def SetParameters(self, u):
u_alpha_gf = mfem.GridFunction(self.fespace)
u_alpha_gf.SetFromTrueDofs(u)
for i in range(u_alpha_gf.Size()):
u_alpha_gf[i] = self.kappa + self.alpha * u_alpha_gf[i]
self.K = mfem.BilinearForm(self.fespace)
u_coeff = mfem.GridFunctionCoefficient(u_alpha_gf)
self.K.AddDomainIntegrator(mfem.DiffusionIntegrator(u_coeff))
self.K.Assemble()
self.K.FormSystemMatrix(self.ess_tdof_list, self.Kmat)
self.T = None
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)
# VectorFunctionCoefficient 'x_init' which in turn is based on the
# function 'InitDisplacement'.
b = mfem.LinearForm(fespace)
print('r.h.s ...')
integrator = mfem.DGElasticityDirichletLFIntegrator(init_x, lambda_c, mu_c, alpha, kappa)
b.AddBdrFaceIntegrator(integrator , dir_bdr)
b.Assemble()
# 9. Set up the bilinear form a(.,.) on the DG finite element space
# corresponding to the linear elasticity integrator with coefficients
# lambda and mu as defined above. The additional interior face integrator
# ensures the weak continuity of the displacement field. The additional
# boundary face integrator works together with the boundary integrator
# added to the linear form b(.) to impose weakly the Dirichlet boundary
# conditions.
a = mfem.BilinearForm(fespace)
a.AddDomainIntegrator(mfem.ElasticityIntegrator(lambda_c, mu_c))
a.AddInteriorFaceIntegrator(mfem.DGElasticityIntegrator(lambda_c, mu_c, alpha, kappa))
a.AddBdrFaceIntegrator(mfem.DGElasticityIntegrator(lambda_c, mu_c, alpha, kappa), dir_bdr)
print('matrix ...')
a.Assemble()
A = mfem.SparseMatrix()
B = mfem.Vector()
X = mfem.Vector()
a.FormLinearSystem(ess_tdof_list, x, b, A, X, B);
print('...done')
A.PrintInfo(sys.stdout)
return 0.0
# 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
x = mfem.BlockVector(block_offsets) rhs = mfem.BlockVector(block_offsets) fform = mfem.LinearForm() fform.Update(R_space, rhs.GetBlock(0), 0) fform.AddDomainIntegrator(mfem.VectorFEDomainLFIntegrator(fcoeff)) fform.AddBoundaryIntegrator(mfem.VectorFEBoundaryFluxLFIntegrator(fnatcoeff)) fform.Assemble() gform = mfem.LinearForm() gform.Update(W_space, rhs.GetBlock(1), 0) gform.AddDomainIntegrator(mfem.DomainLFIntegrator(gcoeff)) gform.Assemble() mVarf = mfem.BilinearForm(R_space) bVarf = mfem.MixedBilinearForm(R_space, W_space) mVarf.AddDomainIntegrator(mfem.VectorFEMassIntegrator(k)) mVarf.Assemble() mVarf.Finalize() M = mVarf.SpMat() bVarf.AddDomainIntegrator(mfem.VectorFEDivergenceIntegrator()) bVarf.Assemble() bVarf.Finalize() B = bVarf.SpMat() B *= -1 BT = mfem.Transpose(B) darcyOp = mfem.BlockOperator(block_offsets)
def run(order=1,
static_cond=False,
meshfile=def_meshfile,
visualization=False):
mesh = mfem.Mesh(meshfile, 1, 1)
dim = mesh.Dimension()
# 3. Refine the mesh to increase the resolution. In this example we do
# 'ref_levels' of uniform refinement. We choose 'ref_levels' to be the
# largest number that gives a final mesh with no more than 50,000
# elements.
ref_levels = int(np.floor(
np.log(50000. / mesh.GetNE()) / np.log(2.) / dim))
for x in range(ref_levels):
mesh.UniformRefinement()
#5. Define a finite element space on the mesh. Here we use vector finite
# elements, i.e. dim copies of a scalar finite element space. The vector
# dimension is specified by the last argument of the FiniteElementSpace
# constructor. For NURBS meshes, we use the (degree elevated) NURBS space
# associated with the mesh nodes.
if order > 0:
fec = mfem.H1_FECollection(order, dim)
elif mesh.GetNodes():
fec = mesh.GetNodes().OwnFEC()
prinr("Using isoparametric FEs: " + str(fec.Name()))
else:
order = 1
fec = mfem.H1_FECollection(order, dim)
fespace = mfem.FiniteElementSpace(mesh, fec)
print('Number of finite element unknowns: ' + str(fespace.GetTrueVSize()))
# 5. Determine the list of true (i.e. conforming) essential boundary dofs.
# In this example, the boundary conditions are defined by marking all
# the boundary attributes from the mesh as essential (Dirichlet) and
# converting them to a list of true dofs.
ess_tdof_list = mfem.intArray()
if mesh.bdr_attributes.Size() > 0:
ess_bdr = mfem.intArray([1] * mesh.bdr_attributes.Max())
ess_bdr = mfem.intArray(mesh.bdr_attributes.Max())
ess_bdr.Assign(1)
fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list)
#6. Set up the linear form b(.) which corresponds to the right-hand side of
# the FEM linear system, which in this case is (1,phi_i) where phi_i are
# the basis functions in the finite element fespace.
b = mfem.LinearForm(fespace)
one = mfem.ConstantCoefficient(1.0)
b.AddDomainIntegrator(mfem.DomainLFIntegrator(one))
b.Assemble()
#7. Define the solution vector x as a finite element grid function
# corresponding to fespace. Initialize x with initial guess of zero,
# which satisfies the boundary conditions.
x = mfem.GridFunction(fespace)
x.Assign(0.0)
#8. Set up the bilinear form a(.,.) on the finite element space
# corresponding to the Laplacian operator -Delta, by adding the Diffusion
# domain integrator.
a = mfem.BilinearForm(fespace)
a.AddDomainIntegrator(mfem.DiffusionIntegrator(one))
#9. Assemble the bilinear form and the corresponding linear system,
# applying any necessary transformations such as: eliminating boundary
# conditions, applying conforming constraints for non-conforming AMR,
# static condensation, etc.
if static_cond: a.EnableStaticCondensation()
a.Assemble()
A = mfem.OperatorPtr()
B = mfem.Vector()
X = mfem.Vector()
a.FormLinearSystem(ess_tdof_list, x, b, A, X, B)
print("Size of linear system: " + str(A.Height()))
# 10. Solve
AA = mfem.OperatorHandle2SparseMatrix(A)
M = mfem.GSSmoother(AA)
mfem.PCG(AA, M, B, X, 1, 200, 1e-12, 0.0)
# 11. Recover the solution as a finite element grid function.
a.RecoverFEMSolution(X, b, x)
# 12. Save the refined mesh and the solution. This output can be viewed later
# using GLVis: "glvis -m refined.mesh -g sol.gf".
mesh.Print('refined.mesh', 8)
x.Save('sol.gf', 8)
#13. Send the solution by socket to a GLVis server.
if (visualization):
sol_sock = mfem.socketstream("localhost", 19916)
sol_sock.precision(8)
sol_sock.send_solution(mesh, x)
def __init__(self, fespace, ess_bdr, visc, mu, K):
mfem.PyTimeDependentOperator.__init__(self, 2 * fespace.GetVSize(),
0.0)
rel_tol = 1e-8
skip_zero_entries = 0
ref_density = 1.0
self.z = mfem.Vector(self.Height() / 2)
self.fespace = fespace
self.viscosity = visc
M = mfem.BilinearForm(fespace)
S = mfem.BilinearForm(fespace)
H = mfem.NonlinearForm(fespace)
self.M = M
self.H = H
self.S = S
rho = mfem.ConstantCoefficient(ref_density)
M.AddDomainIntegrator(mfem.VectorMassIntegrator(rho))
M.Assemble(skip_zero_entries)
M.EliminateEssentialBC(ess_bdr)
M.Finalize(skip_zero_entries)
M_solver = mfem.CGSolver()
M_prec = mfem.DSmoother()
M_solver.iterative_mode = False
M_solver.SetRelTol(rel_tol)
M_solver.SetAbsTol(0.0)
M_solver.SetMaxIter(30)
M_solver.SetPrintLevel(0)
M_solver.SetPreconditioner(M_prec)
M_solver.SetOperator(M.SpMat())
self.M_solver = M_solver
self.M_prec = M_prec
model = mfem.NeoHookeanModel(mu, K)
H.AddDomainIntegrator(mfem.HyperelasticNLFIntegrator(model))
H.SetEssentialBC(ess_bdr)
self.model = model
visc_coeff = mfem.ConstantCoefficient(visc)
S.AddDomainIntegrator(mfem.VectorDiffusionIntegrator(visc_coeff))
S.Assemble(skip_zero_entries)
S.EliminateEssentialBC(ess_bdr)
S.Finalize(skip_zero_entries)
self.backward_euler_oper = BackwardEulerOperator(M, S, H)
J_prec = mfem.DSmoother(1)
J_minres = mfem.MINRESSolver()
J_minres.SetRelTol(rel_tol)
J_minres.SetAbsTol(0.0)
J_minres.SetMaxIter(300)
J_minres.SetPrintLevel(-1)
J_minres.SetPreconditioner(J_prec)
self.J_solver = J_minres
self.J_prec = J_prec
newton_solver = mfem.NewtonSolver()
newton_solver.iterative_mode = False
newton_solver.SetSolver(self.J_solver)
newton_solver.SetOperator(self.backward_euler_oper)
newton_solver.SetPrintLevel(1)
#print Newton iterations
newton_solver.SetRelTol(rel_tol)
newton_solver.SetAbsTol(0.0)
newton_solver.SetMaxIter(10)
self.newton_solver = newton_solver
# and the stiffness matrix on the continuous trial space, S0. ess_bdr = mfem.intArray(mesh.bdr_attributes.Max()) ess_bdr.Assign(1) 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()
