def __init__(self, spaces, ess_bdr, block_offsets, rel_tol, abs_tol, iter,
mu):
# Array<Vector *> -> tuple
super(RubberOperator,
self).__init__(spaces[0].GetVSize() + spaces[1].GetVSize())
rhs = (None, None)
self.spaces = spaces
self.mu = mfem.ConstantCoefficient(mu)
self.block_offsets = block_offsets
Hform = mfem.BlockNonlinearForm(spaces)
Hform.AddDomainIntegrator(
mfem.IncompressibleNeoHookeanIntegrator(self.mu))
Hform.SetEssentialBC(ess_bdr, rhs)
self.Hform = Hform
a = mfem.BilinearForm(self.spaces[1])
one = mfem.ConstantCoefficient(1.0)
a.AddDomainIntegrator(mfem.MassIntegrator(one))
a.Assemble()
a.Finalize()
pressure_mass = a.LoseMat()
self.j_prec = JacobianPreconditioner(spaces, pressure_mass,
block_offsets)
j_gmres = mfem.GMRESSolver()
j_gmres.iterative_mode = False
j_gmres.SetRelTol(1e-12)
j_gmres.SetAbsTol(1e-12)
j_gmres.SetMaxIter(300)
j_gmres.SetPrintLevel(0)
j_gmres.SetPreconditioner(self.j_prec)
self.j_solver = j_gmres
newton_solver = mfem.NewtonSolver()
# Set the newton solve parameters
newton_solver.iterative_mode = True
newton_solver.SetSolver(self.j_solver)
newton_solver.SetOperator(self)
newton_solver.SetPrintLevel(1)
newton_solver.SetRelTol(rel_tol)
newton_solver.SetAbsTol(abs_tol)
newton_solver.SetMaxIter(iter)
self.newton_solver = newton_solver
def __init__(self, fespace, alpha, kappa, u):
mfem.PyTimeDependentOperator.__init__(self, fespace.GetTrueVSize(),
0.0)
rel_tol = 1e-8
self.alpha = alpha
self.kappa = kappa
self.T = None
self.K = None
self.M = None
self.fespace = fespace
self.ess_tdof_list = intArray()
self.Mmat = mfem.SparseMatrix()
self.Kmat = mfem.SparseMatrix()
self.M_solver = mfem.CGSolver()
self.M_prec = mfem.DSmoother()
self.T_solver = mfem.CGSolver()
self.T_prec = mfem.DSmoother()
self.z = mfem.Vector(self.Height())
self.M = mfem.BilinearForm(fespace)
self.M.AddDomainIntegrator(mfem.MassIntegrator())
self.M.Assemble()
self.M.FormSystemMatrix(self.ess_tdof_list, self.Mmat)
self.M_solver.iterative_mode = False
self.M_solver.SetRelTol(rel_tol)
self.M_solver.SetAbsTol(0.0)
self.M_solver.SetMaxIter(30)
self.M_solver.SetPrintLevel(0)
self.M_solver.SetPreconditioner(self.M_prec)
self.M_solver.SetOperator(self.Mmat)
self.T_solver.iterative_mode = False
self.T_solver.SetRelTol(rel_tol)
self.T_solver.SetAbsTol(0.0)
self.T_solver.SetMaxIter(100)
self.T_solver.SetPrintLevel(0)
self.T_solver.SetPreconditioner(self.T_prec)
self.SetParameters(u)
def __init__(self, vfes, A, A_flux):
self.dim = vfes.GetFE(0).GetDim()
self.vfes = vfes
self.A = A
self.Aflux = A_flux
self.Me_inv = mfem.DenseTensor(vfes.GetFE(0).GetDof(),
vfes.GetFE(0).GetDof(),
vfes.GetNE())
self.state = mfem.Vector(num_equation)
self.f = mfem.DenseMatrix(num_equation, self.dim)
self.flux = mfem.DenseTensor(vfes.GetNDofs(), self.dim, num_equation)
self.z = mfem.Vector(A.Height())
dof = vfes.GetFE(0).GetDof()
Me = mfem.DenseMatrix(dof)
inv = mfem.DenseMatrixInverse(Me)
mi = mfem.MassIntegrator()
for i in range(vfes.GetNE()):
mi.AssembleElementMatrix(vfes.GetFE(i), vfes.GetElementTransformation(i), Me)
inv.Factor()
inv.GetInverseMatrix(self.Me_inv(i))
super(FE_Evolution, self).__init__(A.Height())
# Inflow boundary condition (zero for the problems considered in this example)
class inflow_coeff(mfem.PyCoefficient):
def EvalValue(self, x):
return 0
# 6. Set up and assemble the bilinear and linear forms corresponding to the
# DG discretization. The DGTraceIntegrator involves integrals over mesh
# interior faces.
velocity = velocity_coeff(dim)
inflow = inflow_coeff()
u0 = u0_coeff()
m = mfem.BilinearForm(fes)
m.AddDomainIntegrator(mfem.MassIntegrator())
k = mfem.BilinearForm(fes)
k.AddDomainIntegrator(mfem.ConvectionIntegrator(velocity, -1.0))
k.AddInteriorFaceIntegrator(
mfem.TransposeIntegrator(mfem.DGTraceIntegrator(velocity, 1.0, -0.5)))
k.AddBdrFaceIntegrator(
mfem.TransposeIntegrator(mfem.DGTraceIntegrator(velocity, 1.0, -0.5)))
b = mfem.LinearForm(fes)
b.AddBdrFaceIntegrator(
mfem.BoundaryFlowIntegrator(inflow, velocity, -1.0, -0.5))
m.Assemble()
m.Finalize()
skip_zeros = 0
k.Assemble(skip_zeros)
B0 = mfem.MixedBilinearForm(x0_space,test_space); B0.AddDomainIntegrator(mfem.DiffusionIntegrator(one)) B0.Assemble() B0.EliminateTrialDofs(ess_bdr, x.GetBlock(x0_var), F) B0.Finalize() Bhat = mfem.MixedBilinearForm(xhat_space,test_space) Bhat.AddTraceFaceIntegrator(mfem.TraceJumpIntegrator()) Bhat.Assemble() Bhat.Finalize() Sinv = mfem.BilinearForm(test_space) Sum = mfem.SumIntegrator() Sum.AddIntegrator(mfem.DiffusionIntegrator(one)) Sum.AddIntegrator(mfem.MassIntegrator(one)) Sinv.AddDomainIntegrator(mfem.InverseIntegrator(Sum)) Sinv.Assemble() Sinv.Finalize() S0 = mfem.BilinearForm(x0_space) S0.AddDomainIntegrator(mfem.DiffusionIntegrator(one)) S0.Assemble() S0.EliminateEssentialBC(ess_bdr) S0.Finalize() matB0 = B0.SpMat() matBhat = Bhat.SpMat() matSinv = Sinv.SpMat() matS0 = S0.SpMat()
rhs_coef = analytic_rhs() sol_coef = analytic_solution() b.AddDomainIntegrator(mfem.DomainLFIntegrator(rhs_coef)) b.Assemble() # 6. Define the solution vector x as a finite element grid function # corresponding to fespace. Initialize x with initial guess of zero. x = mfem.GridFunction(fespace) x.Assign(0.0) # 7. Set up the bilinear form a(.,.) on the finite element space # corresponding to the Laplacian operator -Delta, by adding the Diffusion # and Mass domain integrators. a = mfem.BilinearForm(fespace) a.AddDomainIntegrator(mfem.DiffusionIntegrator(one)) a.AddDomainIntegrator(mfem.MassIntegrator(one)) # 8. Assemble the linear system, apply conforming constraints, etc. a.Assemble() A = mfem.SparseMatrix() B = mfem.Vector() X = mfem.Vector() empty_tdof_list = mfem.intArray() a.FormLinearSystem(empty_tdof_list, x, b, A, X, B) M = mfem.GSSmoother(A) mfem.PCG(A, M, B, X, 1, 200, 1e-12, 0.0) # 10. Recover the solution as a finite element grid function. a.RecoverFEMSolution(X, b, x)