def NewWindow(self):
self.socks.append(mfem.socketstream(self.host, self.port))
self.output = self.socks[-1]
self.output.precision(8)
self.socks
self.sid = self.sid + 1
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)
one = mfem.ConstantCoefficient(1.0)
bdr = BdrCoefficient()
rhs = RhsCoefficient()
integ = mfem.DiffusionIntegrator(one)
a.AddDomainIntegrator(integ)
b.AddDomainIntegrator(mfem.DomainLFIntegrator(rhs))
# 7. The solution vector x and the associated finite element grid function
# will be maintained over the AMR iterations.
x = mfem.GridFunction(fespace)
# 8. Connect to GLVis.
if visualization:
sout = mfem.socketstream("localhost", 19916)
sout.precision(8)
# 9. As in Example 6, we set up a Zienkiewicz-Zhu estimator that will be
# used to obtain element error indicators. The integrator needs to
# provide the method ComputeElementFlux. The smoothed flux space is a
# vector valued H1 space here.
flux_fespace = mfem.FiniteElementSpace(mesh, fec, sdim)
# own_flux_fes = False indicate flux_fespace is passed by reference
# this is actually default action, but for the sake of explanaiton
# it is explicitly set. If you want to pass pointer use own_flux_fes = True
estimator = mfem.ZienkiewiczZhuEstimator(integ,
x,
flux_fespace,
own_flux_fes=False)
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 ex19_main(args):
ref_levels = args.refine
order = args.order
visualization = args.visualization
mu = args.shear_modulus
newton_rel_tol = args.relative_tolerance
newton_abs_tol = args.absolute_tolerance
newton_iter = args.newton_iterations
parser.print_options(args)
meshfile = expanduser(join(path, 'data', args.mesh))
mesh = mfem.Mesh(meshfile, 1, 1)
dim = mesh.Dimension()
for lev in range(ref_levels):
mesh.UniformRefinement()
# 4. Define the shear modulus for the incompressible Neo-Hookean material
c_mu = mfem.ConstantCoefficient(mu)
# 5. Define the finite element spaces for displacement and pressure
# (Taylor-Hood elements). By default, the displacement (u/x) is a second
# order vector field, while the pressure (p) is a linear scalar function.
quad_coll = mfem.H1_FECollection(order, dim)
lin_coll = mfem.H1_FECollection(order - 1, dim)
R_space = mfem.FiniteElementSpace(mesh, quad_coll, dim,
mfem.Ordering.byVDIM)
W_space = mfem.FiniteElementSpace(mesh, lin_coll)
spaces = [R_space, W_space]
R_size = R_space.GetVSize()
W_size = W_space.GetVSize()
# 6. Define the Dirichlet conditions (set to boundary attribute 1 and 2)
ess_bdr_u = mfem.intArray(R_space.GetMesh().bdr_attributes.Max())
ess_bdr_p = mfem.intArray(W_space.GetMesh().bdr_attributes.Max())
ess_bdr_u.Assign(0)
ess_bdr_u[0] = 1
ess_bdr_u[1] = 1
ess_bdr_p.Assign(0)
ess_bdr = [ess_bdr_u, ess_bdr_p]
print("***********************************************************")
print("dim(u) = " + str(R_size))
print("dim(p) = " + str(W_size))
print("dim(u+p) = " + str(R_size + W_size))
print("***********************************************************")
block_offsets = intArray([0, R_size, W_size])
block_offsets.PartialSum()
xp = mfem.BlockVector(block_offsets)
# 9. Define grid functions for the current configuration, reference
# configuration, final deformation, and pressure
x_gf = mfem.GridFunction(R_space)
x_ref = mfem.GridFunction(R_space)
x_def = mfem.GridFunction(R_space)
p_gf = mfem.GridFunction(W_space)
x_gf.MakeRef(R_space, xp.GetBlock(0), 0)
p_gf.MakeRef(W_space, xp.GetBlock(1), 0)
deform = InitialDeformation(dim)
refconfig = ReferenceConfiguration(dim)
x_gf.ProjectCoefficient(deform)
x_ref.ProjectCoefficient(refconfig)
p_gf.Assign(0.0)
# 10. Initialize the incompressible neo-Hookean operator
oper = RubberOperator(spaces, ess_bdr, block_offsets, newton_rel_tol,
newton_abs_tol, newton_iter, mu)
# 11. Solve the Newton system
oper.Solve(xp)
# 12. Compute the final deformation
mfem.subtract_vector(x_gf, x_ref, x_def)
# 13. Visualize the results if requested
if (visualization):
vis_u = mfem.socketstream("localhost", 19916)
visualize(vis_u, mesh, x_gf, x_def, "Deformation", True)
vis_p = mfem.socketstream("localhost", 19916)
visualize(vis_p, mesh, x_gf, p_gf, "Deformation", True)
# 14. Save the displaced mesh, the final deformation, and the pressure
nodes = x_gf
owns_nodes = 0
nodes, owns_nodes = mesh.SwapNodes(nodes, owns_nodes)
mesh.Print('deformed.mesh', 8)
p_gf.Save('pressure.sol', 8)
x_def.Save("deformation.sol", 8)
