def apply_essential(self, engine, gf, kfes, real=False, **kwargs):
mesh = engine.get_mesh(mm=self)
ibdr = mesh.bdr_attributes.ToList()
bdr_attr = [0] * mesh.bdr_attributes.Max()
for idx in self._sel_index:
bdr_attr[idx - 1] = 1
if kfes == 0:
coeff1 = mfem.VectorArrayCoefficient(3)
coeff1.Set(0, mfem.ConstantCoefficient(0.0))
coeff1.Set(1, mfem.ConstantCoefficient(0.0))
coeff1.Set(2, mfem.ConstantCoefficient(0.0))
gf.ProjectBdrCoefficientTangent(coeff1, mfem.intArray(bdr_attr))
def __init__(self, spaces, ess_bdr, block_offsets, rel_tol, abs_tol, iter,
mu):
# Array<Vector *> -> tuple
super(RubberOperator,
self).__init__(spaces[0].TrueVSize() + spaces[1].TrueVSize())
rhs = (None, None)
self.spaces = spaces
self.mu = mfem.ConstantCoefficient(mu)
self.block_offsets = block_offsets
Hform = mfem.ParBlockNonlinearForm(spaces)
Hform.AddDomainIntegrator(
mfem.IncompressibleNeoHookeanIntegrator(self.mu))
Hform.SetEssentialBC(ess_bdr, rhs)
self.Hform = Hform
a = mfem.ParBilinearForm(self.spaces[1])
one = mfem.ConstantCoefficient(1.0)
mass = mfem.OperatorHandle(mfem.Operator.Hypre_ParCSR)
a.AddDomainIntegrator(mfem.MassIntegrator(one))
a.Assemble()
a.Finalize()
a.ParallelAssemble(mass)
mass.SetOperatorOwner(False)
pressure_mass = mass.Ptr()
self.j_prec = JacobianPreconditioner(spaces, pressure_mass,
block_offsets)
j_gmres = mfem.GMRESSolver(MPI.COMM_WORLD)
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(MPI.COMM_WORLD)
# 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 assemble(self, *args, **kwargs):
'''
integral()
integral('boundary', [1,3]) # selection type and selection
'''
engine = self._engine()
self.process_kwargs(engine, kwargs)
if len(args)>0: self._sel_mode = args[0]
if len(args)>1: self._sel = args[1]
lf1 = engine.new_lf(self._fes1())
one = mfem.ConstantCoefficient(1.0)
coff = self.restrict_coeff(one, self._fes1())
if self._sel_mode == 'domain':
intg = mfem.DomainLFIntegrator(coff)
elif self._sel_mode == 'boundary':
intg = mfem.BoundaryLFIntegrator(coff)
else:
assert False, "Selection Type must be either domain or boundary"
lf1.AddDomainIntegrator(intg)
lf1.Assemble()
from mfem.common.chypre import LF2PyVec, PyVec2PyMat, MfemVec2PyVec
v1 = MfemVec2PyVec(engine.b2B(lf1), None)
v1 = PyVec2PyMat(v1)
if not self._transpose:
v1 = v1.transpose()
return v1
def run_test():
#meshfile = expanduser(join(mfem_path, 'data', 'semi_circle.mesh'))
meshfile = "../data/amr-quad.mesh"
mesh = mfem.Mesh(meshfile, 1, 1)
dim = mesh.Dimension()
sdim = mesh.SpaceDimension()
fec = mfem.H1_FECollection(1, dim)
fespace = mfem.FiniteElementSpace(mesh, fec, 1)
print('Number of finite element unknowns: ' + str(fespace.GetTrueVSize()))
c = mfem.ConstantCoefficient(1.0)
gf = mfem.GridFunction(fespace)
gf.ProjectCoefficient(c)
print("write mesh to STDOUT")
mesh.Print(mfem.STDOUT)
print("creat VTK file to file")
mesh.PrintVTK('mesh.vtk', 1)
print("creat VTK to STDOUT")
mesh.PrintVTK(mfem.STDOUT, 1)
print("save GridFunction to file")
gf.Save('out_test_gridfunc.gf')
gf.SaveVTK(mfem.wFILE('out_test_gridfunc1.vtk'), 'data', 1)
print("save GridFunction to file in VTK format")
gf.SaveVTK('out_test_gridfunc2.vtk', 'data', 1)
print("Gridfunction to STDOUT")
gf.Save(mfem.STDOUT)
o = io.StringIO()
count = gf.Save(o)
count2 = gf.SaveVTK(o, 'data', 1)
print("length of data ", count, count2)
print('result: ', o.getvalue())
def updMassMatMS(self, elmLst, elmCompDiagMassMat, rho=1.0):
self.M = mfem.ParBilinearForm(self.fespace)
self.ro = mfem.ConstantCoefficient(rho)
self.M.AddDomainIntegrator(mfem.VectorMassIntegrator(self.ro))
print("in updateMass")
self.M.Assemble(0, elmLst, elmCompDiagMassMat, True, True)
self.M.EliminateEssentialBC(self.vess_bdr)
self.M.Finalize(0)
self.Mmat = self.M.ParallelAssemble()
self.M_solver.SetOperator(self.Mmat)
def apply_essential(self, engine, gf, real = False, kfes = 0):
if kfes > 1: return
if real:
dprint1("Apply Ess.(real)" + str(self._sel_index))
else:
dprint1("Apply Ess.(imag)" + str(self._sel_index))
Erphiz = self.vt.make_value_or_expression(self)
mesh = engine.get_mesh(mm = self)
ibdr = mesh.bdr_attributes.ToList()
bdr_attr = [0]*mesh.bdr_attributes.Max()
for idx in self._sel_index:
bdr_attr[idx-1] = 1
if kfes == 0:
coeff1 = mfem.VectorArrayCoefficient(2)
coeff1.Set(0, mfem.ConstantCoefficient(0.0))
coeff1.Set(1, mfem.ConstantCoefficient(0.0))
gf.ProjectBdrCoefficientTangent(coeff1,
mfem.intArray(bdr_attr))
elif kfes == 1:
coeff1 = mfem.ConstantCoefficient(0.0)
gf.ProjectBdrCoefficient(coeff1,
mfem.intArray(bdr_attr))
def run_test():
#meshfile =expanduser(join(mfem_path, 'data', 'beam-tri.mesh'))
meshfile = expanduser(join(mfem_path, 'data', 'semi_circle.mesh'))
mesh = mfem.Mesh(meshfile, 1, 1)
dim = mesh.Dimension()
sdim = mesh.SpaceDimension()
fec = mfem.H1_FECollection(1, dim)
fespace = mfem.FiniteElementSpace(mesh, fec, 1)
print('Number of finite element unknowns: ' + str(fespace.GetTrueVSize()))
c = mfem.ConstantCoefficient(1.0)
gf = mfem.GridFunction(fespace)
gf.ProjectCoefficient(c)
gf.Save('out_test_gridfunc.gf')
def apply_essential(self, engine, gf, real=False, kfes=0):
if kfes > 0: return
if real:
dprint1("Apply Ess.(real)" + str(self._sel_index))
else:
dprint1("Apply Ess.(imag)" + str(self._sel_index))
mesh = engine.get_mesh(mm=self)
ibdr = mesh.bdr_attributes.ToList()
bdr_attr = [0] * mesh.bdr_attributes.Max()
for idx in self._sel_index:
bdr_attr[idx - 1] = 1
coeff1 = mfem.ConstantCoefficient(0.0)
gf.ProjectBdrCoefficient(coeff1, mfem.intArray(bdr_attr))
def apply_essential(self, engine, gf, real = False, kfes = 0):
if kfes == 0: return
if real:
dprint1("Apply Ess.(real)" + str(self._sel_index))
coeff = mfem.ConstantCoefficient(float(self.psi0))
else:
return
#dprint1("Apply Ess.(imag)" + str(self._sel_index))
#coeff = mfem.ConstantCoefficient(complex(self.psi0).imag)
coeff = self.restrict_coeff(coeff, engine)
mesh = engine.get_mesh(mm = self)
ibdr = mesh.bdr_attributes.ToList()
bdr_attr = [0]*mesh.bdr_attributes.Max()
ess_bdr = self.get_essential_idx(1)
dprint1("Essential boundaries", ess_bdr)
for idx in ess_bdr:
bdr_attr[idx-1] = 1
gf.ProjectBdrCoefficient(coeff, mfem.intArray(bdr_attr))
def run_test():
#meshfile = expanduser(join(mfem_path, 'data', 'semi_circle.mesh'))
meshfile = "../data/amr-quad.mesh"
mesh = mfem.Mesh(meshfile, 1, 1)
dim = mesh.Dimension()
sdim = mesh.SpaceDimension()
fec = mfem.H1_FECollection(1, dim)
fespace = mfem.FiniteElementSpace(mesh, fec, 1)
print('Number of finite element unknowns: ' + str(fespace.GetTrueVSize()))
c = mfem.ConstantCoefficient(1.0)
gf = mfem.GridFunction(fespace)
gf.ProjectCoefficient(c)
odata = gf.GetDataArray().copy()
gf.Save("out_test_gz.gf")
gf2 = mfem.GridFunction(mesh, "out_test_gz.gf")
odata2 = gf2.GetDataArray().copy()
check(odata, odata2, "text file does not agree with original")
gf.Save("out_test_gz.gz")
gf2.Assign(0.0)
gf2 = mfem.GridFunction(mesh, "out_test_gz.gz")
odata2 = gf2.GetDataArray().copy()
check(odata, odata2, ".gz file does not agree with original")
gf.Print("out_test_gz.dat")
gf2.Assign(0.0)
gf2.Load("out_test_gz.dat", gf.Size())
odata2 = gf2.GetDataArray().copy()
check(odata, odata2, ".dat file does not agree with original")
gf.Print("out_test_gz.dat.gz")
gf2.Assign(0.0)
gf2.Load("out_test_gz.dat.gz", gf.Size())
odata2 = gf2.GetDataArray().copy()
check(odata, odata2, ".dat file does not agree with original (gz)")
import gzip
import io
gf.Print("out_test_gz.dat2.gz")
with gzip.open("out_test_gz.dat2.gz", 'rt') as f:
sio = io.StringIO(f.read())
gf3 = mfem.GridFunction(fespace)
gf3.Load(sio, gf.Size())
odata3 = gf3.GetDataArray().copy()
check(odata, odata3, ".dat file does not agree with original(gz-io)")
c = mfem.ConstantCoefficient(2.0)
gf.ProjectCoefficient(c)
odata = gf.GetDataArray().copy()
o = io.StringIO()
gf.Print(o)
gf2.Load(o, gf.Size())
odata2 = gf2.GetDataArray().copy()
check(odata, odata2, "StringIO does not agree with original")
print("GridFunction .gf, .gz .dat and StringIO agree with original")
mesh2 = mfem.Mesh()
mesh.Print("out_test_gz.mesh")
mesh2.Load("out_test_gz.mesh")
check_mesh(mesh, mesh2, ".mesh does not agree with original")
mesh2 = mfem.Mesh()
mesh.Print("out_test_gz.mesh.gz")
mesh2.Load("out_test_gz.mesh.gz")
check_mesh(mesh, mesh2, ".mesh.gz does not agree with original")
mesh3 = mfem.Mesh()
mesh.PrintGZ("out_test_gz3.mesh")
mesh3.Load("out_test_gz3.mesh")
check_mesh(mesh, mesh3,
".mesh (w/o .gz exntension) does not agree with original")
o = io.StringIO()
mesh2 = mfem.Mesh()
mesh.Print(o)
mesh2.Load(o)
check_mesh(mesh, mesh2, ".mesh.gz does not agree with original")
print("Mesh .mesh, .mesh.gz and StringIO agree with original")
print("PASSED")
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)
ess_tdof_list = mfem.intArray()
ess_bdr.Assign(0)
ess_bdr[0] = 1
fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list)
# 9. Set up the parallel linear form b(.) which corresponds to the
# right-hand side of the FEM linear system. In this case, b_i equals the
# boundary integral of f*phi_i where f represents a "pull down" force on
# the Neumann part of the boundary and phi_i are the basis functions in
# the finite element fespace. The force is defined by the object f, which
# is a vector of Coefficient objects. The fact that f is non-zero on
# boundary attribute 2 is indicated by the use of piece-wise constants
# coefficient for its last component.
f = mfem.VectorArrayCoefficient(dim)
for i in range(dim - 1):
f.Set(i, mfem.ConstantCoefficient(0.0))
pull_force = mfem.Vector([0] * pmesh.bdr_attributes.Max())
pull_force[1] = -1.0e-2
f.Set(dim - 1, mfem.PWConstCoefficient(pull_force))
b = mfem.ParLinearForm(fespace)
b.AddBoundaryIntegrator(mfem.VectorBoundaryLFIntegrator(f))
print('r.h.s. ...')
b.Assemble()
# 10. Define the solution vector x as a parallel 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)
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_test():
print("Test complex_operator module")
Nvert = 6
Nelem = 8
Nbelem = 2
mesh = mfem.Mesh(2, Nvert, Nelem, 2, 3)
tri_v = [[1., 0., 0.], [0., 1., 0.], [-1., 0., 0.], [0., -1., 0.],
[0., 0., 1.], [0., 0., -1.]]
tri_e = [[0, 1, 4], [1, 2, 4], [2, 3, 4], [3, 0, 4], [1, 0, 5], [2, 1, 5],
[3, 2, 5], [0, 3, 5]]
tri_l = [[1, 4], [1, 2]]
for j in range(Nvert):
mesh.AddVertex(tri_v[j])
for j in range(Nelem):
mesh.AddTriangle(tri_e[j], 1)
for j in range(Nbelem):
mesh.AddBdrSegment(tri_l[j], 1)
mesh.FinalizeTriMesh(1, 1, True)
dim = mesh.Dimension()
order = 1
fec = mfem.H1_FECollection(order, dim)
if use_parallel:
mesh = mfem.ParMesh(MPI.COMM_WORLD, mesh)
fes = mfem.ParFiniteElementSpace(mesh, fec)
a1 = mfem.ParBilinearForm(fes)
a2 = mfem.ParBilinearForm(fes)
else:
fes = mfem.FiniteElementSpace(mesh, fec)
a1 = mfem.BilinearForm(fes)
a2 = mfem.BilinearForm(fes)
one = mfem.ConstantCoefficient(1.0)
a1.AddDomainIntegrator(mfem.DiffusionIntegrator(one))
a1.Assemble()
a1.Finalize()
a2.AddDomainIntegrator(mfem.DiffusionIntegrator(one))
a2.Assemble()
a2.Finalize()
if use_parallel:
M1 = a1.ParallelAssemble()
M2 = a2.ParallelAssemble()
M1.Print('M1')
width = fes.GetTrueVSize()
#X = mfem.HypreParVector(fes)
#Y = mfem.HypreParVector(fes)
#X.SetSize(fes.TrueVSize())
#Y.SetSize(fes.TrueVSize())
#from mfem.common.parcsr_extra import ToScipyCoo
#MM1 = ToScipyCoo(M1)
#print(MM1.toarray())
#print(MM1.dot(np.ones(6)))
else:
M1 = a1.SpMat()
M2 = a2.SpMat()
M1.Print('M1')
width = fes.GetVSize()
#X = mfem.Vector()
#Y = mfem.Vector()
#X.SetSize(M1.Width())
#Y.SetSize(M1.Height())
#from mfem.common.sparse_utils import sparsemat_to_scipycsr
#MM1 = sparsemat_to_scipycsr(M1, np.float)
#print(MM1.toarray())
#print(MM1.dot(np.ones(6)))
#X.Assign(0.0)
#X[0] = 1.0
#M1.Mult(X, Y)
#print(Y.GetDataArray())
Mc = mfem.ComplexOperator(M1, M2, hermitan=True)
offsets = mfem.intArray([0, width, width])
offsets.PartialSum()
x = mfem.BlockVector(offsets)
y = mfem.BlockVector(offsets)
x.GetBlock(0).Assign(0)
if myid == 0:
x.GetBlock(0)[0] = 1.0
x.GetBlock(1).Assign(0)
if myid == 0:
x.GetBlock(1)[0] = 1.0
Mc.Mult(x, y)
print("x", x.GetDataArray())
print("y", y.GetDataArray())
if myid == 0:
x.GetBlock(1)[0] = -1.0
x.Print()
Mc.Mult(x, y)
print("x", x.GetDataArray())
print("y", y.GetDataArray())
# 9. Define the solution vector x as a finite element grid function # corresponding to fespace. Initialize x by projecting the exact # solution. Note that only values from the boundary edges will be used # when eliminating the non-homogeneous boundary condition to modify the # r.h.s. vector b. x = mfem.ParGridFunction(fespace) E = E_exact() x.ProjectCoefficient(E) # 10. Set up the bilinear form corresponding to the EM diffusion operator # curl muinv curl + sigma I, by adding the curl-curl and the mass domain # integrators. muinv = mfem.ConstantCoefficient(1.0) sigma = mfem.ConstantCoefficient(1.0) a = mfem.ParBilinearForm(fespace) a.AddDomainIntegrator(mfem.CurlCurlIntegrator(muinv)) a.AddDomainIntegrator(mfem.VectorFEMassIntegrator(sigma)) # 11. 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.HypreParMatrix() B = mfem.Vector() X = mfem.Vector()
def ex19_main(args):
ser_ref_levels = args.refine_serial
par_ref_levels = args.refine_parallel
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
if myid == 0: parser.print_options(args)
meshfile = expanduser(join(path, 'data', args.mesh))
mesh = mfem.Mesh(meshfile, 1, 1)
dim = mesh.Dimension()
for lev in range(ser_ref_levels):
mesh.UniformRefinement()
pmesh = mfem.ParMesh(MPI.COMM_WORLD, mesh)
del mesh
for lev in range(par_ref_levels):
pmesh.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.ParFiniteElementSpace(pmesh, quad_coll, dim,
mfem.Ordering.byVDIM)
W_space = mfem.ParFiniteElementSpace(pmesh, lin_coll)
spaces = [R_space, W_space]
glob_R_size = R_space.GlobalTrueVSize()
glob_W_size = W_space.GlobalTrueVSize()
# 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]
if myid == 0:
print("***********************************************************")
print("dim(u) = " + str(glob_R_size))
print("dim(p) = " + str(glob_W_size))
print("dim(u+p) = " + str(glob_R_size + glob_W_size))
print("***********************************************************")
block_offsets = intArray([0, R_space.TrueVSize(), W_space.TrueVSize()])
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.ParGridFunction(R_space)
x_ref = mfem.ParGridFunction(R_space)
x_def = mfem.ParGridFunction(R_space)
p_gf = mfem.ParGridFunction(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)
# 12. Set up the block solution vectors
x_gf.GetTrueDofs(xp.GetBlock(0))
p_gf.GetTrueDofs(xp.GetBlock(1))
# 13. Initialize the incompressible neo-Hookean operator
oper = RubberOperator(spaces, ess_bdr, block_offsets, newton_rel_tol,
newton_abs_tol, newton_iter, mu)
# 14. Solve the Newton system
oper.Solve(xp)
# 15. Distribute the shared degrees of freedom
x_gf.Distribute(xp.GetBlock(0))
p_gf.Distribute(xp.GetBlock(1))
# 16. Compute the final deformation
mfem.subtract_vector(x_gf, x_ref, x_def)
# 17. Visualize the results if requested
if (visualization):
vis_u = mfem.socketstream("localhost", 19916)
visualize(vis_u, pmesh, x_gf, x_def, "Deformation", True)
MPI.COMM_WORLD.Barrier()
vis_p = mfem.socketstream("localhost", 19916)
visualize(vis_p, pmesh, 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 = pmesh.SwapNodes(nodes, owns_nodes)
smyid = '.' + '{:0>6d}'.format(myid)
pmesh.PrintToFile('deformed.mesh' + smyid, 8)
p_gf.SaveToFile('pressure.sol' + smyid, 8)
x_def.SaveToFile("deformation.sol" + smyid, 8)
def __init__(self,
fespace,
lmbda=1.,
mu=1.,
rho=1.,
visc=0.0,
vess_tdof_list=None,
vess_bdr=None,
xess_tdof_list=None,
xess_bdr=None,
v_gfBdr=None,
x_gfBdr=None,
deform=None,
velo=None,
vx=None):
mfem.PyTimeDependentOperator.__init__(self, 2 * fespace.GetTrueVSize(),
0.0)
self.lmbda = lmbda
self.mu = mu
self.viscosity = visc
self.deform = deform
self.velo = velo
self.x_gfBdr = x_gfBdr
self.v_gfBdr = v_gfBdr
self.vx = vx
self.z = mfem.Vector(self.Height() / 2)
self.z.Assign(0.0)
self.w = mfem.Vector(self.Height() / 2)
self.w.Assign(0.0)
self.tmpVec = mfem.Vector(self.Height() / 2)
self.tmpVec.Assign(0.0)
self.fespace = fespace
self.xess_bdr = xess_bdr
self.vess_bdr = vess_bdr
self.xess_tdof_list = xess_tdof_list
self.vess_tdof_list = vess_tdof_list
# setting up linear form
cv = mfem.Vector(3)
cv.Assign(0.0)
#self.zero_coef = mfem.ConstantCoefficient(0.0)
self.zero_coef = mfem.VectorConstantCoefficient(cv)
self.bx = mfem.LinearForm(self.fespace)
self.bx.AddDomainIntegrator(
mfem.VectorBoundaryLFIntegrator(self.zero_coef))
self.bx.Assemble()
self.bv = mfem.LinearForm(self.fespace)
self.bv.AddDomainIntegrator(
mfem.VectorBoundaryLFIntegrator(self.zero_coef))
self.bv.Assemble()
self.Bx = mfem.Vector()
self.Bv = mfem.Vector()
# setting up bilinear forms
self.M = mfem.ParBilinearForm(self.fespace)
self.K = mfem.ParBilinearForm(self.fespace)
self.S = mfem.ParBilinearForm(self.fespace)
self.ro = mfem.ConstantCoefficient(rho)
self.M.AddDomainIntegrator(mfem.VectorMassIntegrator(self.ro))
self.M.Assemble(0)
self.M.EliminateEssentialBC(self.vess_bdr)
self.M.Finalize(0)
self.Mmat = self.M.ParallelAssemble()
self.M_solver = mfem.CGSolver(self.fespace.GetComm())
self.M_solver.iterative_mode = False
self.M_solver.SetRelTol(1e-8)
self.M_solver.SetAbsTol(0.0)
self.M_solver.SetMaxIter(30)
self.M_solver.SetPrintLevel(0)
self.M_prec = mfem.HypreSmoother()
self.M_prec.SetType(mfem.HypreSmoother.Jacobi)
self.M_solver.SetPreconditioner(self.M_prec)
self.M_solver.SetOperator(self.Mmat)
lambVec = mfem.Vector(self.fespace.GetMesh().attributes.Max())
print('Number of volume attributes : ' +
str(self.fespace.GetMesh().attributes.Max()))
lambVec.Assign(lmbda)
lambVec[0] = lambVec[1] * 1.0
lambda_func = mfem.PWConstCoefficient(lambVec)
muVec = mfem.Vector(self.fespace.GetMesh().attributes.Max())
muVec.Assign(mu)
muVec[0] = muVec[1] * 1.0
mu_func = mfem.PWConstCoefficient(muVec)
self.K.AddDomainIntegrator(
mfem.ElasticityIntegrator(lambda_func, mu_func))
self.K.Assemble(0)
# to set essential BC to zero value uncomment
#self.K.EliminateEssentialBC(self.xess_bdr)
#self.K.Finalize(0)
#self.Kmat = self.K.ParallelAssemble()
# to set essential BC to non-zero uncomment
self.Kmat = mfem.HypreParMatrix()
visc_coeff = mfem.ConstantCoefficient(visc)
self.S.AddDomainIntegrator(mfem.VectorDiffusionIntegrator(visc_coeff))
self.S.Assemble(0)
#self.S.EliminateEssentialBC(self.vess_bdr)
#self.S.Finalize(0)
#self.Smat = self.S.ParallelAssemble()
self.Smat = mfem.HypreParMatrix()
# VX solver for implicit time-stepping
self.VX_solver = mfem.CGSolver(self.fespace.GetComm())
self.VX_solver.iterative_mode = False
self.VX_solver.SetRelTol(1e-8)
self.VX_solver.SetAbsTol(0.0)
self.VX_solver.SetMaxIter(30)
self.VX_solver.SetPrintLevel(0)
self.VX_prec = mfem.HypreSmoother()
self.VX_prec.SetType(mfem.HypreSmoother.Jacobi)
self.VX_solver.SetPreconditioner(self.VX_prec)
# setting up operators
empty_tdof_list = intArray()
self.S.FormLinearSystem(empty_tdof_list, self.v_gfBdr, self.bv,
self.Smat, self.vx.GetBlock(0), self.Bv, 1)
self.K.FormLinearSystem(empty_tdof_list, self.x_gfBdr, self.bx,
self.Kmat, self.vx.GetBlock(1), self.Bx, 1)
def __init__(self, fespace, ess_bdr, visc, mu, K):
mfem.PyTimeDependentOperator.__init__(self, 2 * fespace.TrueVSize(),
0.0)
rel_tol = 1e-8
skip_zero_entries = 0
ref_density = 1.0
self.ess_tdof_list = intArray()
self.z = mfem.Vector(self.Height() // 2)
self.fespace = fespace
self.viscosity = visc
self.newton_solver = mfem.NewtonSolver(fespace.GetComm())
M = mfem.ParBilinearForm(fespace)
S = mfem.ParBilinearForm(fespace)
H = mfem.ParNonlinearForm(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)
self.Mmat = M.ParallelAssemble()
fespace.GetEssentialTrueDofs(ess_bdr, self.ess_tdof_list)
self.Mmat.EliminateRowsCols(self.ess_tdof_list)
M_solver = mfem.CGSolver(fespace.GetComm())
M_prec = mfem.HypreSmoother()
M_solver.iterative_mode = False
M_solver.SetRelTol(rel_tol)
M_solver.SetAbsTol(0.0)
M_solver.SetMaxIter(30)
M_solver.SetPrintLevel(0)
M_prec.SetType(mfem.HypreSmoother.Jacobi)
M_solver.SetPreconditioner(M_prec)
M_solver.SetOperator(self.Mmat)
self.M_solver = M_solver
self.M_prec = M_prec
model = mfem.NeoHookeanModel(mu, K)
H.AddDomainIntegrator(mfem.HyperelasticNLFIntegrator(model))
H.SetEssentialTrueDofs(self.ess_tdof_list)
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.reduced_oper = ReducedSystemOperator(M, S, H, self.ess_tdof_list)
J_hypreSmoother = mfem.HypreSmoother()
J_hypreSmoother.SetType(mfem.HypreSmoother.l1Jacobi)
J_hypreSmoother.SetPositiveDiagonal(True)
J_prec = J_hypreSmoother
J_minres = mfem.MINRESSolver(fespace.GetComm())
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(fespace.GetComm())
newton_solver.iterative_mode = False
newton_solver.SetSolver(self.J_solver)
newton_solver.SetOperator(self.reduced_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
b.Assemble()
# 9. Define the solution vector x as a parallel finite element grid function
# corresponding to fespace. Initialize x by projecting the exact
# solution. Note that only values from the boundary faces will be used
# when eliminating the non-homogeneous boundary condition to modify the
# r.h.s. vector b.
x = mfem.ParGridFunction(fespace)
F = E_exact(sdim)
x.ProjectCoefficient(F)
# 10. Set up the parallel bilinear form corresponding to the H(div)
# diffusion operator grad alpha div + beta I, by adding the div-div and
# the mass domain integrators.
alpha = mfem.ConstantCoefficient(1.0)
beta = mfem.ConstantCoefficient(1.0)
a = mfem.ParBilinearForm(fespace)
a.AddDomainIntegrator(mfem.DivDivIntegrator(alpha))
a.AddDomainIntegrator(mfem.VectorFEMassIntegrator(beta))
# 11. Assemble the parallel bilinear form and the corresponding linear
# system, applying any necessary transformations such as: parallel
# assembly, eliminating boundary conditions, applying conforming
# constraints for non-conforming AMR, static condensation,
# hybridization, etc.
if (static_cond): a.EnableStaticCondensation()
elif (hybridization):
hfec = mfem.DG_Interface_FECollection(order - 1, dim)
hfes = mfem.ParFiniteElementSpace(mesh, hfec)
a.EnableHybridization(hfes, mfem.NormalTraceJumpIntegrator(),
del mesh
for x in range(par_ref_levels):
pmesh.UniformRefinement()
# 6. Define a parallel finite element space on the parallel mesh. Here we
# use discontinuous finite elements of the specified order >= 0.
fec = mfem.DG_FECollection(order, dim)
fespace = mfem.ParFiniteElementSpace(pmesh, fec)
glob_size = fespace.GlobalTrueVSize()
if (myid == 0):
print('Number of unknowns: ' + str(glob_size))
# 7. Set up the parallel linear form b(.) which corresponds to the
# right-hand side of the FEM linear system.
b = mfem.ParLinearForm(fespace)
one = mfem.ConstantCoefficient(1.0)
zero = mfem.ConstantCoefficient(0.0)
b.AddDomainIntegrator(mfem.DomainLFIntegrator(one))
b.AddBdrFaceIntegrator(mfem.DGDirichletLFIntegrator(zero, one, sigma, kappa))
b.Assemble()
# 8. Define the solution vector x as a parallel finite element grid function
# corresponding to fespace. Initialize x with initial guess of zero.
x = mfem.ParGridFunction(fespace)
x.Assign(0.0)
# 9. Set up the bilinear form a(.,.) on the finite element space
# corresponding to the Laplacian operator -Delta, by adding the Diffusion
# domain integrator and the interior and boundary DG face integrators.
# Note that boundary conditions are imposed weakly in the form, so there
# is no need for dof elimination. After serial and parallel assembly we
ess_bdr.Assign(0); ess_bdr[0] = 1
fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list)
print("here")
# 9. Set up the parallel linear form b(.) which corresponds to the
# right-hand side of the FEM linear system. In this case, b_i equals the
# boundary integral of f*phi_i where f represents a "pull down" force on
# the Neumann part of the boundary and phi_i are the basis functions in
# the finite element fespace. The force is defined by the object f, which
# is a vector of Coefficient objects. The fact that f is non-zero on
# boundary attribute 2 is indicated by the use of piece-wise constants
# coefficient for its last component.
print dim
f = mfem.VectorArrayCoefficient(dim)
c1 = mfem.ConstantCoefficient(0.0);
c2 = mfem.ConstantCoefficient(0.0);
c3 = mfem.ConstantCoefficient(0.0);
#for i in range(dim-1):
f.Set(0, c1)
f.Set(1, c2)
print [0]*pmesh.bdr_attributes.Max()
pull_force = mfem.Vector([0]*pmesh.bdr_attributes.Max())
pull_force[1] = -1.0e-2;
pull_force.Print()
c3 = mfem.PWConstCoefficient(pull_force)
f.Set(dim-1, c3)
b = mfem.ParLinearForm(fespace)
'''
del mesh
ess_bdr = mfem.intArray(pmesh.bdr_attributes.Max())
ess_bdr.Assign(1)
# 6. Define a finite element space on the mesh. The polynomial order is one
# (linear) by default, but this can be changed on the command line.
fec = mfem.H1_FECollection(order, dim)
fespace = mfem.ParFiniteElementSpace(pmesh, fec)
# 7. As in Example 1p, we set up bilinear and linear forms corresponding to
# the Laplace problem -\Delta u = 1. We don't assemble the discrete
# problem yet, this will be done in the inner loop.
a = mfem.ParBilinearForm(fespace)
b = mfem.ParLinearForm(fespace)
one = mfem.ConstantCoefficient(1.0)
bdr = BdrCoefficient()
rhs = RhsCoefficient()
integ = mfem.DiffusionIntegrator(one)
a.AddDomainIntegrator(integ)
b.AddDomainIntegrator(mfem.DomainLFIntegrator(rhs))
# 8. The solution vector x and the associated finite element grid function
# will be maintained over the AMR iterations.
x = mfem.ParGridFunction(fespace)
# 9. Connect to GLVis.
if visualization:
sout = mfem.socketstream("localhost", 19916)
sout.precision(8)
def do_integration(expr, solvars, phys, mesh, kind, attrs,
order, num):
from petram.helper.variables import (Variable,
var_g,
NativeCoefficientGenBase,
CoefficientVariable)
from petram.phys.coefficient import SCoeff
st = parser.expr(expr)
code= st.compile('<string>')
names = code.co_names
g = {}
#print solvars.keys()
for key in phys._global_ns.keys():
g[key] = phys._global_ns[key]
for key in solvars.keys():
g[key] = solvars[key]
l = var_g.copy()
ind_vars = ','.join(phys.get_independent_variables())
if kind == 'Domain':
size = max(max(mesh.attributes.ToList()), max(attrs))
else:
size = max(max(mesh.bdr_attributes.ToList()), max(attrs))
arr = [0]*(size)
for k in attrs:
arr[k-1] = 1
flag = mfem.intArray(arr)
s = SCoeff(expr, ind_vars, l, g, return_complex=False)
## note L2 does not work for boundary....:D
if kind == 'Domain':
fec = mfem.L2_FECollection(order, mesh.Dimension())
else:
fec = mfem.H1_FECollection(order, mesh.Dimension())
fes = mfem.FiniteElementSpace(mesh, fec)
one = mfem.ConstantCoefficient(1)
gf = mfem.GridFunction(fes)
gf.Assign(0.0)
if kind == 'Domain':
gf.ProjectCoefficient(mfem.RestrictedCoefficient(s, flag))
else:
gf.ProjectBdrCoefficient(mfem.RestrictedCoefficient(s, flag), flag)
b = mfem.LinearForm(fes)
one = mfem.ConstantCoefficient(1)
if kind == 'Domain':
itg = mfem.DomainLFIntegrator(one)
b.AddDomainIntegrator(itg)
else:
itg = mfem.BoundaryLFIntegrator(one)
b.AddBoundaryIntegrator(itg)
b.Assemble()
from petram.engine import SerialEngine
en = SerialEngine()
ans = mfem.InnerProduct(en.x2X(gf), en.b2B(b))
if not np.isfinite(ans):
print("not finite", ans, arr)
print(size, mesh.bdr_attributes.ToList())
from mfem.common.chypre import LF2PyVec, PyVec2PyMat, Array2PyVec, IdentityPyMat
#print(list(gf.GetDataArray()))
print(len(gf.GetDataArray()), np.sum(gf.GetDataArray()))
print(np.sum(list(b.GetDataArray())))
return ans