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)
# 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)
# 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:
import numpy as np
from scipy.sparse import csr_matrix
import mfem.ser as mfem
smat = csr_matrix([[
1,
2,
3,
], [0, 0, 1], [2, 0, 0]])
print mfem.SparseMatrix(smat)
print smat
mmat = mfem.SparseMatrix(smat)
mmat.Print()
import sys
import numpy as np
from scipy.sparse import csr_matrix
if len(sys.argv) < 2:
import mfem.ser as mfem
elif sys.argv[1] == 'par':
import mfem.par as mfem
smat = csr_matrix([[
1,
2,
3,
], [0, 0, 1], [2, 0, 0]])
mmat = mfem.SparseMatrix(smat)
offset1 = mfem.intArray([0, 3, 6])
offset2 = mfem.intArray([0, 3, 6])
m = mfem.BlockMatrix(offset1, offset2)
m.SetBlock(0, 0, mmat)
print m._offsets
print m._linked_mat
m = mfem.BlockMatrix(offset1)
m.SetBlock(0, 1, mmat)
m.SetBlock(1, 0, mmat)
print m._offsets
print m._linked_mat
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.SparseMatrix()
B = mfem.Vector()
X = mfem.Vector()
a.FormLinearSystem(ess_tdof_list, x, b, A, X, B)
print("Size of linear system: " + str(A.Size()))
# 10. Solve
M = mfem.GSSmoother(A)
mfem.PCG(A, 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.PrintToFile('refined.mesh', 8)
x.SaveToFile('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)
import numpy as np
from scipy.sparse import csr_matrix
import mfem.ser as mfem
smat = csr_matrix([[
1,
2,
3,
], [0, 0, 1], [2, 0, 0]])
print(mfem.SparseMatrix(smat))
print(smat)
mmat = mfem.SparseMatrix(smat)
mmat.Print()