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|
! Copyright (C) 2006 Imperial College London and others.
!
! Please see the AUTHORS file in the main source directory for a full list
! of copyright holders.
!
! Prof. C Pain
! Applied Modelling and Computation Group
! Department of Earth Science and Engineering
! Imperial College London
!
! amcgsoftware@imperial.ac.uk
!
! This library is free software; you can redistribute it and/or
! modify it under the terms of the GNU Lesser General Public
! License as published by the Free Software Foundation,
! version 2.1 of the License.
!
! This library is distributed in the hope that it will be useful,
! but WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
! Lesser General Public License for more details.
!
! You should have received a copy of the GNU Lesser General Public
! License along with this library; if not, write to the Free Software
! Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
! USA
#include "fdebug.h"
module differential_operator_diagnostics
! these 5 need to be on top and in this order, so as not to confuse silly old intel compiler
use quadrature
use elements
use sparse_tools
use fields
use state_module
!
use diagnostic_source_fields
use divergence_matrix_cg
use eventcounter
use field_derivatives
use field_options
use fldebug
use geostrophic_pressure
use global_parameters, only : OPTION_PATH_LEN
use solvers
use sparse_matrices_fields
use sparsity_patterns_meshes
use spud
use state_fields_module
implicit none
private
public :: calculate_grad, calculate_div, calculate_curl, calculate_perp, &
& calculate_curl_2d, calculate_finite_element_divergence, &
& calculate_finite_element_divergence_transpose, &
& calculate_scalar_advection, calculate_scalar_laplacian, &
& calculate_vector_advection, calculate_vector_laplacian
contains
subroutine calculate_grad(state, v_field)
type(state_type), intent(in) :: state
type(vector_field), intent(inout) :: v_field
type(scalar_field), pointer :: source_field
type(vector_field), pointer :: positions
source_field => scalar_source_field(state, v_field)
positions => extract_vector_field(state, "Coordinate")
call check_source_mesh_derivative(source_field, "grad")
call grad(source_field, positions, v_field)
end subroutine calculate_grad
subroutine calculate_div(state, s_field)
type(state_type), intent(in) :: state
type(scalar_field), intent(inout) :: s_field
type(vector_field), pointer :: positions, source_field
source_field => vector_source_field(state, s_field)
positions => extract_vector_field(state, "Coordinate")
call check_source_mesh_derivative(source_field, "div")
call div(source_field, positions, s_field)
end subroutine calculate_div
subroutine calculate_finite_element_divergence(state, s_field)
type(state_type), intent(inout) :: state
type(scalar_field), intent(inout) :: s_field
character(len = OPTION_PATH_LEN) :: path
type(block_csr_matrix) :: ct_m
type(csr_sparsity), pointer :: divergence_sparsity
type(csr_matrix), pointer :: mass
type(scalar_field) :: ctfield, ct_rhs
type(scalar_field), pointer :: masslump
type(vector_field), pointer :: positions, source_field
source_field => vector_source_field(state, s_field)
path = trim(complete_field_path(s_field%option_path)) // "/algorithm"
if(use_divergence_matrix_cache(state)) then
ct_m = extract_block_csr_matrix(state, trim(s_field%name) // "DivergenceMatrix")
call incref(ct_m)
ct_rhs = extract_scalar_field(state, trim(s_field%name) // "DivergenceRHS")
call incref(ct_rhs)
else
positions => extract_vector_field(state, "Coordinate")
divergence_sparsity => get_csr_sparsity_firstorder(state, s_field%mesh, source_field%mesh)
call allocate(ct_m, divergence_sparsity, (/1, source_field%dim/), name = "DivergenceMatrix" )
call allocate(ct_rhs, s_field%mesh, name = "CTRHS")
call assemble_divergence_matrix_cg(ct_m, state, ct_rhs = ct_rhs, &
& test_mesh = s_field%mesh, field = source_field, &
& option_path = path)
call insert(state, ct_m, trim(s_field%name) // "DivergenceMatrix")
call insert(state, ct_rhs, trim(s_field%name) // "DivergenceRHS")
end if
call allocate(ctfield, s_field%mesh, name = "CTField")
call mult(ctfield, ct_m, source_field)
call addto(ctfield, ct_rhs, -1.0)
call deallocate(ct_rhs)
if(have_option(trim(path) // "/lump_mass")) then
masslump => get_lumped_mass(state, s_field%mesh)
s_field%val = ctfield%val / masslump%val
else
mass => get_mass_matrix(state, s_field%mesh)
call petsc_solve(s_field, mass, ctfield, option_path = path)
end if
call deallocate(ct_m)
call deallocate(ctfield)
contains
function use_divergence_matrix_cache(state) result(use_cache)
type(state_type), intent(in) :: state
logical :: use_cache
integer, save :: last_mesh_movement = -1
if(has_block_csr_matrix(state, trim(s_field%name) // "DivergenceMatrix")) then
use_cache = (last_mesh_movement == eventcount(EVENT_MESH_MOVEMENT))
else
use_cache = .false.
end if
if(use_cache) then
ewrite(2, *) "Using cached divergence matrix"
else
ewrite(2, *) "Not using cached divergence matrix"
last_mesh_movement = eventcount(EVENT_MESH_MOVEMENT)
end if
end function use_divergence_matrix_cache
end subroutine calculate_finite_element_divergence
subroutine calculate_finite_element_divergence_transpose(state, v_field)
type(state_type), intent(inout) :: state
type(vector_field), intent(inout) :: v_field
character(len = FIELD_NAME_LEN) :: bcfield_name
character(len = OPTION_PATH_LEN) :: path
type(cmc_matrices) :: matrices
type(scalar_field), pointer :: source_field
type(vector_field), pointer :: bcfield
source_field => scalar_source_field(state, v_field)
path = trim(complete_field_path(v_field%option_path)) // "/algorithm"
if(have_option(trim(path) // "/bc_field")) then
call get_option(trim(path) // "/bc_field/name", bcfield_name)
bcfield => extract_vector_field(state, bcfield_name)
call allocate(matrices, state, v_field, source_field, bcfield = bcfield, option_path = path, add_cmc = .false.)
else
call allocate(matrices, state, v_field, source_field, option_path = path, add_cmc = .false.)
end if
call compute_conservative(matrices, v_field, source_field)
call deallocate(matrices)
end subroutine calculate_finite_element_divergence_transpose
subroutine calculate_perp(state, v_field)
type(state_type), intent(inout) :: state
type(vector_field), intent(inout) :: v_field
character(len = OPTION_PATH_LEN) :: path
integer :: i
type(csr_matrix), pointer :: mass
type(scalar_field), pointer :: masslump
type(scalar_field), pointer :: source_field
type(vector_field) :: rhs
type(vector_field), pointer :: positions
write(1, *) "In calculate_perp"
source_field => scalar_source_field(state, v_field)
ewrite(2, *) "Calculating perp of field: " // trim(source_field%name)
ewrite(2, *) "On mesh: " // trim(source_field%mesh%name)
ewrite(2, *) "Diagnostic field: " // trim(v_field%name)
ewrite(2, *) "On mesh: " // trim(v_field%mesh%name)
if(v_field%dim /= 2) then
FLExit("Can only calculate perp in 2D")
end if
call check_source_mesh_derivative(source_field, "perp")
positions => extract_vector_field(state, "Coordinate")
path = trim(complete_field_path(v_field%option_path)) // "/algorithm"
if(have_option(trim(path) // "/lump_mass")) then
masslump => get_lumped_mass(state, v_field%mesh)
call zero(v_field)
do i = 1, ele_count(v_field)
call assemble_perp_ele(i, positions, source_field, v_field)
end do
do i = 1, v_field%dim
v_field%val(i,:) = v_field%val(i,:) / masslump%val
end do
else
select case(continuity(v_field))
case(0)
if(.not. have_option(trim(path) // "/solver")) then
FLExit("For continuous perp, must supply solver options when not lumping mass")
end if
mass => get_mass_matrix(state, v_field%mesh)
call allocate(rhs, v_field%dim, v_field%mesh, "PerpRHS")
call zero(rhs)
do i = 1, ele_count(rhs)
call assemble_perp_ele(i, positions, source_field, rhs)
end do
call petsc_solve(v_field, mass, rhs, option_path = path)
call deallocate(rhs)
case(-1)
do i = 1, ele_count(v_field)
call solve_perp_ele(i, positions, source_field, v_field)
end do
case default
ewrite(-1, *) "For mesh continuity: ", continuity(v_field)
FLAbort("Unrecognised mesh continuity")
end select
end if
contains
subroutine assemble_perp_ele(ele, positions, source, rhs)
integer, intent(in) :: ele
type(vector_field), intent(in) :: positions
type(scalar_field), intent(in) :: source
type(vector_field), intent(inout) :: rhs
real, dimension(ele_ngi(positions, ele)) :: detwei
real, dimension(ele_ngi(source, ele), positions%dim) :: grad_source_gi
real, dimension(ele_loc(source, ele), ele_ngi(source, ele), positions%dim) :: dshape
call transform_to_physical(positions, ele, ele_shape(source, ele), &
& dshape = dshape, detwei = detwei)
grad_source_gi = ele_grad_at_quad(source, ele, dshape)
call addto(rhs, 1, ele_nodes(rhs, ele), &
& shape_rhs(ele_shape(rhs, ele), grad_source_gi(:, 2) * detwei))
call addto(rhs, 2, ele_nodes(rhs, ele), &
& shape_rhs(ele_shape(rhs, ele), -grad_source_gi(:, 1) * detwei))
end subroutine assemble_perp_ele
subroutine solve_perp_ele(ele, positions, source, perp)
integer, intent(in) :: ele
type(vector_field), intent(in) :: positions
type(scalar_field), intent(in) :: source
type(vector_field), intent(inout) :: perp
real, dimension(ele_ngi(positions, ele)) :: detwei
real, dimension(ele_ngi(source, ele), positions%dim) :: grad_source_gi
real, dimension(ele_loc(perp, ele), perp%dim) :: little_rhs
real, dimension(ele_loc(perp, ele), ele_loc(perp, ele)) :: little_mass
real, dimension(ele_loc(source, ele), ele_ngi(source, ele), positions%dim) :: dshape
type(element_type), pointer :: shape
call transform_to_physical(positions, ele, ele_shape(source, ele), &
& dshape = dshape, detwei = detwei)
grad_source_gi = ele_grad_at_quad(source, ele, dshape)
shape => ele_shape(perp, ele)
little_mass = shape_shape(shape, shape, detwei)
little_rhs(:, 1) = shape_rhs(shape, grad_source_gi(:, 2) * detwei)
little_rhs(:, 2) = shape_rhs(shape, -grad_source_gi(:, 1) * detwei)
call solve(little_mass, little_rhs)
call set(perp, ele_nodes(perp, ele), transpose(little_rhs))
end subroutine solve_perp_ele
end subroutine calculate_perp
subroutine calculate_curl_2d(state, s_field)
type(state_type), intent(inout) :: state
type(scalar_field), intent(inout) :: s_field
character(len = OPTION_PATH_LEN) :: path
integer :: i
type(csr_matrix), pointer :: mass
type(scalar_field), pointer :: masslump
type(scalar_field) :: rhs
type(vector_field), pointer :: positions, source_field
ewrite(1, *) "In calculate_curl_2d"
source_field => vector_source_field(state, s_field)
ewrite(2, *) "Calculating curl of field: " // trim(source_field%name)
ewrite(2, *) "On mesh: " // trim(source_field%mesh%name)
ewrite(2, *) "Diagnostic field: " // trim(s_field%name)
ewrite(2, *) "On mesh: " // trim(s_field%mesh%name)
if(source_field%dim /= 2) then
FLExit("Can only calculate 2D curl in 2D")
end if
call check_source_mesh_derivative(source_field, "curl_2d")
positions => extract_vector_field(state, "Coordinate")
path = trim(complete_field_path(s_field%option_path)) // "/algorithm"
if(have_option(trim(path) // "/lump_mass")) then
masslump => get_lumped_mass(state, s_field%mesh)
call zero(s_field)
do i = 1, ele_count(s_field)
call assemble_curl_ele(i, positions, source_field, s_field)
end do
s_field%val = s_field%val / masslump%val
else
select case(continuity(s_field))
case(0)
if(.not. have_option(trim(path) // "/solver")) then
FLExit("For continuous curl, must supply solver options when not lumping mass")
end if
mass => get_mass_matrix(state, s_field%mesh)
call allocate(rhs, s_field%mesh, "CurlRHS")
call zero(rhs)
do i = 1, ele_count(rhs)
call assemble_curl_ele(i, positions, source_field, rhs)
end do
call petsc_solve(s_field, mass, rhs, option_path = path)
call deallocate(rhs)
case(-1)
do i = 1, ele_count(s_field)
call solve_curl_ele(i, positions, source_field, s_field)
end do
case default
ewrite(-1, *) "For mesh continuity: ", continuity(s_field)
FLAbort("Unrecognised mesh continuity")
end select
end if
ewrite_minmax(s_field%val)
ewrite(1, *) "Exiting calculate_curl_2d"
contains
subroutine assemble_curl_ele(ele, positions, source, rhs)
integer, intent(in) :: ele
type(vector_field), intent(in) :: positions
type(vector_field), intent(in) :: source
type(scalar_field), intent(inout) :: rhs
real, dimension(ele_ngi(positions, ele)) :: detwei
real, dimension(ele_loc(source, ele), ele_ngi(source, ele), positions%dim) :: dshape
call transform_to_physical(positions, ele, ele_shape(source, ele), &
& dshape = dshape, detwei = detwei)
call addto(rhs, ele_nodes(rhs, ele), &
& shape_rhs(ele_shape(rhs, ele), &
& ele_2d_curl_at_quad(source, ele, dshape) * detwei))
end subroutine assemble_curl_ele
subroutine solve_curl_ele(ele, positions, source, curl)
integer, intent(in) :: ele
type(vector_field), intent(in) :: positions
type(vector_field), intent(in) :: source
type(scalar_field), intent(inout) :: curl
real, dimension(ele_ngi(positions, ele)) :: detwei
real, dimension(ele_loc(curl, ele)) :: little_rhs
real, dimension(ele_loc(curl, ele), ele_loc(curl, ele)) :: little_mass
real, dimension(ele_loc(source, ele), ele_ngi(source, ele), positions%dim) :: dshape
type(element_type), pointer :: shape
call transform_to_physical(positions, ele, ele_shape(source, ele), &
& dshape = dshape, detwei = detwei)
shape => ele_shape(curl, ele)
little_mass = shape_shape(shape, shape, detwei)
little_rhs = shape_rhs(shape, ele_2d_curl_at_quad(source, ele, dshape) * detwei)
call solve(little_mass, little_rhs)
call set(curl, ele_nodes(curl, ele), little_rhs)
end subroutine solve_curl_ele
end subroutine calculate_curl_2d
subroutine calculate_curl(state, v_field)
type(state_type), intent(inout) :: state
type(vector_field), intent(inout) :: v_field
character(len = OPTION_PATH_LEN) :: path
integer :: i
type(csr_matrix), pointer :: mass
type(scalar_field), pointer :: masslump
type(vector_field) :: rhs
type(vector_field), pointer :: positions, source_field
ewrite(1, *) "In calculate_curl"
source_field => vector_source_field(state, v_field)
ewrite(2, *) "Calculating curl of field: " // trim(source_field%name)
ewrite(2, *) "On mesh: " // trim(source_field%mesh%name)
ewrite(2, *) "Diagnostic field: " // trim(v_field%name)
ewrite(2, *) "On mesh: " // trim(v_field%mesh%name)
if(source_field%dim /= 3) then
FLExit("Can only calculate curl in 3D")
end if
call check_source_mesh_derivative(source_field, "curl")
positions => extract_vector_field(state, "Coordinate")
path = trim(complete_field_path(v_field%option_path)) // "/algorithm"
if(have_option(trim(path) // "/lump_mass")) then
masslump => get_lumped_mass(state, v_field%mesh)
call zero(v_field)
do i = 1, ele_count(v_field)
call assemble_curl_ele(i, positions, source_field, v_field)
end do
do i = 1, v_field%dim
v_field%val(i,:) = v_field%val(i,:) / masslump%val
end do
else
select case(continuity(v_field))
case(0)
if(.not. have_option(trim(path) // "/solver")) then
FLExit("For continuous curl, must supply solver options when not lumping mass")
end if
mass => get_mass_matrix(state, v_field%mesh)
call allocate(rhs, v_field%dim, v_field%mesh, "CurlRHS")
call zero(rhs)
do i = 1, ele_count(rhs)
call assemble_curl_ele(i, positions, source_field, rhs)
end do
call petsc_solve(v_field, mass, rhs, option_path = path)
call deallocate(rhs)
case(-1)
do i = 1, ele_count(v_field)
call solve_curl_ele(i, positions, source_field, v_field)
end do
case default
ewrite(-1, *) "For mesh continuity: ", continuity(v_field)
FLAbort("Unrecognised mesh continuity")
end select
end if
do i = 1, v_field%dim
ewrite_minmax(v_field%val(i,:))
end do
ewrite(1, *) "Exiting calculate_curl"
contains
subroutine assemble_curl_ele(ele, positions, source, rhs)
integer, intent(in) :: ele
type(vector_field), intent(in) :: positions
type(vector_field), intent(in) :: source
type(vector_field), intent(inout) :: rhs
real, dimension(ele_ngi(positions, ele)) :: detwei
real, dimension(ele_loc(source, ele), ele_ngi(source, ele), positions%dim) :: dshape
call transform_to_physical(positions, ele, ele_shape(source, ele), &
& dshape = dshape, detwei = detwei)
call addto(rhs, ele_nodes(rhs, ele), &
& shape_vector_rhs(ele_shape(rhs, ele), &
& ele_curl_at_quad(source, ele, dshape), detwei))
end subroutine assemble_curl_ele
subroutine solve_curl_ele(ele, positions, source, curl)
integer, intent(in) :: ele
type(vector_field), intent(in) :: positions
type(vector_field), intent(in) :: source
type(vector_field), intent(inout) :: curl
real, dimension(ele_ngi(positions, ele)) :: detwei
real, dimension(ele_loc(curl, ele), curl%dim) :: little_rhs
real, dimension(ele_loc(curl, ele), ele_loc(curl, ele)) :: little_mass
real, dimension(ele_loc(source, ele), ele_ngi(source, ele), positions%dim) :: dshape
type(element_type), pointer :: shape
call transform_to_physical(positions, ele, ele_shape(source, ele), &
& dshape = dshape, detwei = detwei)
shape => ele_shape(curl, ele)
little_mass = shape_shape(shape, shape, detwei)
little_rhs = transpose(shape_vector_rhs(shape, &
& ele_curl_at_quad(source, ele, dshape), detwei))
call solve(little_mass, little_rhs)
call set(curl, ele_nodes(curl, ele), transpose(little_rhs))
end subroutine solve_curl_ele
end subroutine calculate_curl
subroutine calculate_scalar_advection(state, s_field)
type(state_type), intent(in) :: state
type(scalar_field), intent(inout) :: s_field
integer :: stat
type(scalar_field), pointer :: source_field
type(vector_field), pointer :: positions, velocity
source_field => scalar_source_field(state, s_field)
velocity => extract_vector_field(state, "Velocity", stat = stat)
if(stat /= 0) then
ewrite(0, *) "For field " // trim(s_field%name)
ewrite(0, *) "Warning: Calculating advection with no velocity"
call zero(s_field)
return
end if
call check_source_mesh_derivative(source_field, "scalar_advection")
positions => extract_vector_field(state, "Coordinate")
call u_dot_nabla(velocity, source_field, positions, s_field)
end subroutine calculate_scalar_advection
subroutine calculate_vector_advection(state, v_field)
type(state_type), intent(in) :: state
type(vector_field), intent(inout) :: v_field
integer :: stat
type(vector_field), pointer :: positions, source_field, velocity
source_field => vector_source_field(state, v_field)
velocity => extract_vector_field(state, "Velocity", stat = stat)
if(stat /= 0) then
ewrite(0, *) "For field " // trim(v_field%name)
ewrite(0, *) "Warning: Calculating advection with no velocity"
call zero(v_field)
return
end if
call check_source_mesh_derivative(source_field, "vector_advection")
positions => extract_vector_field(state, "Coordinate")
call u_dot_nabla(velocity, source_field, positions, v_field)
end subroutine calculate_vector_advection
subroutine calculate_vector_laplacian(state, v_field)
type(state_type), intent(inout) :: state
type(vector_field), intent(inout) :: v_field
integer :: i, j
type(scalar_field) :: source_field_comp, v_field_comp
type(scalar_field), pointer :: masslump
type(vector_field), pointer :: positions, source_field
ewrite(1, *) "In calculate_vector_laplacian"
ewrite(2, *) "Computing laplacian for field " // trim(v_field%name)
source_field => vector_source_field(state, v_field)
assert(ele_count(source_field) == ele_count(v_field))
assert(source_field%dim == v_field%dim)
do i = 1, source_field%dim
ewrite_minmax(source_field%val(i,:))
end do
call check_source_mesh_derivative(source_field, "vector_laplacian")
positions => extract_vector_field(state, "Coordinate")
assert(ele_count(positions) == ele_count(v_field))
call zero(v_field)
do i = 1, ele_count(v_field)
call assemble_vector_laplacian_ele(i, v_field, positions, source_field)
end do
do i = 1, v_field%dim
v_field_comp = extract_scalar_field(v_field, i)
source_field_comp = extract_scalar_field(source_field, i)
do j = 1, surface_element_count(v_field)
! This could be made more efficent by assembling all components at the
! same time
call assemble_scalar_laplacian_face(j, v_field_comp, positions, source_field_comp)
end do
end do
do i = 1, v_field%dim
ewrite_minmax(v_field%val(i,:))
end do
masslump => get_lumped_mass(state, v_field%mesh)
do i = 1, v_field%dim
v_field%val(i,:) = v_field%val(i,:) / masslump%val
end do
do i = 1, v_field%dim
ewrite_minmax(v_field%val(i,:))
end do
ewrite(1, *) "Exiting calculate_vector_laplacian"
end subroutine calculate_vector_laplacian
subroutine assemble_vector_laplacian_ele(ele, v_field, positions, source_field)
integer, intent(in) :: ele
type(vector_field), intent(inout) :: v_field
type(vector_field), intent(in) :: positions
type(vector_field), intent(in) :: source_field
integer :: i, j
integer, dimension(:), pointer :: element_nodes
real, dimension(ele_ngi(v_field, ele)) :: detwei
real, dimension(source_field%dim, ele_ngi(source_field, ele)) :: grad_gi
real, dimension(ele_loc(source_field, ele), ele_ngi(source_field, ele), source_field%dim) :: dn_t
assert(ele_ngi(positions, ele) == ele_ngi(v_field, ele))
assert(ele_ngi(source_field, ele) == ele_ngi(v_field, ele))
call transform_to_physical(positions, ele, ele_shape(source_field, ele), &
& dshape = dn_t, detwei = detwei)
element_nodes => ele_nodes(v_field, ele)
do i = 1, source_field%dim
do j = 1, source_field%dim
grad_gi(j, :) = matmul(ele_val(source_field, i, ele), dn_t(:, :, j))
end do
call addto(v_field, i, element_nodes, -dshape_dot_vector_rhs(dn_t, grad_gi, detwei))
end do
end subroutine assemble_vector_laplacian_ele
subroutine assemble_scalar_laplacian_face(face, s_field, positions, source_field)
integer, intent(in) :: face
type(scalar_field), intent(inout) :: s_field
type(vector_field), intent(in) :: positions
type(scalar_field), intent(in) :: source_field
integer :: ele, lface, i, j
real, dimension(face_ngi(s_field, face)) :: detwei, grad_sgi_n
real, dimension(positions%dim, face_ngi(s_field, face)) :: grad_sgi, normal
real, dimension(positions%dim, positions%dim, ele_ngi(s_field, face_ele(s_field, face))) :: invj
real, dimension(positions%dim, positions%dim, face_ngi(s_field, face)) :: invj_face
real, dimension(ele_loc(s_field, face_ele(source_field, face)), face_ngi(s_field, face), positions%dim) :: dshape_face
real, dimension(ele_loc(s_field, face_ele(source_field, face))) :: s_ele_val
type(element_type) :: augmented_shape
type(element_type), pointer :: fshape, source_shape, positions_shape
ele = face_ele(s_field, face)
lface = local_face_number(s_field, face)
positions_shape => ele_shape(positions, ele)
fshape => face_shape(s_field, face)
source_shape => ele_shape(source_field, ele)
if(associated(source_shape%dn_s)) then
augmented_shape = source_shape
call incref(augmented_shape)
else
augmented_shape = make_element_shape(positions_shape%loc, source_shape%dim, &
& source_shape%degree, source_shape%quadrature, &
& quad_s = fshape%quadrature)
end if
call transform_facet_to_physical(positions, face, &
& detwei_f = detwei, normal = normal)
call compute_inverse_jacobian( &
& ele_val(positions, ele), positions_shape, &
& invj = invj)
assert(positions_shape%degree == 1)
assert(ele_numbering_family(positions_shape) == FAMILY_SIMPLEX)
invj_face = spread(invj(:, :, 1), 3, size(invj_face, 3))
dshape_face = eval_volume_dshape_at_face_quad(augmented_shape, lface, invj_face)
call deallocate(augmented_shape)
s_ele_val = ele_val(source_field, ele)
forall(i = 1:positions%dim, j = 1:face_ngi(s_field, face))
grad_sgi(i, j) = dot_product(s_ele_val, dshape_face(:, j, i))
end forall
do i = 1, face_ngi(s_field, face)
grad_sgi_n = dot_product(grad_sgi(:, i), normal(:, i))
end do
call addto(s_field, face_global_nodes(s_field, face), shape_rhs(fshape, detwei * grad_sgi_n))
end subroutine assemble_scalar_laplacian_face
subroutine calculate_scalar_laplacian(state, s_field)
type(state_type), intent(inout) :: state
type(scalar_field), intent(inout) :: s_field
integer :: i
type(scalar_field), pointer :: masslump, source_field
type(vector_field), pointer :: positions
ewrite(1, *) "In calculate_scalar_laplacian"
ewrite(2, *) "Computing laplacian for field " // trim(s_field%name)
source_field => scalar_source_field(state, s_field)
assert(ele_count(source_field) == ele_count(s_field))
assert(mesh_dim(source_field) == mesh_dim(s_field))
ewrite_minmax(source_field%val)
call check_source_mesh_derivative(source_field, "scalar_laplacian")
positions => extract_vector_field(state, "Coordinate")
assert(ele_count(positions) == ele_count(s_field))
call zero(s_field)
do i = 1, ele_count(s_field)
call assemble_scalar_laplacian_ele(i, s_field, positions, source_field)
end do
do i = 1, surface_element_count(s_field)
call assemble_scalar_laplacian_face(i, s_field, positions, source_field)
end do
ewrite_minmax(s_field%val)
masslump => get_lumped_mass(state, s_field%mesh)
s_field%val = s_field%val / masslump%val
ewrite_minmax(s_field%val)
ewrite(1, *) "Exiting calculate_scalar_laplacian"
end subroutine calculate_scalar_laplacian
subroutine assemble_scalar_laplacian_ele(ele, s_field, positions, source_field)
integer, intent(in) :: ele
type(scalar_field), intent(inout) :: s_field
type(vector_field), intent(in) :: positions
type(scalar_field), intent(in) :: source_field
integer, dimension(:), pointer :: element_nodes
real, dimension(ele_ngi(s_field, ele)) :: detwei
real, dimension(ele_loc(source_field, ele), ele_ngi(source_field, ele), mesh_dim(source_field)) :: dn_t
assert(ele_ngi(positions, ele) == ele_ngi(s_field, ele))
assert(ele_ngi(source_field, ele) == ele_ngi(s_field, ele))
call transform_to_physical(positions, ele, ele_shape(source_field, ele), &
& dshape = dn_t, detwei = detwei)
element_nodes => ele_nodes(s_field, ele)
call addto(s_field, element_nodes, -dshape_dot_vector_rhs(dn_t, transpose(ele_grad_at_quad(source_field, ele, dn_t)), detwei))
end subroutine assemble_scalar_laplacian_ele
end module differential_operator_diagnostics
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