def __init__(self, spaces, mass, offsets):
self.pressure_mass = mass
self.block_offsets = offsets
super(JacobianPreconditioner, self).__init__(offsets[2])
self.gamma = 0.00001
# The mass matrix and preconditioner do not change every Newton cycle, so we
# only need to define them once
self.mass_prec = mfem.GSSmoother(mass)
mass_pcg = mfem.CGSolver()
mass_pcg.SetRelTol(1e-12)
mass_pcg.SetAbsTol(1e-12)
mass_pcg.SetMaxIter(200)
mass_pcg.SetPrintLevel(0)
mass_pcg.SetPreconditioner(self.mass_prec)
mass_pcg.SetOperator(self.pressure_mass)
mass_pcg.iterative_mode = False
self.mass_pcg = mass_pcg
# The stiffness matrix does change every Newton cycle, so we will define it
# during SetOperator
self.stiff_pcg = None
self.stiff_prec = None
def SetOperator(self, op):
self.jacobian = mfem.Opr2BlockOpr(op)
if (self.stiff_prec == None):
# Initialize the stiffness preconditioner and solver
stiff_prec_gs = mfem.GSSmoother()
self.stiff_prec = stiff_prec_gs
stiff_pcg_iter = mfem.GMRESSolver()
stiff_pcg_iter.SetRelTol(1e-8)
stiff_pcg_iter.SetAbsTol(1e-8)
stiff_pcg_iter.SetMaxIter(200)
stiff_pcg_iter.SetPrintLevel(0)
stiff_pcg_iter.SetPreconditioner(self.stiff_prec)
stiff_pcg_iter.iterative_mode = False
self.stiff_pcg = stiff_pcg_iter
# At each Newton cycle, compute the new stiffness preconditioner by updating
# the iterative solver which, in turn, updates its preconditioner
self.stiff_pcg.SetOperator(self.jacobian.GetBlock(0, 0))
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)
# 11. Define a simple symmetric Gauss-Seidel preconditioner and use it to
# solve the system Ax=b with PCG for the symmetric formulation, or GMRES
# for the non-symmetric.
M = mfem.GSSmoother(A)
rtol = 1e-6
if (alpha == -1.0):
mfem.PCG(A, M, B, X, 3, 5000, rtol*rtol, 0.0)
else:
mfem.GMRES(A, M, B, X, 3, 5000, 50, rtol*rtol, 0.0)
# 12. Recover the solution as a finite element grid function 'x'.
a.RecoverFEMSolution(X, b, x)
# 13. Use the DG solution space as the mesh nodal space. This allows us to
# save the displaced mesh as a curved DG mesh.
mesh.SetNodalFESpace(fespace)
reference_nodes = mfem.Vector()
if (visualization):
reference_nodes.Assign(mesh.GetNodes())
BT = mfem.Transpose(B)
darcyOp = mfem.BlockOperator(block_offsets)
darcyOp.SetBlock(0, 0, M)
darcyOp.SetBlock(0, 1, BT)
darcyOp.SetBlock(1, 0, B)
MinvBt = mfem.Transpose(B)
Md = mfem.Vector(M.Height())
M.GetDiag(Md)
for i in range(Md.Size()):
MinvBt.ScaleRow(i, 1 / Md[i])
S = mfem.Mult(B, MinvBt)
invM = mfem.DSmoother(M)
invS = mfem.GSSmoother(S)
invM.iterative_mode = False
invS.iterative_mode = False
darcyPrec = mfem.BlockDiagonalPreconditioner(block_offsets)
darcyPrec.SetDiagonalBlock(0, invM)
darcyPrec.SetDiagonalBlock(1, invS)
maxIter = 500
rtol = 1e-6
atol = 1e-10
stime = clock()
solver = mfem.MINRESSolver()
solver.SetAbsTol(atol)
solver.SetRelTol(rtol)
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)
