# the basis functions in the finite element fespace.
class analytic_rhs(mfem.PyCoefficient):
def EvalValue(self, x):
l2 = np.sum(x**2)
return 7. * x[0] * x[1] / l2
class analytic_solution(mfem.PyCoefficient):
def EvalValue(self, x):
l2 = np.sum(x**2)
return x[0] * x[1] / l2
b = mfem.ParLinearForm(fespace)
one = mfem.ConstantCoefficient(1.0)
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.ParGridFunction(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.ParBilinearForm(fespace)
k = mfem.ConstantCoefficient(1.0) fcoeff = fFunc(dim) fnatcoeff = f_natural() gcoeff = gFunc() ucoeff = uFunc_ex(dim) pcoeff = pFunc_ex() x = mfem.BlockVector(block_offsets) rhs = mfem.BlockVector(block_offsets) trueX = mfem.BlockVector(block_trueOffsets) trueRhs = mfem.BlockVector(block_trueOffsets) fform = mfem.ParLinearForm() fform.Update(R_space, rhs.GetBlock(0), 0) fform.AddDomainIntegrator(mfem.VectorFEDomainLFIntegrator(fcoeff)) fform.AddBoundaryIntegrator(mfem.VectorFEBoundaryFluxLFIntegrator(fnatcoeff)) fform.Assemble() fform.ParallelAssemble(trueRhs.GetBlock(0)) gform = mfem.ParLinearForm() gform.Update(W_space, rhs.GetBlock(1), 0) gform.AddDomainIntegrator(mfem.DomainLFIntegrator(gcoeff)) gform.Assemble() gform.ParallelAssemble(trueRhs.GetBlock(1)) mVarf = mfem.ParBilinearForm(R_space) bVarf = mfem.ParMixedBilinearForm(R_space, W_space)
def run(order = 1, static_cond = False,
meshfile = def_meshfile, visualization = False,
use_strumpack = False):
mesh = mfem.Mesh(meshfile, 1,1)
dim = mesh.Dimension()
ref_levels = int(np.floor(np.log(10000./mesh.GetNE())/np.log(2.)/dim))
for x in range(ref_levels):
mesh.UniformRefinement();
mesh.ReorientTetMesh();
pmesh = mfem.ParMesh(MPI.COMM_WORLD, mesh)
del mesh
par_ref_levels = 2
for l in range(par_ref_levels):
pmesh.UniformRefinement();
if order > 0:
fec = mfem.H1_FECollection(order, dim)
elif mesh.GetNodes():
fec = mesh.GetNodes().OwnFEC()
print( "Using isoparametric FEs: " + str(fec.Name()));
else:
order = 1
fec = mfem.H1_FECollection(order, dim)
fespace =mfem.ParFiniteElementSpace(pmesh, fec)
fe_size = fespace.GlobalTrueVSize()
if (myid == 0):
print('Number of finite element unknowns: '+ str(fe_size))
ess_tdof_list = mfem.intArray()
if pmesh.bdr_attributes.Size()>0:
ess_bdr = mfem.intArray(pmesh.bdr_attributes.Max())
ess_bdr.Assign(1)
fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list)
# the basis functions in the finite element fespace.
b = mfem.ParLinearForm(fespace)
one = mfem.ConstantCoefficient(1.0)
b.AddDomainIntegrator(mfem.DomainLFIntegrator(one))
b.Assemble();
x = mfem.ParGridFunction(fespace);
x.Assign(0.0)
a = mfem.ParBilinearForm(fespace);
a.AddDomainIntegrator(mfem.DiffusionIntegrator(one))
if static_cond: a.EnableStaticCondensation()
a.Assemble();
A = mfem.HypreParMatrix()
B = mfem.Vector()
X = mfem.Vector()
a.FormLinearSystem(ess_tdof_list, x, b, A, X, B)
if (myid == 0):
print("Size of linear system: " + str(x.Size()))
print("Size of linear system: " + str(A.GetGlobalNumRows()))
if use_strumpack:
import mfem.par.strumpack as strmpk
Arow = strmpk.STRUMPACKRowLocMatrix(A)
args = ["--sp_hss_min_sep_size", "128", "--sp_enable_hss"]
strumpack = strmpk.STRUMPACKSolver(args, MPI.COMM_WORLD)
strumpack.SetPrintFactorStatistics(True)
strumpack.SetPrintSolveStatistics(False)
strumpack.SetKrylovSolver(strmpk.KrylovSolver_DIRECT);
strumpack.SetReorderingStrategy(strmpk.ReorderingStrategy_METIS)
strumpack.SetMC64Job(strmpk.MC64Job_NONE)
# strumpack.SetSymmetricPattern(True)
strumpack.SetOperator(Arow)
strumpack.SetFromCommandLine()
strumpack.Mult(B, X);
else:
amg = mfem.HypreBoomerAMG(A)
cg = mfem.CGSolver(MPI.COMM_WORLD)
cg.SetRelTol(1e-12)
cg.SetMaxIter(200)
cg.SetPrintLevel(1)
cg.SetPreconditioner(amg)
cg.SetOperator(A)
cg.Mult(B, X);
a.RecoverFEMSolution(X, b, x)
smyid = '{:0>6d}'.format(myid)
mesh_name = "mesh."+smyid
sol_name = "sol."+smyid
pmesh.Print(mesh_name, 8)
x.Save(sol_name, 8)
def run(order = 1, static_cond = False,
meshfile = def_meshfile, visualization = False):
mesh = mfem.Mesh(meshfile, 1,1)
dim = mesh.Dimension()
ref_levels = int(np.floor(np.log(10000./mesh.GetNE())/np.log(2.)/dim))
for x in range(ref_levels):
mesh.UniformRefinement();
mesh.ReorientTetMesh();
pmesh = mfem.ParMesh(MPI.COMM_WORLD, mesh)
del mesh
par_ref_levels = 2
for l in range(par_ref_levels):
pmesh.UniformRefinement();
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.ParFiniteElementSpace(pmesh, fec)
fe_size = fespace.GlobalTrueVSize()
if (myid == 0):
print('Number of finite element unknowns: '+ str(fe_size))
ess_tdof_list = mfem.intArray()
if pmesh.bdr_attributes.Size()>0:
ess_bdr = mfem.intArray(pmesh.bdr_attributes.Max())
ess_bdr.Assign(1)
fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list)
# the basis functions in the finite element fespace.
b = mfem.ParLinearForm(fespace)
one = mfem.ConstantCoefficient(1.0)
b.AddDomainIntegrator(mfem.DomainLFIntegrator(one))
b.Assemble();
x = mfem.ParGridFunction(fespace);
x.Assign(0.0)
a = mfem.ParBilinearForm(fespace);
a.AddDomainIntegrator(mfem.DiffusionIntegrator(one))
if static_cond: a.EnableStaticCondensation()
a.Assemble();
A = mfem.HypreParMatrix()
B = mfem.Vector()
X = mfem.Vector()
a.FormLinearSystem(ess_tdof_list, x, b, A, X, B)
if (myid == 0):
print("Size of linear system: " + str(x.Size()))
print("Size of linear system: " + str(A.GetGlobalNumRows()))
amg = mfem.HypreBoomerAMG(A)
pcg = mfem.HyprePCG(A)
pcg.SetTol(1e-12)
pcg.SetMaxIter(200)
pcg.SetPrintLevel(2)
pcg.SetPreconditioner(amg)
pcg.Mult(B, X);
a.RecoverFEMSolution(X, b, x)
smyid = '{:0>6d}'.format(myid)
mesh_name = "mesh."+smyid
sol_name = "sol."+smyid
pmesh.PrintToFile(mesh_name, 8)
x.SaveToFile(sol_name, 8)
# interior faces.
velocity = velocity_coeff(dim)
inflow = inflow_coeff()
u0 = u0_coeff()
m = mfem.ParBilinearForm(fes)
m.AddDomainIntegrator(mfem.MassIntegrator())
k = mfem.ParBilinearForm(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.ParLinearForm(fes)
b.AddBdrFaceIntegrator(
mfem.BoundaryFlowIntegrator(inflow, velocity, -1.0, -0.5))
m.Assemble()
m.Finalize()
skip_zeros = 0
k.Assemble(skip_zeros)
k.Finalize(skip_zeros)
b.Assemble()
M = m.ParallelAssemble()
K = k.ParallelAssemble()
B = b.ParallelAssemble()
# 7. Define the initial conditions, save the corresponding grid function to
glob_true_s_test = test_space.GlobalTrueVSize()
if myid == 0:
print('\n'.join([
"nNumber of Unknowns", " Trial space, X0 : " +
str(glob_true_s0) + " (order " + str(trial_order) + ")",
" Interface space, Xhat : " + str(glob_true_s1) + " (order " +
str(trace_order) + ")", " Test space, Y : " +
str(glob_true_s_test) + " (order " + str(test_order) + ")"
]))
# 7. Set up the linear form F(.) which corresponds to the right-hand side of
# the FEM linear system, which in this case is (f,phi_i) where f=1.0 and
# phi_i are the basis functions in the test finite element fespace.
one = mfem.ConstantCoefficient(1.0)
F = mfem.ParLinearForm(test_space)
F.AddDomainIntegrator(mfem.DomainLFIntegrator(one))
F.Assemble()
x0 = mfem.ParGridFunction(x0_space)
x0.Assign(0.0)
# 8. Set up the mixed bilinear form for the primal trial unknowns, B0,
# the mixed bilinear form for the interfacial unknowns, Bhat,
# the inverse stiffness matrix on the discontinuous test space, Sinv,
# and the stiffness matrix on the continuous trial space, S0.
ess_bdr = mfem.intArray(pmesh.bdr_attributes.Max())
ess_bdr.Assign(1)
ess_dof = mfem.intArray()
x0_space.GetEssentialVDofs(ess_bdr, ess_dof)
