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# Copyright (C) 2021 Jørgen S. Dokken
#
# This file is part of DOLFINX_MPC
#
# SPDX-License-Identifier: MIT
from typing import Tuple
import cffi
import dolfinx.cpp as _cpp
import dolfinx.fem as _fem
import dolfinx.log as _log
import numpy
import numpy.typing as npt
from dolfinx.common import Timer
from dolfinx_mpc.multipointconstraint import MultiPointConstraint
from petsc4py import PETSc as _PETSc
import numba
from .helpers import _forms, extract_slave_cells, pack_slave_facet_info
from .numba_setup import initialize_petsc
ffi, _ = initialize_petsc()
def assemble_vector(form: _forms, constraint: MultiPointConstraint, b: _PETSc.Vec = None) -> _PETSc.Vec:
"""
Assemble a compiled DOLFINx form into vector b.
Parameters
----------
form
The complied linear form
constraint
The multi point constraint
b
PETSc vector to assemble into (optional)
"""
_log.log(_log.LogLevel.INFO, "Assemble MPC vector")
timer_vector = Timer("~MPC: Assemble vector (numba)")
# Unpack Function space data
V = form.function_spaces[0]
pos = V.mesh.geometry.dofmap.offsets
x_dofs = V.mesh.geometry.dofmap.array
x = V.mesh.geometry.x
dofs = V.dofmap.list().array
block_size = V.dofmap.index_map_bs
# Data from multipointconstraint
coefficients = constraint.coefficients()[0]
masters_adj = constraint.masters
c_to_s_adj = constraint.cell_to_slaves
cell_to_slave = c_to_s_adj.array
c_to_s_off = c_to_s_adj.offsets
is_slave = constraint.is_slave
mpc_data = (masters_adj.array, coefficients, masters_adj.offsets, cell_to_slave, c_to_s_off, is_slave)
slave_cells = extract_slave_cells(c_to_s_off)
# Get index map and ghost info
if b is None:
index_map = constraint.function_space.dofmap.index_map
vector = _cpp.la.petsc.create_vector(index_map, block_size)
else:
vector = b
# Pack constants and coefficients
form_coeffs = _cpp.fem.pack_coefficients(form)
form_consts = _cpp.fem.pack_constants(form)
tdim = V.mesh.topology.dim
num_dofs_per_element = V.dofmap.dof_layout.num_dofs
# Assemble vector with all entries
with vector.localForm() as b_local:
_cpp.fem.assemble_vector(b_local.array_w, form, form_consts, form_coeffs)
# Check if we need facet permutations
# FIXME: access apply_dof_transformations here
e0 = form.function_spaces[0].element
needs_transformation_data = e0.needs_dof_transformations or form.needs_facet_permutations
cell_perms = numpy.array([], dtype=numpy.uint32)
if needs_transformation_data:
V.mesh.topology.create_entity_permutations()
cell_perms = V.mesh.topology.get_cell_permutation_info()
if e0.needs_dof_transformations:
raise NotImplementedError("Dof transformations not implemented")
# Assemble over cells
subdomain_ids = form.integral_ids(_fem.IntegralType.cell)
num_cell_integrals = len(subdomain_ids)
is_complex = numpy.issubdtype(_PETSc.ScalarType, numpy.complexfloating)
nptype = "complex128" if is_complex else "float64"
ufcx_form = form.ufcx_form
if num_cell_integrals > 0:
V.mesh.topology.create_entity_permutations()
for i, id in enumerate(subdomain_ids):
cell_kernel = getattr(ufcx_form.integrals(_fem.IntegralType.cell)[i], f"tabulate_tensor_{nptype}")
active_cells = form.domains(_fem.IntegralType.cell, id)
coeffs_i = form_coeffs[(_fem.IntegralType.cell, id)]
with vector.localForm() as b:
assemble_cells(numpy.asarray(b), cell_kernel, active_cells[numpy.isin(active_cells, slave_cells)],
(pos, x_dofs, x), coeffs_i, form_consts,
cell_perms, dofs, block_size, num_dofs_per_element, mpc_data)
# Assemble exterior facet integrals
subdomain_ids = form.integral_ids(_fem.IntegralType.exterior_facet)
num_exterior_integrals = len(subdomain_ids)
if num_exterior_integrals > 0:
V.mesh.topology.create_entities(tdim - 1)
V.mesh.topology.create_connectivity(tdim - 1, tdim)
# Get facet permutations if required
facet_perms = numpy.array([], dtype=numpy.uint8)
if form.needs_facet_permutations:
facet_perms = V.mesh.topology.get_facet_permutations()
perm = (cell_perms, form.needs_facet_permutations, facet_perms)
for i, id in enumerate(subdomain_ids):
facet_kernel = getattr(ufcx_form.integrals(_fem.IntegralType.exterior_facet)[i],
f"tabulate_tensor_{nptype}")
coeffs_i = form_coeffs[(_fem.IntegralType.exterior_facet, id)]
facets = form.domains(_fem.IntegralType.exterior_facet, id)
facet_info = pack_slave_facet_info(facets, slave_cells)
num_facets_per_cell = len(V.mesh.topology.connectivity(tdim, tdim - 1).links(0))
with vector.localForm() as b:
assemble_exterior_slave_facets(numpy.asarray(b), facet_kernel, facet_info, (pos, x_dofs, x),
coeffs_i, form_consts, perm,
dofs, block_size, num_dofs_per_element, mpc_data, num_facets_per_cell)
timer_vector.stop()
return vector
@numba.njit
def assemble_cells(b: npt.NDArray[_PETSc.ScalarType],
kernel: cffi.FFI, active_cells: npt.NDArray[numpy.int32],
mesh: Tuple[npt.NDArray[numpy.int32], npt.NDArray[numpy.int32],
npt.NDArray[numpy.float64]],
coeffs: npt.NDArray[_PETSc.ScalarType],
constants: npt.NDArray[_PETSc.ScalarType],
permutation_info: npt.NDArray[numpy.uint32],
dofmap: npt.NDArray[numpy.int32],
block_size: int,
num_dofs_per_element: int,
mpc: Tuple[npt.NDArray[numpy.int32], npt.NDArray[_PETSc.ScalarType],
npt.NDArray[numpy.int32], npt.NDArray[numpy.int32],
npt.NDArray[numpy.int32], npt.NDArray[numpy.int32]]):
"""Assemble additional MPC contributions for cell integrals"""
ffi_fb = ffi.from_buffer
# Empty arrays mimicking Nullpointers
facet_index = numpy.zeros(0, dtype=numpy.int32)
facet_perm = numpy.zeros(0, dtype=numpy.uint8)
# Unpack mesh data
pos, x_dofmap, x = mesh
# NOTE: All cells are assumed to be of the same type
geometry = numpy.zeros((pos[1] - pos[0], 3))
b_local = numpy.zeros(block_size * num_dofs_per_element, dtype=_PETSc.ScalarType)
for cell_index in active_cells:
num_vertices = pos[cell_index + 1] - pos[cell_index]
cell = pos[cell_index]
# Compute mesh geometry for cell
geometry[:, :] = x[x_dofmap[cell:cell + num_vertices]]
# Assemble local element vector
b_local.fill(0.0)
kernel(ffi_fb(b_local), ffi_fb(coeffs[cell_index, :]),
ffi_fb(constants), ffi_fb(geometry), ffi_fb(facet_index),
ffi_fb(facet_perm))
# NOTE: Here we need to add the apply_dof_transformation function
# Modify global vector and local cell contributions
b_local_copy = b_local.copy()
modify_mpc_contributions(b, cell_index, b_local, b_local_copy, mpc, dofmap,
block_size, num_dofs_per_element)
for j in range(num_dofs_per_element):
for k in range(block_size):
position = dofmap[num_dofs_per_element * cell_index + j] * block_size + k
b[position] += (b_local[j * block_size + k] - b_local_copy[j * block_size + k])
@numba.njit
def assemble_exterior_slave_facets(b: npt.NDArray[_PETSc.ScalarType],
kernel: cffi.FFI,
facet_info: npt.NDArray[numpy.int32],
mesh: Tuple[npt.NDArray[numpy.int32], npt.NDArray[numpy.int32],
npt.NDArray[numpy.float64]],
coeffs: npt.NDArray[_PETSc.ScalarType],
constants: npt.NDArray[_PETSc.ScalarType],
permutation_info: npt.NDArray[numpy.uint32],
dofmap: npt.NDArray[numpy.int32],
block_size: int,
num_dofs_per_element: int,
mpc: Tuple[npt.NDArray[numpy.int32], npt.NDArray[_PETSc.ScalarType],
npt.NDArray[numpy.int32], npt.NDArray[numpy.int32],
npt.NDArray[numpy.int32], npt.NDArray[numpy.int32]],
num_facets_per_cell: int):
"""Assemble additional MPC contributions for facets"""
ffi_fb = ffi.from_buffer
# Unpack facet permutation info
cell_perms, needs_facet_perm, facet_perms = permutation_info
facet_index = numpy.zeros(1, dtype=numpy.int32)
facet_perm = numpy.zeros(1, dtype=numpy.uint8)
# Unpack mesh data
pos, x_dofmap, x = mesh
geometry = numpy.zeros((pos[1] - pos[0], 3))
b_local = numpy.zeros(block_size * num_dofs_per_element, dtype=_PETSc.ScalarType)
for i in range(facet_info.shape[0]):
# Extract cell index (local to process) and facet index (local to cell) for kernel
cell_index, local_facet = facet_info[i]
facet_index[0] = local_facet
# Extract cell geometry
cell = pos[cell_index]
num_vertices = pos[cell_index + 1] - pos[cell_index]
geometry[:, :] = x[x_dofmap[cell:cell + num_vertices]]
# Compute local facet kernel
b_local.fill(0.0)
if needs_facet_perm:
facet_perm[0] = facet_perms[cell_index * num_facets_per_cell + local_facet]
kernel(ffi_fb(b_local), ffi_fb(coeffs[cell_index, :]), ffi_fb(constants), ffi_fb(geometry),
ffi_fb(facet_index), ffi_fb(facet_perm))
# NOTE: Here we need to add the apply_dof_transformation
# Modify local contributions and add global MPC contributions
b_local_copy = b_local.copy()
modify_mpc_contributions(b, cell_index, b_local, b_local_copy,
mpc, dofmap, block_size, num_dofs_per_element)
for j in range(num_dofs_per_element):
for k in range(block_size):
position = dofmap[num_dofs_per_element * cell_index + j] * block_size + k
b[position] += (b_local[j * block_size + k] - b_local_copy[j * block_size + k])
@numba.njit(cache=True)
def modify_mpc_contributions(b: npt.NDArray[_PETSc.ScalarType], cell_index: int,
b_local: npt.NDArray[_PETSc.ScalarType],
b_copy: npt.NDArray[_PETSc.ScalarType],
mpc: Tuple[npt.NDArray[numpy.int32], npt.NDArray[_PETSc.ScalarType],
npt.NDArray[numpy.int32], npt.NDArray[numpy.int32],
npt.NDArray[numpy.int32], npt.NDArray[numpy.int32]],
dofmap: npt.NDArray[numpy.int32],
block_size: int,
num_dofs_per_element: int):
"""
Modify local entries of b_local with MPC info and add modified
entries to global vector b.
"""
# Unwrap MPC data
masters, coefficients, offsets, cell_to_slave, cell_to_slave_offset, is_slave = mpc
# Determine which slaves are in this cell,
# and which global index they have in 1D arrays
cell_slaves = cell_to_slave[cell_to_slave_offset[cell_index]:
cell_to_slave_offset[cell_index + 1]]
# Get local index of slaves in cell
cell_blocks = dofmap[num_dofs_per_element * cell_index:
num_dofs_per_element * cell_index + num_dofs_per_element]
local_index = numpy.empty(len(cell_slaves), dtype=numpy.int32)
for i in range(num_dofs_per_element):
for j in range(block_size):
dof = cell_blocks[i] * block_size + j
if is_slave[dof]:
location = numpy.flatnonzero(cell_slaves == dof)[0]
local_index[location] = i * block_size + j
# Move contribution from each slave to the corresponding master dof
# and zero out local b
for local, slave in zip(local_index, cell_slaves):
cell_masters = masters[offsets[slave]: offsets[slave + 1]]
cell_coeffs = coefficients[offsets[slave]: offsets[slave + 1]]
for m0, c0 in zip(cell_masters, cell_coeffs):
b[m0] += c0 * b_copy[local]
b_local[local] = 0
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