def build_transfer_matrices(self):
V1 = self.V1
V2 = self.V2
VO = self.VO
self.B1 = PETScDMCollection.create_transfer_matrix(V1, VO)
self.B2 = PETScDMCollection.create_transfer_matrix(V2, VO)
self.BO1 = PETScDMCollection.create_transfer_matrix(VO, V1)
self.BO2 = PETScDMCollection.create_transfer_matrix(VO, V2)
coord2[1142] = np.array([0.27136816, 0.27167537, 0.50056124])
coord2[1448] = np.array([0.80807753, 0.90899875, 0.77327936])
coord2[1654] = np.array([0.80824022, 0.90899337, 0.77317984])
# level four
coord3 = mesh3.coordinates()
coord3[235] = np.array([0.73388744, 0.42498976, 0.60173443])
# ==========================================================================
# Find the transfer operators, puse is the prolongation operator list
# note the order is from fine to coarse
puse = []
for il in range(nl-1):
pmat = PETScDMCollection.create_transfer_matrix(Vspace[il+1], Vspace[il])
pmat = pmat.mat()
puse.append(pmat)
# ==========================================================================
# Use FEniCS to formulate the FEM problem. A is the matrix, b is the rhs.
u_D = Constant(0.0)
tol = 1E-14
def boundary_D(x, on_boundary):
return on_boundary and (near(x[0], 0, tol) or near(x[0], 1.0, tol))
def save_files_visualization(visualization_folder, dvp_, t, save_deg, v_deg, p_deg, mesh, domains, **namespace):
# Files for storing results
if not "d_file" in namespace.keys():
d_file = XDMFFile(MPI.comm_world, str(visualization_folder.joinpath("displacement.xdmf")))
v_file = XDMFFile(MPI.comm_world, str(visualization_folder.joinpath("velocity.xdmf")))
p_file = XDMFFile(MPI.comm_world, str(visualization_folder.joinpath("pressure.xdmf")))
for tmp_t in [d_file, v_file, p_file]:
tmp_t.parameters["flush_output"] = True
tmp_t.parameters["rewrite_function_mesh"] = False
if save_deg > 1:
# Create function space for d, v and p
dve = VectorElement('CG', mesh.ufl_cell(), v_deg)
pe = FiniteElement('CG', mesh.ufl_cell(), p_deg)
FSdv = FunctionSpace(mesh, dve) # Higher degree FunctionSpace for d and v
FSp= FunctionSpace(mesh, pe) # Higher degree FunctionSpace for p
# Copy mesh
mesh_viz = Mesh(mesh)
for i in range(save_deg-1):
mesh_viz = refine(mesh_viz) # refine the mesh
domains_viz = adapt(domains,mesh_viz) # refine the domains (so we can output domain IDs of refined mesh)
# Create visualization function space for d, v and p
dve_viz = VectorElement('CG', mesh_viz.ufl_cell(), 1)
pe_viz = FiniteElement('CG', mesh_viz.ufl_cell(), 1)
FSdv_viz = FunctionSpace(mesh_viz, dve_viz) # Visualisation FunctionSpace for d and v
FSp_viz = FunctionSpace(mesh_viz, pe_viz) # Visualisation FunctionSpace for p
# Create lower-order function for visualization on refined mesh
d_viz = Function(FSdv_viz)
v_viz = Function(FSdv_viz)
p_viz = Function(FSp_viz)
# Create a transfer matrix between higher degree and lower degree (visualization) function spaces
dv_trans = PETScDMCollection.create_transfer_matrix(FSdv,FSdv_viz)
p_trans = PETScDMCollection.create_transfer_matrix(FSp,FSp_viz)
return_dict = dict(v_file=v_file, d_file=d_file, p_file=p_file, d_viz=d_viz,v_viz=v_viz, p_viz=p_viz,
dv_trans=dv_trans, p_trans=p_trans, mesh_viz=mesh_viz, domains_viz=domains_viz)
else:
return_dict = dict(v_file=v_file, d_file=d_file, p_file=p_file)
namespace.update(return_dict)
else:
return_dict = {}
# Split function
d = dvp_["n"].sub(0, deepcopy=True)
v = dvp_["n"].sub(1, deepcopy=True)
p = dvp_["n"].sub(2, deepcopy=True)
if save_deg > 1: # To save higher-order nodes
# Interpolate by using the transfer matrix between higher degree and lower degree (visualization) function spaces
namespace["d_viz"].vector()[:] = namespace["dv_trans"]*d.vector()
namespace["v_viz"].vector()[:] = namespace["dv_trans"]*v.vector()
namespace["p_viz"].vector()[:] = namespace["p_trans"]*p.vector()
write_solution(namespace["d_viz"], namespace["v_viz"], namespace["p_viz"],
namespace["d_file"], namespace["v_file"], namespace["p_file"], t) # Write results
else: # To save only the corner nodes
write_solution(d, v, p, namespace["d_file"], namespace["v_file"], namespace["p_file"], t) # Write results
return return_dict