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)
exit
# 5. Refine the mesh to increase the resolution. In this example we do
# 'ref_levels' of uniform refinement, where 'ref_levels' is a
# command-line parameter. If the mesh is of NURBS type, we convert it to
# a (piecewise-polynomial) high-order mesh.
for lev in range(ser_ref_levels):
mesh.UniformRefinement()
if mesh.NURBSext:
mesh.SetCurvature(max(order, 1))
bb_min, bb_max = mesh.GetBoundingBox(max(order, 1))
# 6. Define the parallel mesh by a partitioning of the serial mesh. Refine
# this mesh further in parallel to increase the resolution. Once the
# parallel mesh is defined, the serial mesh can be deleted.
pmesh = mfem.ParMesh(MPI.COMM_WORLD, mesh)
for k in range(par_ref_levels):
pmesh.UniformRefinement()
# 7. Define the discontinuous DG finite element space of the given
# polynomial order on the refined mesh.
fec = mfem.DG_FECollection(order, dim)
fes = mfem.ParFiniteElementSpace(pmesh, fec)
global_vSize = fes.GlobalTrueVSize()
if myid == 0:
print("Number of unknowns: " + str(global_vSize))
#
# Define coefficient using VecotrPyCoefficient and PyCoefficient
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)
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 volume(mesh, in_attr, filename='', precision=8):
'''
make a new mesh which contains only spedified attributes.
note:
1) boundary elements are also copied and bdr_attributes
are maintained
2) in parallel, new mesh must be geometrically continuous.
this routine does not check it
mesh must have sdim == 3:
in_attr : domain attribute
filename : an option to save the file
return new volume mesh
'''
in_attr = np.atleast_1d(in_attr)
sdim = mesh.SpaceDimension()
dim = mesh.Dimension()
Nodal = mesh.GetNodalFESpace()
hasNodal = (Nodal is not None)
if sdim != 3: assert False, "sdim must be three for volume mesh"
if dim != 3: assert False, "sdim must be three for volume mesh"
idx, attrs, ivert, nverts, base = _collect_data(in_attr, mesh, 'dom')
v2s = mesh.extended_connectivity['vol2surf']
in_battr = np.unique(np.hstack([v2s[k]
for k in in_attr])).astype(int, copy=False)
if isParMesh(mesh):
in_battr = np.unique(allgather_vector(in_battr))
bidx, battrs, bivert, nbverts, bbase = _collect_data(in_battr, mesh, 'bdr')
iface = np.array([mesh.GetBdrElementEdgeIndex(i) for i in bidx], dtype=int)
# note u is sorted unique
u, indices = np.unique(np.hstack((ivert, bivert)), return_inverse=True)
kbelem = np.array([True] * len(bidx), dtype=bool)
u_own = u
if isParMesh(mesh):
shared_info = distribute_shared_entity(mesh)
u_own, ivert, bivert = _gather_shared_vertex(mesh, u, shared_info,
ivert, bivert)
if len(u_own) > 0:
vtx = np.vstack([mesh.GetVertexArray(i) for i in u_own])
else:
vtx = np.array([]).reshape((-1, sdim))
if isParMesh(mesh):
#
# distribute vertex/element data
#
base = allgather_vector(base)
nverts = allgather_vector(nverts)
attrs = allgather_vector(attrs)
ivert = allgather_vector(ivert)
bivert = allgather_vector(bivert)
vtx = allgather_vector(vtx.flatten()).reshape(-1, sdim)
u, indices = np.unique(np.hstack([ivert, bivert]), return_inverse=True)
#
# take care of shared boundary (face)
#
# 2018.11.28
# skip_adding is on. This basically skip shared_element
# processing. Check em3d_TEwg7 if you need to remov this.
#
kbelem, battrs, nbverts, bbase, bivert = (_gather_shared_element(
mesh,
'face',
shared_info,
iface,
kbelem,
battrs,
nbverts,
bbase,
bivert,
skip_adding=True))
#indices0 = np.array([np.where(u == biv)[0][0] for biv in ivert])
#bindices0 = np.array([np.where(u == biv)[0][0] for biv in bivert])
iv, ivi = np.unique(ivert, return_inverse=True)
tmp = np.where(np.in1d(u, ivert, assume_unique=True))[0]
indices = tmp[ivi]
iv, ivi = np.unique(bivert, return_inverse=True)
tmp = np.where(np.in1d(u, bivert, assume_unique=True))[0]
bindices = tmp[ivi]
#print('check', np.sum(np.abs(indices - indices0)))
Nvert = len(vtx)
Nelem = len(attrs)
Nbelem = np.sum(kbelem) #len(battrs)
if myid == 0:
print("NV, NBE, NE: " +
",".join([str(x) for x in (Nvert, Nbelem, Nelem)]))
omesh = mfem.Mesh(3, Nvert, Nelem, Nbelem, sdim)
#omesh = mfem.Mesh(3, Nvert, Nelem, 0, sdim)
_fill_mesh_elements(omesh, vtx, indices, nverts, attrs, base)
_fill_mesh_bdr_elements(omesh, vtx, bindices, nbverts, battrs, bbase,
kbelem)
omesh.FinalizeTopology()
omesh.Finalize(refine=True, fix_orientation=True)
if hasNodal:
odim = omesh.Dimension()
fec = Nodal.FEColl()
dNodal = mfem.FiniteElementSpace(omesh, fec, sdim)
omesh.SetNodalFESpace(dNodal)
omesh._nodal = dNodal
GetXDofs = Nodal.GetElementDofs
GetNX = Nodal.GetNE
dGetXDofs = dNodal.GetElementDofs
dGetNX = dNodal.GetNE
DofToVDof = Nodal.DofToVDof
dDofToVDof = dNodal.DofToVDof
#nicePrint(dGetNX(),',', GetNX())
nodes = mesh.GetNodes()
node_ptx1 = nodes.GetDataArray()
onodes = omesh.GetNodes()
node_ptx2 = onodes.GetDataArray()
#nicePrint(len(idx), idx)
if len(idx) > 0:
dof1_idx = np.hstack([[DofToVDof(i, d) for d in range(sdim)]
for j in idx for i in GetXDofs(j)])
data = node_ptx1[dof1_idx]
else:
dof1_idx = np.array([])
data = np.array([])
if isParMesh(mesh): data = allgather_vector(data)
if isParMesh(mesh): idx = allgather_vector(idx)
#nicePrint(len(data), ',', len(idx))
dof2_idx = np.hstack([[dDofToVDof(i, d) for d in range(sdim)]
for j in range(len(idx)) for i in dGetXDofs(j)])
node_ptx2[dof2_idx] = data
#nicePrint(len(dof2_idx))
if isParMesh(mesh):
omesh = mfem.ParMesh(comm, omesh)
if filename != '':
if isParMesh(mesh):
smyid = '{:0>6d}'.format(myid)
filename = filename + '.' + smyid
omesh.PrintToFile(filename, precision)
return omesh
def surface(mesh, in_attr, filename='', precision=8):
'''
mesh must be
if sdim == 3:
a domain of 2D mesh
a boundary of 3D mesh
if sdim == 2:
a domain in 2D mesh
in_attr : eihter
filename : an option to save the file
return new surface mesh
'''
sdim = mesh.SpaceDimension()
dim = mesh.Dimension()
Nodal = mesh.GetNodalFESpace()
hasNodal = (Nodal is not None)
if sdim == 3 and dim == 3:
mode = 'bdr', 'edge'
elif sdim == 3 and dim == 2:
mode = 'dom', 'bdr'
elif sdim == 2 and dim == 2:
mode = 'dom', 'bdr'
else:
assert False, "unsupported mdoe"
idx, attrs, ivert, nverts, base = _collect_data(in_attr, mesh, mode[0])
s2l = mesh.extended_connectivity['surf2line']
in_eattr = np.unique(np.hstack([s2l[k]
for k in in_attr])).astype(int, copy=False)
if isParMesh(mesh):
in_eattr = np.unique(allgather_vector(in_eattr))
eidx, eattrs, eivert, neverts, ebase = _collect_data(
in_eattr, mesh, mode[1])
u, indices = np.unique(np.hstack((ivert, eivert)), return_inverse=True)
keelem = np.array([True] * len(eidx), dtype=bool)
u_own = u
if isParMesh(mesh):
shared_info = distribute_shared_entity(mesh)
u_own, ivert, eivert = _gather_shared_vertex(mesh, u, shared_info,
ivert, eivert)
Nvert = len(u)
if len(u_own) > 0:
vtx = np.vstack([mesh.GetVertexArray(i) for i in u_own])
else:
vtx = np.array([]).reshape((-1, sdim))
if isParMesh(mesh):
#
# distribute vertex/element data
#
base = allgather_vector(base)
nverts = allgather_vector(nverts)
attrs = allgather_vector(attrs)
ivert = allgather_vector(ivert)
eivert = allgather_vector(eivert)
vtx = allgather_vector(vtx.flatten()).reshape(-1, sdim)
u, indices = np.unique(np.hstack([ivert, eivert]), return_inverse=True)
#
# take care of shared boundary (edge)
#
keelem, eattrs, neverts, ebase, eivert = (_gather_shared_element(
mesh,
'edge',
shared_info,
eidx,
keelem,
eattrs,
neverts,
ebase,
eivert,
skip_adding=True))
#indices = np.array([np.where(u == biv)[0][0] for biv in ivert])
#eindices = np.array([np.where(u == biv)[0][0] for biv in eivert])
iv, ivi = np.unique(ivert, return_inverse=True)
tmp = np.where(np.in1d(u, ivert, assume_unique=True))[0]
indices = tmp[ivi]
iv, ivi = np.unique(eivert, return_inverse=True)
tmp = np.where(np.in1d(u, eivert, assume_unique=True))[0]
eindices = tmp[ivi]
Nvert = len(vtx)
Nelem = len(attrs)
Nbelem = len(eattrs)
if myid == 0:
print("NV, NBE, NE: " +
",".join([str(x) for x in (Nvert, Nbelem, Nelem)]))
omesh = mfem.Mesh(2, Nvert, Nelem, Nbelem, sdim)
_fill_mesh_elements(omesh, vtx, indices, nverts, attrs, base)
_fill_mesh_bdr_elements(omesh, vtx, eindices, neverts, eattrs, ebase,
keelem)
omesh.FinalizeTopology()
omesh.Finalize(refine=True, fix_orientation=True)
if hasNodal:
odim = omesh.Dimension()
print("odim, dim, sdim", odim, " ", dim, " ", sdim)
fec = Nodal.FEColl()
dNodal = mfem.FiniteElementSpace(omesh, fec, sdim)
omesh.SetNodalFESpace(dNodal)
omesh._nodal = dNodal
if sdim == 3:
if dim == 3:
GetXDofs = Nodal.GetBdrElementDofs
GetNX = Nodal.GetNBE
elif dim == 2:
GetXDofs = Nodal.GetElementDofs
GetNX = Nodal.GetNE
else:
assert False, "not supported ndim 1"
if odim == 3:
dGetXDofs = dNodal.GetBdrElementDofs
dGetNX = dNodal.GetNBE
elif odim == 2:
dGetXDofs = dNodal.GetElementDofs
dGetNX = dNodal.GetNE
else:
assert False, "not supported ndim (3->1)"
elif sdim == 2:
GetNX = Nodal.GetNE
dGetNX = dNodal.GetNE
GetXDofs = Nodal.GetElementDofs
dGetXDofs = dNodal.GetElementDofs
DofToVDof = Nodal.DofToVDof
dDofToVDof = dNodal.DofToVDof
#nicePrint(dGetNX(),',', GetNX())
nodes = mesh.GetNodes()
node_ptx1 = nodes.GetDataArray()
onodes = omesh.GetNodes()
node_ptx2 = onodes.GetDataArray()
#nicePrint(len(idx), idx)
if len(idx) > 0:
dof1_idx = np.hstack([[DofToVDof(i, d) for d in range(sdim)]
for j in idx for i in GetXDofs(j)])
data = node_ptx1[dof1_idx]
else:
dof1_idx = np.array([])
data = np.array([])
if isParMesh(mesh): data = allgather_vector(data)
if isParMesh(mesh): idx = allgather_vector(idx)
#nicePrint(len(data), ',', len(idx))
dof2_idx = np.hstack([[dDofToVDof(i, d) for d in range(sdim)]
for j in range(len(idx)) for i in dGetXDofs(j)])
node_ptx2[dof2_idx] = data
#nicePrint(len(dof2_idx))
if isParMesh(mesh):
omesh = mfem.ParMesh(comm, omesh)
if filename != '':
if isParMesh(mesh):
smyid = '{:0>6d}'.format(myid)
filename = filename + '.' + smyid
omesh.PrintToFile(filename, precision)
return omesh
def initialize(self, inMeshObj=None, inMeshFile=None):
# 2. Problem initialization
self.parser = ArgParser(description='Based on MFEM Ex16p')
self.parser.add_argument('-m',
'--mesh',
default='beam-tet.mesh',
action='store',
type=str,
help='Mesh file to use.')
self.parser.add_argument('-rs',
'--refine-serial',
action='store',
default=1,
type=int,
help="Number of times to refine the mesh \
uniformly in serial")
self.parser.add_argument('-rp',
'--refine-parallel',
action='store',
default=0,
type=int,
help="Number of times to refine the mesh \
uniformly in parallel")
self.parser.add_argument('-o',
'--order',
action='store',
default=1,
type=int,
help="Finite element order (polynomial \
degree)")
self.parser.add_argument(
'-s',
'--ode-solver',
action='store',
default=3,
type=int,
help='\n'.join([
"ODE solver: 1 - Backward Euler, 2 - SDIRK2, \
3 - SDIRK3", "\t\t 11 - Forward Euler, \
12 - RK2, 13 - RK3 SSP, 14 - RK4."
]))
self.parser.add_argument('-t',
'--t-final',
action='store',
default=20.,
type=float,
help="Final time; start time is 0.")
self.parser.add_argument("-dt",
"--time-step",
action='store',
default=5e-3,
type=float,
help="Time step.")
self.parser.add_argument("-v",
"--viscosity",
action='store',
default=0.00,
type=float,
help="Viscosity coefficient.")
self.parser.add_argument('-L',
'--lmbda',
action='store',
default=1.e0,
type=float,
help='Lambda of Hooks law')
self.parser.add_argument('-mu',
'--shear-modulus',
action='store',
default=1.e0,
type=float,
help='Shear modulus for Hooks law')
self.parser.add_argument('-rho',
'--density',
action='store',
default=1.0,
type=float,
help='mass density')
self.parser.add_argument('-vis',
'--visualization',
action='store_true',
help='Enable GLVis visualization')
self.parser.add_argument('-vs',
'--visualization-steps',
action='store',
default=25,
type=int,
help="Visualize every n-th timestep.")
args = self.parser.parse_args()
self.ser_ref_levels = args.refine_serial
self.par_ref_levels = args.refine_parallel
self.order = args.order
self.dt = args.time_step
self.visc = args.viscosity
self.t_final = args.t_final
self.lmbda = args.lmbda
self.mu = args.shear_modulus
self.rho = args.density
self.visualization = args.visualization
self.ti = 1
self.vis_steps = args.visualization_steps
self.ode_solver_type = args.ode_solver
self.t = 0.0
self.last_step = False
if self.myId == 0: self.parser.print_options(args)
# 3. Reading mesh
if inMeshObj is None:
self.meshFile = inMeshFile
if self.meshFile is None:
self.meshFile = args.mesh
self.mesh = mfem.Mesh(self.meshFile, 1, 1)
else:
self.mesh = inMeshObj
self.dim = self.mesh.Dimension()
print("Mesh dimension: %d" % self.dim)
print("Number of vertices in the mesh: %d " % self.mesh.GetNV())
print("Number of elements in the mesh: %d " % self.mesh.GetNE())
# 4. Define the ODE solver used for time integration.
# Several implicit singly diagonal implicit
# Runge-Kutta (SDIRK) methods, as well as
# explicit Runge-Kutta methods are available.
if self.ode_solver_type == 1:
self.ode_solver = BackwardEulerSolver()
elif self.ode_solver_type == 2:
self.ode_solver = mfem.SDIRK23Solver(2)
elif self.ode_solver_type == 3:
self.ode_solver = mfem.SDIRK33Solver()
elif self.ode_solver_type == 11:
self.ode_solver = ForwardEulerSolver()
elif self.ode_solver_type == 12:
self.ode_solver = mfem.RK2Solver(0.5)
elif self.ode_solver_type == 13:
self.ode_solver = mfem.RK3SSPSolver()
elif self.ode_solver_type == 14:
self.ode_solver = mfem.RK4Solver()
elif self.ode_solver_type == 22:
self.ode_solver = mfem.ImplicitMidpointSolver()
elif self.ode_solver_type == 23:
self.ode_solver = mfem.SDIRK23Solver()
elif self.ode_solver_type == 24:
self.ode_solver = mfem.SDIRK34Solver()
else:
print("Unknown ODE solver type: " + str(self.ode_solver_type))
exit
# 5. Refine the mesh in serial to increase the
# resolution. In this example we do
# 'ser_ref_levels' of uniform refinement, where
# 'ser_ref_levels' is a command-line parameter.
for lev in range(self.ser_ref_levels):
self.mesh.UniformRefinement()
# 6. Define a parallel mesh by a partitioning of
# the serial mesh. Refine this mesh further
# in parallel to increase the resolution. Once the
# parallel mesh is defined, the serial mesh can
# be deleted.
self.pmesh = mfem.ParMesh(MPI.COMM_WORLD, self.mesh)
for lev in range(self.par_ref_levels):
self.pmesh.UniformRefinement()
# 7. Define the vector finite element space
# representing the current and the
# initial temperature, u_ref.
self.fe_coll = mfem.H1_FECollection(self.order, self.dim)
self.fespace = mfem.ParFiniteElementSpace(self.pmesh, self.fe_coll,
self.dim)
self.fe_size = self.fespace.GlobalTrueVSize()
if self.myId == 0:
print("FE Number of unknowns: " + str(self.fe_size))
true_size = self.fespace.TrueVSize()
self.true_offset = mfem.intArray(3)
self.true_offset[0] = 0
self.true_offset[1] = true_size
self.true_offset[2] = 2 * true_size
self.vx = mfem.BlockVector(self.true_offset)
self.v_gf = mfem.ParGridFunction(self.fespace)
self.v_gfbnd = mfem.ParGridFunction(self.fespace)
self.x_gf = mfem.ParGridFunction(self.fespace)
self.x_gfbnd = mfem.ParGridFunction(self.fespace)
self.x_ref = mfem.ParGridFunction(self.fespace)
self.pmesh.GetNodes(self.x_ref)
# 8. Set the initial conditions for u.
#self.velo = InitialVelocity(self.dim)
self.velo = velBCs(self.dim)
#self.deform = InitialDeformation(self.dim)
self.deform = defBCs(self.dim)
self.v_gf.ProjectCoefficient(self.velo)
self.v_gfbnd.ProjectCoefficient(self.velo)
self.x_gf.ProjectCoefficient(self.deform)
self.x_gfbnd.ProjectCoefficient(self.deform)
#self.v_gf.GetTrueDofs(self.vx.GetBlock(0));
#self.x_gf.GetTrueDofs(self.vx.GetBlock(1));
# setup boundary-conditions
self.xess_bdr = mfem.intArray(
self.fespace.GetMesh().bdr_attributes.Max())
self.xess_bdr.Assign(0)
self.xess_bdr[0] = 1
self.xess_bdr[1] = 1
self.xess_tdof_list = intArray()
self.fespace.GetEssentialTrueDofs(self.xess_bdr, self.xess_tdof_list)
#print('True x essential BCs are')
#self.xess_tdof_list.Print()
self.vess_bdr = mfem.intArray(
self.fespace.GetMesh().bdr_attributes.Max())
self.vess_bdr.Assign(0)
self.vess_bdr[0] = 1
self.vess_bdr[1] = 1
self.vess_tdof_list = intArray()
self.fespace.GetEssentialTrueDofs(self.vess_bdr, self.vess_tdof_list)
#print('True v essential BCs are')
#self.vess_tdof_list.Print()
# 9. Initialize the stiffness operator
self.oper = StiffnessOperator(self.fespace, self.lmbda, self.mu,
self.rho, self.visc, self.vess_tdof_list,
self.vess_bdr, self.xess_tdof_list,
self.xess_bdr, self.v_gfbnd,
self.x_gfbnd, self.deform, self.velo,
self.vx)
# 10. Setting up file output
self.smyid = '{:0>2d}'.format(self.myId)
# initializing ode solver
self.ode_solver.Init(self.oper)
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())
def edge(mesh, in_attr, filename='', precision=8):
'''
make a new mesh which contains only spedified edges.
in_attr : eihter
filename : an option to save the file
return new surface mesh
'''
sdim = mesh.SpaceDimension()
dim = mesh.Dimension()
Nodal = mesh.GetNodalFESpace()
hasNodal = (Nodal is not None)
if sdim == 3 and dim == 3:
mode = 'edge', 'vertex'
elif sdim == 3 and dim == 2:
mode = 'bdr', 'vertex'
elif sdim == 2 and dim == 2:
mode = 'bdr', 'vertex'
elif sdim == 2 and dim == 1:
mode = 'dom', 'vertex'
else:
assert False, "unsupported mdoe"
idx, attrs, ivert, nverts, base = _collect_data(in_attr, mesh, mode[0])
l2v = mesh.extended_connectivity['line2vert']
in_eattr = np.unique(np.hstack([l2v[k]
for k in in_attr])).astype(int, copy=False)
if isParMesh(mesh):
in_eattr = np.unique(allgather_vector(in_eattr))
eidx, eattrs, eivert, neverts, ebase = _collect_data(
in_eattr, mesh, mode[1])
u, indices = np.unique(np.hstack((ivert, eivert)), return_inverse=True)
keelem = np.array([True] * len(eidx), dtype=bool)
u_own = u
if isParMesh(mesh):
shared_info = distribute_shared_entity(mesh)
u_own, ivert, eivert = _gather_shared_vertex(mesh, u, shared_info,
ivert, eivert)
Nvert = len(u)
if len(u_own) > 0:
vtx = np.vstack([mesh.GetVertexArray(i) for i in u_own])
else:
vtx = np.array([]).reshape((-1, sdim))
if isParMesh(mesh):
#
# distribute vertex/element data
#
base = allgather_vector(base)
nverts = allgather_vector(nverts)
attrs = allgather_vector(attrs)
ivert = allgather_vector(ivert)
eivert = allgather_vector(eivert)
vtx = allgather_vector(vtx.flatten()).reshape(-1, sdim)
u, indices = np.unique(np.hstack([ivert, eivert]), return_inverse=True)
#
# take care of shared boundary (edge)
#
keelem, eattrs, neverts, ebase, eivert = (_gather_shared_element(
mesh, 'vertex', shared_info, eidx, keelem, eattrs, neverts, ebase,
eivert))
indices = np.array([np.where(u == biv)[0][0] for biv in ivert])
eindices = np.array([np.where(u == biv)[0][0] for biv in eivert])
Nvert = len(vtx)
Nelem = len(attrs)
Nbelem = len(eattrs)
dprint1("NV, NBE, NE: " +
",".join([str(x) for x in (Nvert, Nbelem, Nelem)]))
omesh = mfem.Mesh(1, Nvert, Nelem, Nbelem, sdim)
_fill_mesh_elements(omesh, vtx, indices, nverts, attrs, base)
_fill_mesh_bdr_elements(omesh, vtx, eindices, neverts, eattrs, ebase,
keelem)
omesh.FinalizeTopology()
if hasNodal:
odim = omesh.Dimension()
dprint1("odim, dim, sdim", odim, " ", dim, " ", sdim)
fec = Nodal.FEColl()
dNodal = mfem.FiniteElementSpace(omesh, fec, sdim)
omesh.SetNodalFESpace(dNodal)
omesh._nodal = dNodal
GetXDofs = Nodal.GetElementDofs
if dim == 3:
GetXDofs = Nodal.GetEdgeDofs
elif dim == 2:
GetXDofs = Nodal.GetBdrElementDofs
elif dim == 1:
GetXDofs = Nodal.GetElementDofs
dGetXDofs = dNodal.GetElementDofs
DofToVDof = Nodal.DofToVDof
dDofToVDof = dNodal.DofToVDof
#nicePrint(dGetNX(),',', GetNX())
nodes = mesh.GetNodes()
node_ptx1 = nodes.GetDataArray()
onodes = omesh.GetNodes()
node_ptx2 = onodes.GetDataArray()
#nicePrint(len(idx), idx)
if len(idx) > 0:
dof1_idx = np.hstack([[DofToVDof(i, d) for d in range(sdim)]
for j in idx for i in GetXDofs(j)])
data = node_ptx1[dof1_idx]
else:
dof1_idx = np.array([])
data = np.array([])
if isParMesh(mesh): data = allgather_vector(data)
if isParMesh(mesh): idx = allgather_vector(idx)
#nicePrint(len(data), ',', len(idx))
dof2_idx = np.hstack([[dDofToVDof(i, d) for d in range(sdim)]
for j in range(len(idx)) for i in dGetXDofs(j)])
node_ptx2[dof2_idx] = data
#nicePrint(len(dof2_idx))
# this should be after setting HO nodals...
omesh.Finalize(refine=True, fix_orientation=True)
if isParMesh(mesh):
if omesh.GetNE() < nprc * 3:
parts = omesh.GeneratePartitioning(1, 1)
else:
parts = None
omesh = mfem.ParMesh(comm, omesh, parts)
if filename != '':
if isParMesh(mesh):
smyid = '{:0>6d}'.format(myid)
filename = filename + '.' + smyid
omesh.PrintToFile(filename, precision)
return omesh