def plot_partitioning(axs, field, cell_tasks, gfd, output_dir, size): """ Plot the partitioning of the domain and field DOFs. """ mesh = field.domain.mesh ax = pc.plot_wireframe(axs[0], mesh.cmesh) coors = field.get_coor() econn = field.econn ax = pd.plot_global_dofs(ax, coors, econn) ax.set_title('global DOFs') ax.figure.savefig(os.path.join(output_dir, 'global_dofs.png'), bbox_inches='tight') ax = pc.plot_wireframe(axs[1], mesh.cmesh) fig = ax.figure coors = field.get_coor() econn = field.econn id_map = gfd.id_map colors = nm.zeros((field.n_nod, 4)) for ir, dof_map in ordered_iteritems(gfd.dof_maps): aux = id_map[dof_map[0]] colors[aux] = [0, 0, float(ir + 1) / size, 0.6] for aux in dof_map[1]: colors[id_map[aux]] = [0, 0, float(ir + 1) / size, 0.9] from sfepy.discrete.fem.utils import prepare_translate aux = prepare_translate(id_map[econn], econn) ax = label_dofs(ax, coors[aux], id_map, colors) mark_subdomains(ax, mesh.cmesh, cell_tasks, size, 0, 0.7) ax.set_title('subdomains of tasks and PETSc DOFs') fig.savefig(os.path.join(output_dir, 'petsc_dofs.png'), bbox_inches='tight') ax.set_title('') axis = ax.axis() for ir, ocells in enumerate(gfd.overlap_cells): aux = nm.zeros_like(cell_tasks) aux[ocells] = 10 aux[gfd.cell_parts[ir]] = 1 ax = fig.add_axes(ax.get_position(), frameon=False, label='aux') mark_subdomains(ax, mesh.cmesh, aux, 11, 1, 0.3, True) ax.axis(axis) ax.set_title('overlap cells on task %d' % ir) fig.savefig(os.path.join(output_dir, 'petsc_overlaps_%02d.png' % ir), bbox_inches='tight') fig.delaxes(ax)
def _setup_facet_dofs(self, dim, facet_desc, offset): """ Helper function to setup facet DOF connectivity, works for both edges and faces. """ facet_desc = nm.array(facet_desc) n_dof_per_facet = facet_desc.shape[1] cmesh = self.domain.cmesh facets = self.region.entities[dim] ii = nm.arange(facets.shape[0], dtype=nm.int32) all_dofs = offset + expand_nodes_to_dofs(ii, n_dof_per_facet) # Prepare global facet id remapping to field-local numbering. remap = prepare_remap(facets, cmesh.num[dim]) cconn = self.region.domain.cmesh.get_conn(self.region.tdim, dim) offs = cconn.offsets n_f = self.gel.edges.shape[0] if dim == 1 else self.gel.faces.shape[0] n_fp = 2 if dim == 1 else self.gel.surface_facet.n_vertex oris = cmesh.get_orientations(dim) ap = self.ap gcells = self.region.get_cells() n_el = gcells.shape[0] # Elements of facets. iel = nm.arange(n_el, dtype=nm.int32).repeat(n_f) ies = nm.tile(nm.arange(n_f, dtype=nm.int32), n_el) aux = offs[gcells][:, None] + ies.reshape((n_el, n_f)) indices = cconn.indices[aux] facets_of_cells = remap[indices].ravel() # Define global facet dof numbers. gdofs = offset + expand_nodes_to_dofs(facets_of_cells, n_dof_per_facet) # DOF columns in econn for each facet (repeating same values for # each element. iep = facet_desc[ies] ap.econn[iel[:, None], iep] = gdofs ori = oris[aux].ravel() if (n_fp == 2) and (ap.interp.gel.name in ['2_4', '3_8']): tp_edges = ap.interp.gel.edges ecs = ap.interp.gel.coors[tp_edges] # True = positive, False = negative edge orientation w.r.t. # reference tensor product axes. tp_edge_ori = (nm.diff(ecs, axis=1).sum(axis=2) > 0).squeeze() aux = nm.tile(tp_edge_ori, n_el) ori = nm.where(aux, ori, 1 - ori) if n_fp == 2: # Edges. # ori == 1 means the basis has to be multiplied by -1. ps = ap.interp.poly_spaces['v'] orders = ps.node_orders eori = nm.repeat(ori[:, None], n_dof_per_facet, 1) eoo = orders[iep] % 2 # Odd orders. ap.ori[iel[:, None], iep] = eori * eoo elif n_fp == 3: # Triangular faces. raise NotImplementedError else: # Quadrilateral faces. # ori encoding in 3 bits: # 0: axis swap, 1: axis 1 sign, 2: axis 2 sign # 0 = + or False, 1 = - or True # 63 -> 000 = 0 # 0 -> 001 = 1 # 30 -> 010 = 2 # 33 -> 011 = 3 # 11 -> 100 = 4 # 7 -> 101 = 5 # 52 -> 110 = 6 # 56 -> 111 = 7 # Special cases: # Both orders same and even -> 000 # Both orders same and odd -> 0?? # Bits 1, 2 are multiplied by (swapped) axial order % 2. new = nm.repeat(nm.arange(8, dtype=nm.int32), 3) translate = prepare_translate([31, 59, 63, 0, 1, 4, 22, 30, 62, 32, 33, 41, 11, 15, 43, 3, 6, 7, 20, 52, 60, 48, 56, 57], new) ori = translate[ori] eori = nm.repeat(ori[:, None], n_dof_per_facet, 1) ps = ap.interp.poly_spaces['v'] orders = ps.face_axes_nodes[iep - ps.face_indx[0]] eoo = orders % 2 eoo0, eoo1 = eoo[..., 0], eoo[..., 1] i0 = nm.where(eori < 4) i1 = nm.where(eori >= 4) eori[i0] = nm.bitwise_and(eori[i0], 2*eoo0[i0] + 5) eori[i0] = nm.bitwise_and(eori[i0], eoo1[i0] + 6) eori[i1] = nm.bitwise_and(eori[i1], eoo0[i1] + 6) eori[i1] = nm.bitwise_and(eori[i1], 2*eoo1[i1] + 5) ap.ori[iel[:, None], iep] = eori n_dof = n_dof_per_facet * facets.shape[0] assert_(n_dof == nm.prod(all_dofs.shape)) return n_dof, all_dofs, remap
def _setup_facet_dofs(self, dim, facet_desc, offset): """ Helper function to setup facet DOF connectivity, works for both edges and faces. """ facet_desc = nm.array(facet_desc) n_dof_per_facet = facet_desc.shape[1] cmesh = self.domain.cmesh facets = self.region.entities[dim] ii = nm.arange(facets.shape[0], dtype=nm.int32) all_dofs = offset + expand_nodes_to_dofs(ii, n_dof_per_facet) # Prepare global facet id remapping to field-local numbering. remap = prepare_remap(facets, cmesh.num[dim]) cconn = self.region.domain.cmesh.get_conn(self.region.tdim, dim) offs = cconn.offsets n_f = self.gel.edges.shape[0] if dim == 1 else self.gel.faces.shape[0] n_fp = 2 if dim == 1 else self.gel.surface_facet.n_vertex oris = cmesh.get_orientations(dim) ap = self.ap gcells = self.region.get_cells() n_el = gcells.shape[0] # Elements of facets. iel = nm.arange(n_el, dtype=nm.int32).repeat(n_f) ies = nm.tile(nm.arange(n_f, dtype=nm.int32), n_el) aux = offs[gcells][:, None] + ies.reshape((n_el, n_f)) indices = cconn.indices[aux] facets_of_cells = remap[indices].ravel() # Define global facet dof numbers. gdofs = offset + expand_nodes_to_dofs(facets_of_cells, n_dof_per_facet) # DOF columns in econn for each facet (repeating same values for # each element. iep = facet_desc[ies] ap.econn[iel[:, None], iep] = gdofs ori = oris[aux].ravel() if (n_fp == 2) and (ap.interp.gel.name in ['2_4', '3_8']): tp_edges = ap.interp.gel.edges ecs = ap.interp.gel.coors[tp_edges] # True = positive, False = negative edge orientation w.r.t. # reference tensor product axes. tp_edge_ori = (nm.diff(ecs, axis=1).sum(axis=2) > 0).squeeze() aux = nm.tile(tp_edge_ori, n_el) ori = nm.where(aux, ori, 1 - ori) if n_fp == 2: # Edges. # ori == 1 means the basis has to be multiplied by -1. ps = ap.interp.poly_spaces['v'] orders = ps.node_orders eori = nm.repeat(ori[:, None], n_dof_per_facet, 1) eoo = orders[iep] % 2 # Odd orders. ap.ori[iel[:, None], iep] = eori * eoo elif n_fp == 3: # Triangular faces. raise NotImplementedError else: # Quadrilateral faces. # ori encoding in 3 bits: # 0: axis swap, 1: axis 1 sign, 2: axis 2 sign # 0 = + or False, 1 = - or True # 63 -> 000 = 0 # 0 -> 001 = 1 # 30 -> 010 = 2 # 33 -> 011 = 3 # 11 -> 100 = 4 # 7 -> 101 = 5 # 52 -> 110 = 6 # 56 -> 111 = 7 # Special cases: # Both orders same and even -> 000 # Both orders same and odd -> 0?? # Bits 1, 2 are multiplied by (swapped) axial order % 2. new = nm.repeat(nm.arange(8, dtype=nm.int32), 3) translate = prepare_translate([ 31, 59, 63, 0, 1, 4, 22, 30, 62, 32, 33, 41, 11, 15, 43, 3, 6, 7, 20, 52, 60, 48, 56, 57 ], new) ori = translate[ori] eori = nm.repeat(ori[:, None], n_dof_per_facet, 1) ps = ap.interp.poly_spaces['v'] orders = ps.face_axes_nodes[iep - ps.face_indx[0]] eoo = orders % 2 eoo0, eoo1 = eoo[..., 0], eoo[..., 1] i0 = nm.where(eori < 4) i1 = nm.where(eori >= 4) eori[i0] = nm.bitwise_and(eori[i0], 2 * eoo0[i0] + 5) eori[i0] = nm.bitwise_and(eori[i0], eoo1[i0] + 6) eori[i1] = nm.bitwise_and(eori[i1], eoo0[i1] + 6) eori[i1] = nm.bitwise_and(eori[i1], 2 * eoo1[i1] + 5) ap.ori[iel[:, None], iep] = eori n_dof = n_dof_per_facet * facets.shape[0] assert_(n_dof == nm.prod(all_dofs.shape)) return n_dof, all_dofs, remap