def boundary_grid_from_fenics_mesh(fenics_mesh):
"""
Return a boundary grid from a FEniCS Mesh.
"""
from bempp import grid_from_element_data
bm = _dolfin.BoundaryMesh(fenics_mesh, "exterior", False)
bm_coords = bm.coordinates()
bm_cells = bm.cells()
bempp_boundary_grid = grid_from_element_data(bm_coords.transpose(),bm_cells.transpose())
return bempp_boundary_grid
def p1_trace(fenics_space):
import dolfin
from .coupling import fenics_space_info
from bempp import function_space, grid_from_element_data
import numpy as np
family, degree = fenics_space_info(fenics_space)
if not (family == 'Lagrange' and degree == 1):
raise ValueError("fenics_space must be a p1 Lagrange space")
mesh = fenics_space.mesh()
bm = dolfin.BoundaryMesh(mesh, "exterior", False)
bm_nodes = bm.entity_map(0).array().astype(np.int64)
bm_coords = bm.coordinates()
bm_cells = bm.cells()
bempp_boundary_grid = grid_from_element_data(bm_coords.transpose(),
bm_cells.transpose())
# First get trace space
space = function_space(bempp_boundary_grid, "P", 1)
# Now compute the mapping from BEM++ dofs to FEniCS dofs
# First the BEM++ dofs to the boundary vertices
from ._lagrange_coupling import p1_vertex_map
from scipy.sparse import coo_matrix
vertex_to_dof_map = p1_vertex_map(space)
vertex_indices = np.arange(space.global_dof_count)
data = np.ones(space.global_dof_count)
bempp_dofs_from_b_vertices = coo_matrix(
(data, (vertex_to_dof_map, vertex_indices)), dtype='float64').tocsr()
# Now the boundary vertices to all the vertices
b_vertices_from_vertices = coo_matrix(
(np.ones(len(bm_nodes)), (np.arange(len(bm_nodes)), bm_nodes)),
shape=(len(bm_nodes), mesh.num_vertices()),
dtype='float64').tocsr()
# Finally the vertices to FEniCS dofs
vertices_from_fenics_dofs = coo_matrix(
(np.ones(mesh.num_vertices()), (dolfin.dof_to_vertex_map(fenics_space),
np.arange(mesh.num_vertices()))),
shape=(mesh.num_vertices(), mesh.num_vertices()),
dtype='float64').tocsr()
# Get trace matrix by multiplication
trace_matrix = bempp_dofs_from_b_vertices * b_vertices_from_vertices * vertices_from_fenics_dofs
# Now return everything
return (space, trace_matrix)
def p1_trace(fenics_space):
import dolfin
from .coupling import fenics_space_info
from bempp import function_space,grid_from_element_data
import numpy as np
family,degree = fenics_space_info(fenics_space)
if not (family=='Lagrange' and degree == 1):
raise ValueError("fenics_space must be a p1 Lagrange space")
mesh = fenics_space.mesh()
bm = dolfin.BoundaryMesh(mesh,"exterior",False)
bm_nodes = bm.entity_map(0).array().astype(np.int64)
bm_coords = bm.coordinates()
bm_cells = bm.cells()
bempp_boundary_grid = grid_from_element_data(bm_coords.transpose(),bm_cells.transpose())
# First get trace space
space = function_space(bempp_boundary_grid,"P",1)
# Now compute the mapping from BEM++ dofs to FEniCS dofs
# First the BEM++ dofs to the boundary vertices
from ._lagrange_coupling import p1_vertex_map
from scipy.sparse import coo_matrix
vertex_to_dof_map = p1_vertex_map(space)
vertex_indices = np.arange(space.global_dof_count)
data = np.ones(space.global_dof_count)
bempp_dofs_from_b_vertices = coo_matrix((data,(vertex_to_dof_map,vertex_indices)),dtype='float64').tocsr()
# Now the boundary vertices to all the vertices
b_vertices_from_vertices = coo_matrix((
np.ones(len(bm_nodes)),(np.arange(len(bm_nodes)),bm_nodes)),
shape=(len(bm_nodes),mesh.num_vertices()),dtype='float64').tocsr()
# Finally the vertices to FEniCS dofs
vertices_from_fenics_dofs = coo_matrix((
np.ones(mesh.num_vertices()),(dolfin.dof_to_vertex_map(fenics_space),np.arange(mesh.num_vertices()))),
shape=(mesh.num_vertices(),mesh.num_vertices()),dtype='float64').tocsr()
# Get trace matrix by multiplication
trace_matrix = bempp_dofs_from_b_vertices*b_vertices_from_vertices*vertices_from_fenics_dofs
# Now return everything
return (space,trace_matrix)
