HiptmairMatrices[1], HiptmairMatrices[6],1e-4,F)) # OptDB = PETSc.Options() PP = PETSc.Mat().create() PP.setSizes([A.size[0], A.size[0]]) #PP = PETSc.Mat().createPython([A.size[0], A.size[0]]) PP.setType('python') pp = MHDmulti.P(FFSS,A,MatrixLinearFluids[1],MatrixLinearFluids[0],kspFp,HiptmairMatrices[6]) PP.setPythonContext(pp) PP.setUp() kspInner.setOperators(PP,PP) kspInner.setFromOptions() scale = b.norm() b = b/scale del A stime = time.time() kspOuter.solve(b,u) Soltime = time.time()- stime NSits += kspOuter.its Mits += kspInner.its u = u*scale SolutionTime = SolutionTime +Soltime MO.PrintStr("Number of outer iterations ="+str(kspOuter.its),60,"+","\n\n","\n\n") MO.PrintStr("Number of inner iterations ="+str(kspInner.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) 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,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(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()
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], HiptmairMatrices[4], HiptmairMatrices[2], HiptmairMatrices[0], HiptmairMatrices[1], HiptmairMatrices[6], 1e-6, 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
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.InnerOuterWITHOUT2inverse( FFSS, kspF, KSPlinearfluids[0], KSPlinearfluids[1], Fp, HiptmairMatrices[3], HiptmairMatrices[4], HiptmairMatrices[2], HiptmairMatrices[0], HiptmairMatrices[1], HiptmairMatrices[6], 1e-6, 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 +=dodm
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 = 1 FFSS = [Velocity,Magnetic,Pressure,Lagrange] pc.setPythonContext(MHDpreconditioner.InnerOuterMAGNETICinverse(FFSS,kspF, KSPlinearfluids[0], KSPlinearfluids[1],Fp, HiptmairMatrices[3], HiptmairMatrices[4], HiptmairMatrices[2], HiptmairMatrices[0], HiptmairMatrices[1], HiptmairMatrices[6],1e-6,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 u = u*scale SolutionTime = SolutionTime +Soltime