def _setup_global_base( self ): """ Setup global DOF/base function indices and connectivity of the field. """ self._setup_facet_orientations() self._init_econn() n_dof = 0 all_dofs = {} remaps = {} for ig, ap in self.aps.iteritems(): ii = self.region.get_cells(ig) nd = nm.prod(ap.econn.shape) group = self.domain.groups[ig] remaps[ig] = prepare_remap(ii, group.shape.n_el) aux = nm.arange(n_dof, n_dof + nd, dtype=nm.int32) aux.shape = ap.econn.shape ap.econn[:] = aux all_dofs[ig] = aux n_dof += nd self.n_nod = n_dof self.n_bubble_dof = n_dof self.bubble_dofs = all_dofs self.bubble_remaps = remaps self.n_vertex_dof = self.n_edge_dof = self.n_face_dof = 0 self._setup_esurface()
def _setup_bubble_dofs(self): """ Setup bubble DOF connectivity. """ if self.node_desc.bubble is None: return 0, None, None offset = self.n_vertex_dof + self.n_edge_dof + self.n_face_dof n_dof = 0 n_dof_per_cell = self.node_desc.bubble.shape[0] all_dofs = {} remaps = {} for ig, ap in self.aps.iteritems(): ii = self.region.get_cells(ig) n_cell = ii.shape[0] nd = n_dof_per_cell * n_cell group = self.domain.groups[ig] remaps[ig] = prepare_remap(ii, group.shape.n_el) aux = nm.arange(offset + n_dof, offset + n_dof + nd, dtype=nm.int32) aux.shape = (n_cell, n_dof_per_cell) iep = self.node_desc.bubble[0] ap.econn[:,iep:] = aux all_dofs[ig] = aux n_dof += nd return n_dof, all_dofs, remaps
def _setup_vertex_dofs(self): """ Setup vertex DOF connectivity. """ if self.node_desc.vertex is None: return 0, None region = self.region vertices = region.get_vertices_of_cells() remap = prepare_remap(vertices, region.n_v_max) n_dof = vertices.shape[0] ## # Remap vertex node connectivity to field-local numbering. for ig, ap in self.aps.iteritems(): group = self.domain.groups[ig] offset = group.shape.n_ep cells = region.get_cells(ig) ap.econn[:,:offset] = nm.take(remap, nm.take(group.conn, cells.astype(nm.int32), axis=0)) return n_dof, remap
def _setup_facet_dofs(self, dim, facet_desc, facet_perms, 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] oris = cmesh.get_orientations(dim) for ig, ap in self.aps.iteritems(): gcells = self.region.get_cells(ig, offset=False) n_el = gcells.shape[0] indices = cconn.indices[offs[gcells[0]]:offs[gcells[-1]+1]] facets_of_cells = remap[indices] ori = oris[offs[gcells[0]]:offs[gcells[-1]+1]] perms = facet_perms[ig][ori] # Define global facet dof numbers. gdofs = offset + expand_nodes_to_dofs(facets_of_cells, n_dof_per_facet) # 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) # DOF columns in econn for each facet. iep = facet_desc[ies] iaux = nm.arange(gdofs.shape[0], dtype=nm.int32) ap.econn[iel[:, None], iep] = gdofs[iaux[:, None], perms] 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, facet_perms, 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] oris = cmesh.get_orientations(dim) for ig, ap in self.aps.iteritems(): gcells = self.region.get_cells(ig, offset=False) n_el = gcells.shape[0] indices = cconn.indices[offs[gcells[0]]:offs[gcells[-1] + 1]] facets_of_cells = remap[indices] ori = oris[offs[gcells[0]]:offs[gcells[-1] + 1]] perms = facet_perms[ig][ori] # Define global facet dof numbers. gdofs = offset + expand_nodes_to_dofs(facets_of_cells, n_dof_per_facet) # 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) # DOF columns in econn for each facet. iep = facet_desc[ies] iaux = nm.arange(gdofs.shape[0], dtype=nm.int32) ap.econn[iel[:, None], iep] = gdofs[iaux[:, None], perms] 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, facets, facet_desc, facet_perms, get_facets, 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] # Prepare global facet id remapping to field-local numbering. uids = [] for ig, ap in self.aps.iteritems(): ii = get_facets(ig) uid_i = facets.uid_i[ii] uids.append(uid_i) uids = nm.unique(nm.concatenate(uids)) n_uid = uids.shape[0] lids = nm.arange(n_uid, dtype=nm.int32) remap = prepare_remap(uids, facets.n_unique) all_dofs = offset + expand_nodes_to_dofs(lids, n_dof_per_facet) for ig, ap in self.aps.iteritems(): ori = facets.oris[ig] perms = facet_perms[ig][ori] ii = get_facets(ig) g_uid = facets.uid_i[ii] uid = remap[g_uid] # Define global facet dof numbers. gdofs = offset + expand_nodes_to_dofs(uid, n_dof_per_facet) # Elements of facets. iel = facets.indices[ii, 1] ies = facets.indices[ii, 2] # DOF columns in econn for each facet. iep = facet_desc[ies] iaux = nm.arange(gdofs.shape[0], dtype=nm.int32) ap.econn[iel[:, None], iep] = gdofs[iaux[:, None], perms] n_dof = n_dof_per_facet * n_uid assert_(n_dof == nm.prod(all_dofs.shape)) return n_dof, all_dofs, remap
def __init__(self, name, region, efaces, volume_econn, ig): """nodes[leconn] == econn""" """nodes are sorted by node number -> same order as region.vertices""" self.name = get_default(name, 'surface_data_%s' % region.name) face_indices = region.get_facet_indices(ig) faces = efaces[face_indices[:,1]] if faces.size == 0: raise ValueError('region with group with no faces! (%s)' % region.name) try: ee = volume_econn[face_indices[:,0]] except: raise ValueError('missing region face indices! (%s)' % region.name) econn = nm.empty(faces.shape, dtype=nm.int32) for ir, face in enumerate( faces ): econn[ir] = ee[ir,face] nodes = nm.unique(econn) remap = prepare_remap(nodes, nodes.max() + 1) leconn = remap[econn].copy() n_fa, n_fp = face_indices.shape[0], faces.shape[1] face_type = 's%d' % n_fp # Store bkey in SurfaceData, so that base function can be # queried later. bkey = 'b%s' % face_type[1:] self.ig = ig self.econn = econn self.fis = nm.ascontiguousarray(face_indices.astype(nm.int32)) self.n_fa, self.n_fp = n_fa, n_fp self.nodes = nodes self.leconn = leconn self.face_type = face_type self.bkey = bkey self.meconn = self.mleconn = None if self.n_fp <= 4: self.ori_map, _, _ = build_orientation_map(self.n_fp) else: self.ori_map = None
def _setup_vertex_dofs(self): """ Setup vertex DOF connectivity. """ if self.node_desc.vertex is None: return 0, None region = self.region remap = prepare_remap(region.all_vertices, region.n_v_max) n_dof = region.all_vertices.shape[0] ## # Remap vertex node connectivity to field-local numbering. for ig, ap in self.aps.iteritems(): group = self.domain.groups[ig] faces = group.gel.get_surface_entities() aux = FESurface('aux', region, faces, group.conn, ig) ap.econn[:,:aux.n_fp] = aux.leconn ap.surface_data[region.name] = aux return n_dof, remap
def setup_mirror_connectivity(self, region): """ Setup mirror surface connectivity required to integrate over a mirror region. 1. Get orientation of the faces: a) for elements in group ig -> ooris (own) b) for elements in group mig -> moris (mirror) 2. orientation -> permutation. """ mregion, ig_map, ig_map_i = region.get_mirror_region() mig = ig_map_i[self.ig] oo = self.ori_map ori_map = nm.zeros((nm.max(oo.keys()) + 1, self.n_fp), dtype=nm.int32) ori_map[oo.keys()] = nm.array([ii[1] for ii in oo.values()]) conn = region.domain.cmesh.get_conn_as_graph(region.dim, region.dim - 1) oris = region.domain.cmesh.facet_oris ofis = region.get_facet_indices(self.ig, offset=False) ooris = oris[conn.indptr[ofis[:, 0]] + ofis[:, 1]] mfis = mregion.get_facet_indices(mig, offset=False) moris = oris[conn.indptr[mfis[:, 0]] + mfis[:, 1]] omap = ori_map[ooris] mmap = ori_map[moris] n_el, n_ep = self.econn.shape ii = nm.repeat(nm.arange(n_el)[:, None], n_ep, 1) self.meconn = nm.empty_like(self.econn) self.meconn[ii, omap] = self.econn[ii, mmap] nodes = nm.unique(self.meconn) remap = prepare_remap(nodes, nodes.max() + 1) self.mleconn = remap[self.meconn].copy()
def _setup_facet_dofs(self, facets, facet_desc, get_facets, 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] # Prepare global facet id remapping to field-local numbering. uids = [] for ig, ap in self.aps.iteritems(): ii = get_facets(ig) uid_i = facets.uid_i[ii] uids.append(uid_i) uids = nm.unique(nm.concatenate(uids)) n_uid = uids.shape[0] lids = nm.arange(n_uid, dtype=nm.int32) remap = prepare_remap(uids, facets.n_unique) all_dofs = offset + expand_nodes_to_dofs(lids, n_dof_per_facet) for ig, ap in self.aps.iteritems(): n_fp = facets.n_fps[ig] 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() else: tp_edge_ori = None ori = facets.get_orientation(ig, tp_edge_ori) ii = get_facets(ig) g_uid = facets.uid_i[ii] uid = remap[g_uid] # Define global facet dof numbers. gdofs = offset + expand_nodes_to_dofs(uid, n_dof_per_facet) # Elements of facets. iel = facets.indices[ii, 1] ies = facets.indices[ii, 2] # DOF columns in econn for each facet (repeating same values for # each element. iep = facet_desc[ies] ap.econn[iel[:, None], iep] = gdofs 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 * n_uid assert_(n_dof == nm.prod(all_dofs.shape)) return n_dof, all_dofs, remap
def _setup_facet_dofs(self, dim, facet_desc, get_facets, 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) for ig, ap in self.aps.iteritems(): gcells = self.region.get_cells(ig, offset=False) n_el = gcells.shape[0] indices = cconn.indices[offs[gcells[0]] : offs[gcells[-1] + 1]] facets_of_cells = remap[indices] # Define global facet dof numbers. gdofs = offset + expand_nodes_to_dofs(facets_of_cells, n_dof_per_facet) # 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) # 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[offs[gcells[0]] : offs[gcells[-1] + 1]] 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