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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 Engineeringp
! 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 supermesh_assembly
! 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 adaptive_interpolation_module
use fldebug
use field_options
use interpolation_module
use intersection_finder_module
use linked_lists
use state_fields_module
use solvers
use supermesh_construction
use transform_elements
implicit none
private
public :: project_donor_shape_to_supermesh, &
& project_target_shape_to_supermesh, construct_supermesh_ele, &
& extruded_shape_function, generate_supermesh_node_ownership, &
& project_donor_field_to_supermesh, project_target_field_to_supermesh, &
& galerkin_projection_scalars, compute_inner_product_sa
interface generate_supermesh_local_coords
module procedure generate_supermesh_local_coords_ele, &
& generate_supermesh_local_coords_eles
end interface generate_supermesh_local_coords
interface project_donor_shape_to_supermesh
module procedure project_donor_shape_to_supermesh_mesh, &
& project_donor_shape_to_supermesh_shape
end interface project_donor_shape_to_supermesh
interface project_target_shape_to_supermesh
module procedure project_target_shape_to_supermesh_mesh, &
& project_target_shape_to_supermesh_shape
end interface project_target_shape_to_supermesh
interface construct_supermesh_dn
module procedure construct_supermesh_dn_ele, construct_supermesh_dn_eles, &
& construct_supermesh_dn_ele_ele_c
end interface construct_supermesh_dn
interface project_donor_field_to_supermesh
module procedure project_donor_field_to_supermesh_scalar
end interface project_donor_field_to_supermesh
interface project_target_field_to_supermesh
module procedure project_target_field_to_supermesh_scalar
end interface project_target_field_to_supermesh
interface construct_supermesh_ele
module procedure construct_supermesh_ele_single_state, &
& construct_supermesh_ele_multiple_states
end interface construct_supermesh_ele
contains
subroutine generate_supermesh_local_coords_ele(ele, positions, positions_c, base_shape_c, &
& l_coords)
integer, intent(in) :: ele
type(vector_field), intent(in) :: positions
type(vector_field), intent(in) :: positions_c
type(element_type), intent(in) :: base_shape_c
real, dimension(ele_loc(positions, ele), ele_ngi(positions, ele), ele_count(positions_c)) :: l_coords
integer :: ele_c
type(mesh_type) :: positions_c_remap_mesh
type(vector_field) :: positions_c_remap
if(ele_shape(positions_c, ele) == base_shape_c) then
positions_c_remap = positions_c
call incref(positions_c_remap)
else
positions_c_remap_mesh = make_mesh(positions_c%mesh, base_shape_c, continuity = -1, name = "CoordinateRemapMesh")
call allocate(positions_c_remap, positions_c%dim, positions_c_remap_mesh, name = "CoordinateRemap")
call deallocate(positions_c_remap_mesh)
call remap_field(positions_c, positions_c_remap)
end if
do ele_c = 1, size(l_coords, 3)
l_coords(:, :, ele_c) = local_coords(positions, ele, ele_val_at_quad(positions_c_remap, ele_c))
end do
call deallocate(positions_c_remap)
end subroutine generate_supermesh_local_coords_ele
subroutine generate_supermesh_local_coords_eles(eles, positions, positions_c, base_shape_c, &
& l_coords)
type(vector_field), intent(in) :: positions_c
integer, dimension(ele_count(positions_c)), intent(in) :: eles
type(vector_field), intent(in) :: positions
type(element_type), intent(in) :: base_shape_c
real, dimension(ele_loc(positions, 1), ele_ngi(positions, 1), ele_count(positions_c)) :: l_coords
integer :: ele_c
type(mesh_type) :: positions_c_remap_mesh
type(vector_field) :: positions_c_remap
assert(ele_count(positions_c) > 0)
if(ele_shape(positions_c, 1) == base_shape_c) then
positions_c_remap = positions_c
call incref(positions_c_remap)
else
positions_c_remap_mesh = make_mesh(positions_c%mesh, base_shape_c, continuity = -1, name = "CoordinateRemapMesh")
call allocate(positions_c_remap, positions_c%dim, positions_c_remap_mesh, name = "CoordinateRemap")
call deallocate(positions_c_remap_mesh)
call remap_field(positions_c, positions_c_remap)
end if
do ele_c = 1, size(l_coords, 3)
l_coords(:, :, ele_c) = local_coords(positions, eles(ele_c), ele_val_at_quad(positions_c_remap, ele_c))
end do
call deallocate(positions_c_remap)
end subroutine generate_supermesh_local_coords_eles
subroutine project_donor_shape_to_supermesh_mesh(positions_a, shape_mesh, positions_c, &
& shapes_c, form_dn)
type(vector_field), intent(in) :: positions_a
type(mesh_type), intent(in) :: shape_mesh
type(vector_field), intent(in) :: positions_c
type(element_type), dimension(:), allocatable, intent(out) :: shapes_c
! If present and .false., do not form the shape function derivatives
logical, optional, intent(in) :: form_dn
assert(ele_count(shape_mesh) > 0)
call project_donor_shape_to_supermesh(positions_a, ele_shape(shape_mesh, 1), positions_c, &
& shapes_c, form_dn = form_dn)
end subroutine project_donor_shape_to_supermesh_mesh
subroutine project_donor_shape_to_supermesh_shape(positions_a, base_shape_c, positions_c, &
& shapes_c, form_dn)
type(vector_field), intent(in) :: positions_a
type(element_type), target, intent(in) :: base_shape_c
type(vector_field), intent(in) :: positions_c
type(element_type), dimension(:), allocatable, intent(out) :: shapes_c
! If present and .false., do not form the shape function derivatives
logical, optional, intent(in) :: form_dn
integer :: dim, degree, coords, i, j, loc, ngi
integer, dimension(:), pointer :: eles_a
logical :: lform_dn
real, dimension(ele_loc(positions_a, 1), ele_ngi(positions_a, 1), ele_count(positions_c)) :: l_coords
type(quadrature_type), pointer :: quad
type(ele_numbering_type) :: ele_num
lform_dn = .not. present_and_false(form_dn)
eles_a => ele_region_ids(positions_c)
quad => base_shape_c%quadrature
dim = base_shape_c%dim
loc = base_shape_c%loc
ngi = quad%ngi
coords = local_coord_count(base_shape_c)
degree = base_shape_c%degree
if(base_shape_c%degree > 0 .or. lform_dn) then
call generate_supermesh_local_coords(eles_a, positions_a, positions_c, base_shape_c, &
& l_coords)
end if
allocate(shapes_c(ele_count(positions_c)))
do i = 1, size(shapes_c)
ele_num = find_element_numbering(vertices = loc, &
&dimension = dim, degree =&
& degree)
call allocate(shapes_c(i), ele_num=ele_num, ngi = ngi)
shapes_c(i)%degree = degree
shapes_c(i)%numbering => find_element_numbering(vertices = loc, dimension = dim, degree = degree)
shapes_c(i)%quadrature = quad
call incref(quad)
shapes_c(i)%dn = huge(0.0)
assert(.not. associated(shapes_c(i)%dn_s))
assert(.not. associated(shapes_c(i)%n_s))
deallocate(shapes_c(i)%spoly)
nullify(shapes_c(i)%spoly)
deallocate(shapes_c(i)%dspoly)
nullify(shapes_c(i)%dspoly)
select case(base_shape_c%degree)
case(0)
shapes_c(i)%n = 1.0
case(1)
if(ele_numbering_family(base_shape_c) == FAMILY_SIMPLEX) then
shapes_c(i)%n = l_coords(:, :, i)
else
do j = 1, ngi
shapes_c(i)%n(:, j) = eval_shape(base_shape_c, l_coords(:, j, i))
end do
end if
case default
do j = 1, ngi
shapes_c(i)%n(:, j) = eval_shape(base_shape_c, l_coords(:, j, i))
end do
end select
end do
if(lform_dn) then
call construct_supermesh_dn(eles_a, positions_a, positions_c, l_coords, base_shape_c, shapes_c)
end if
end subroutine project_donor_shape_to_supermesh_shape
subroutine project_target_shape_to_supermesh_mesh(ele_b, &
& positions_b, shape_mesh, positions_c, &
& shapes_c, form_dn)
integer, intent(in) :: ele_b
type(vector_field), intent(in) :: positions_b
type(mesh_type), intent(in) :: shape_mesh
type(vector_field), intent(in) :: positions_c
type(element_type), dimension(:), allocatable, intent(out) :: shapes_c
! If present and .false., do not form the shape function derivatives
logical, optional, intent(in) :: form_dn
call project_target_shape_to_supermesh(ele_b, &
& positions_b, ele_shape(shape_mesh, ele_b), positions_c, &
& shapes_c, form_dn = form_dn)
end subroutine project_target_shape_to_supermesh_mesh
subroutine project_target_shape_to_supermesh_shape(ele_b, &
& positions_b, base_shape_c, positions_c, &
& shapes_c, form_dn)
integer, intent(in) :: ele_b
type(vector_field), intent(in) :: positions_b
type(element_type), target, intent(in) :: base_shape_c
type(vector_field), intent(in) :: positions_c
type(element_type), dimension(:), allocatable, intent(out) :: shapes_c
! If present and .false., do not form the shape function derivatives
logical, optional, intent(in) :: form_dn
integer :: dim, degree, coords, i, j, loc, ngi
logical :: lform_dn
real, dimension(ele_loc(positions_b, ele_b), ele_ngi(positions_b, ele_b), ele_count(positions_c)) :: l_coords
type(quadrature_type), pointer :: quad
type(ele_numbering_type) :: ele_num
lform_dn = .not. present_and_false(form_dn)
quad => base_shape_c%quadrature
dim = base_shape_c%dim
loc = base_shape_c%loc
ngi = quad%ngi
coords = local_coord_count(base_shape_c)
degree = base_shape_c%degree
if(base_shape_c%degree > 0 .or. lform_dn) then
call generate_supermesh_local_coords(ele_b, positions_b, positions_c, base_shape_c, &
& l_coords)
end if
allocate(shapes_c(ele_count(positions_c)))
do i = 1, size(shapes_c)
ele_num = find_element_numbering(&
vertices = loc, dimension = dim, degree =&
& degree)
call allocate(shapes_c(i), ele_num, ngi = ngi)
shapes_c(i)%degree = degree
shapes_c(i)%numbering => find_element_numbering(vertices = loc, dimension = dim, degree = degree)
shapes_c(i)%quadrature = quad
call incref(quad)
shapes_c(i)%dn = huge(0.0)
assert(.not. associated(shapes_c(i)%dn_s))
assert(.not. associated(shapes_c(i)%n_s))
deallocate(shapes_c(i)%spoly)
nullify(shapes_c(i)%spoly)
deallocate(shapes_c(i)%dspoly)
nullify(shapes_c(i)%dspoly)
select case(base_shape_c%degree)
case(0)
shapes_c(i)%n = 1.0
case(1)
if(ele_numbering_family(base_shape_c) == FAMILY_SIMPLEX) then
shapes_c(i)%n = l_coords(:, :, i)
else
do j = 1, ngi
shapes_c(i)%n(:, j) = eval_shape(base_shape_c, l_coords(:, j, i))
end do
end if
case default
do j = 1, ngi
shapes_c(i)%n(:, j) = eval_shape(base_shape_c, l_coords(:, j, i))
end do
end select
end do
if(lform_dn) then
call construct_supermesh_dn(ele_b, positions_b, positions_c, l_coords, base_shape_c, shapes_c)
end if
end subroutine project_target_shape_to_supermesh_shape
subroutine construct_supermesh_dn_ele(ele, positions, positions_c, l_coords, base_shape, shapes_c)
integer, intent(in) :: ele
type(vector_field), intent(in) :: positions
type(vector_field), intent(in) :: positions_c
real, dimension(ele_loc(positions, ele), ele_ngi(positions, ele), ele_count(positions_c)), intent(in) :: l_coords
type(element_type), intent(in) :: base_shape
type(element_type), dimension(ele_count(positions_c)), intent(inout) :: shapes_c
integer :: i, j, k
real, dimension(positions%dim, positions%dim, ele_ngi(positions, ele)) :: invj
real, dimension(positions_c%dim, positions_c%dim, ele_ngi(positions, ele)) :: j_c
if(base_shape%degree == 0) then
! This case is nice and easy
do i = 1, size(shapes_c)
shapes_c(i)%dn = 0.0
end do
return
end if
! We need to form dn such that a transform_to_physical gives us the
! transformed shape function derivatives at the quadrature points of the
! supermesh element. A simple eval_dshape(...) isn't going to cut it, so we:
call compute_inverse_jacobian(ele_val(positions, ele), ele_shape(positions, ele), invj)
do i = 1, size(shapes_c)
assert(ele_ngi(positions, ele) == ele_ngi(positions_c, i))
! First evaluate the transformed shape function derivatives at the
! quadrature points of the supermesh element (what we want a
! transform_to_physical to give us)
do j = 1, size(shapes_c(i)%dn, 2)
shapes_c(i)%dn(:, j, :) = eval_dshape_transformed(base_shape, l_coords(:, j, i), invj)
end do
! Then apply the inverse transform on the supermesh element
call compute_jacobian(ele_val(positions_c, i), ele_shape(positions_c, i), j_c)
forall(j = 1:size(shapes_c(i)%dn, 1), k = 1:size(shapes_c(i)%dn, 2))
shapes_c(i)%dn(j, k, :) = matmul(j_c(:, :, k), shapes_c(i)%dn(j, k, :))
end forall
end do
end subroutine construct_supermesh_dn_ele
subroutine construct_supermesh_dn_eles(eles, positions, positions_c, l_coords, base_shape, shapes_c)
type(vector_field), intent(in) :: positions_c
integer, dimension(ele_count(positions_c)), intent(in) :: eles
type(vector_field), intent(in) :: positions
real, dimension(ele_loc(positions, 1), ele_ngi(positions, 1), ele_count(positions_c)), intent(in) :: l_coords
type(element_type), intent(in) :: base_shape
type(element_type), dimension(ele_count(positions_c)), intent(inout) :: shapes_c
integer :: ele_c
do ele_c = 1, size(shapes_c)
call construct_supermesh_dn(eles(ele_c), ele_c, positions, positions_c, l_coords(:, :, ele_c), base_shape, shapes_c(ele_c))
end do
end subroutine construct_supermesh_dn_eles
subroutine construct_supermesh_dn_ele_ele_c(ele, ele_c, positions, positions_c, l_coords, base_shape, shape_c)
integer, intent(in) :: ele
integer, intent(in) :: ele_c
type(vector_field), intent(in) :: positions
type(vector_field), intent(in) :: positions_c
real, dimension(ele_loc(positions, ele), ele_ngi(positions, ele)), intent(in) :: l_coords
type(element_type), intent(in) :: base_shape
type(element_type), intent(inout) :: shape_c
integer :: i, j
real, dimension(positions%dim, positions%dim, ele_ngi(positions, ele)) :: invj
real, dimension(positions_c%dim, positions_c%dim, ele_ngi(positions, ele)) :: j_c
assert(ele_ngi(positions, ele) == ele_ngi(positions_c, ele_c))
if(base_shape%degree == 0) then
! This case is nice and easy
shape_c%dn = 0.0
return
end if
! We need to form dn such that a transform_to_physical gives us the
! transformed shape function derivatives at the quadrature points of the
! supermesh element. A simple eval_dshape(...) isn't going to cut it, so we:
call compute_inverse_jacobian(ele_val(positions, ele), ele_shape(positions, ele), invj)
! First evaluate the transformed shape function derivatives at the
! quadrature points of the supermesh element (what we want a
! transform_to_physical to give us)
do i = 1, size(shape_c%dn, 2)
shape_c%dn(:, i, :) = eval_dshape_transformed(base_shape, l_coords(:, i), invj)
end do
! Then apply the inverse transform on the supermesh element
call compute_jacobian(ele_val(positions_c, ele_c), ele_shape(positions_c, ele_c), j_c)
forall(i = 1:size(shape_c%dn, 1), j = 1:size(shape_c%dn, 2))
shape_c%dn(i, j, :) = matmul(j_c(:, :, j), shape_c%dn(i, j, :))
end forall
end subroutine construct_supermesh_dn_ele_ele_c
function extruded_shape_function(ele_surf, ele_vol, positions_surf, positions_vol, shape_surf, shape_vol, &
& form_dn) result(shape_surf_ext)
!!< Extrude a surface shape function
integer, intent(in) :: ele_surf
integer, intent(in) :: ele_vol
type(vector_field), intent(in) :: positions_surf
type(vector_field), intent(in) :: positions_vol
type(element_type), intent(in) :: shape_surf
type(element_type), target, intent(in) :: shape_vol
! If present and .false., do not form the shape function derivatives
logical, optional, intent(in) :: form_dn
type(ele_numbering_type) :: ele_num
type(element_type) :: shape_surf_ext
integer :: coords, degree, dim, i, loc, ngi
real, dimension(positions_vol%dim - 1, ele_ngi(positions_vol, ele_vol)) :: positions_gi_vol
real, dimension(ele_loc(positions_surf, ele_surf), ele_ngi(positions_vol, ele_vol)) :: l_coords
logical :: lform_dn
type(quadrature_type), pointer :: quad
lform_dn = .not. present_and_false(form_dn)
quad => shape_vol%quadrature
dim = positions_vol%dim
loc = shape_surf%loc
ngi = quad%ngi
coords = local_coord_count(shape_vol)
degree = shape_surf%degree
ele_num = &
&find_element_numbering(vertices = loc, &
&dimension = dim - 1, degree = degree)
! Note that the extruded surface mesh shape function takes its number of
! quadrature points from the volume shape function
call allocate_element(shape_surf_ext, ele_num=ele_num, ngi = ngi)
shape_surf_ext%degree = degree
shape_surf_ext%numbering => find_element_numbering(vertices = loc, dimension = dim - 1, degree = degree)
shape_surf_ext%quadrature = quad
call incref(quad)
shape_surf_ext%dn = huge(0.0)
assert(.not. associated(shape_surf_ext%dn_s))
assert(.not. associated(shape_surf_ext%n_s))
deallocate(shape_surf_ext%spoly)
nullify(shape_surf_ext%spoly)
deallocate(shape_surf_ext%dspoly)
nullify(shape_surf_ext%dspoly)
select case(degree)
case(0)
shape_surf_ext%n = 1.0
case(1)
do i = 1, dim - 1
positions_gi_vol(i, :) = ele_val_at_quad(positions_vol, ele_vol, i)
end do
l_coords = local_coords(positions_surf, ele_surf, positions_gi_vol)
if(ele_numbering_family(shape_surf) == FAMILY_SIMPLEX) then
shape_surf_ext%n = l_coords
else
do i = 1, ngi
shape_surf_ext%n(:, i) = eval_shape(shape_surf, l_coords(:, i))
end do
end if
case default
do i = 1, dim - 1
positions_gi_vol(i, :) = ele_val_at_quad(positions_vol, ele_vol, i)
end do
l_coords = local_coords(positions_surf, ele_surf, positions_gi_vol)
do i = 1, ngi
shape_surf_ext%n(:, i) = eval_shape(shape_surf, l_coords(:, i))
end do
end select
if(lform_dn) then
FLAbort("Shape function derivative extrude not yet available")
end if
end function extruded_shape_function
subroutine generate_supermesh_node_ownership(positions_c, mesh_c, map)
type(vector_field), intent(in) :: positions_c
type(mesh_type), intent(in) :: mesh_c
integer, dimension(:), allocatable, intent(out) :: map
integer :: i
assert(ele_count(mesh_c) > 0)
allocate(map(ele_count(mesh_c) * ele_loc(mesh_c, 1)))
do i = 1, ele_count(mesh_c)
map(ele_nodes(mesh_c, i)) = ele_region_id(positions_c, i)
end do
end subroutine generate_supermesh_node_ownership
function project_donor_field_to_supermesh_scalar(positions_a, positions_c, field_a) result(field_a_c)
!!< Project a donor field onto the supermesh
type(vector_field), intent(in) :: positions_a
type(vector_field), intent(in) :: positions_c
type(scalar_field), intent(in) :: field_a
type(scalar_field) :: field_a_c
integer, dimension(:), allocatable :: map
type(mesh_type) :: mesh_a_c
type(vector_field) :: positions_c_remap
! Allocate the supermesh field
assert(ele_count(field_a) > 0)
mesh_a_c = make_mesh(positions_c%mesh, ele_shape(field_a, 1), continuity = -1)
call allocate(field_a_c, mesh_a_c, name = trim(field_a%name) // "Supermesh")
call deallocate(mesh_a_c)
! Generate the map from nodes in the supermesh field to elements in the
! donor field
call generate_supermesh_node_ownership(positions_c, mesh_a_c, map)
! We need the "target" positions handed to linear_interpolation to share its
! mesh with the supermesh field
if(positions_c%mesh == mesh_a_c) then
positions_c_remap = positions_c
call incref(positions_c_remap)
else
call allocate(positions_c_remap, positions_c%dim, mesh_a_c, name = "CoordinateRemap")
call remap_field(positions_c, positions_c_remap)
end if
! Project - consistent interpolation onto the supermesh is lossless
call linear_interpolation(field_a, positions_a, field_a_c, positions_c_remap, map = map)
! Cleanup
deallocate(map)
call deallocate(positions_c_remap)
end function project_donor_field_to_supermesh_scalar
function project_target_field_to_supermesh_scalar(ele_b, positions_b, positions_c, field_b) result(field_b_c)
!!< Project a target field onto the supermesh
integer, intent(in) :: ele_b
type(vector_field), intent(in) :: positions_b
type(vector_field), intent(in) :: positions_c
type(scalar_field), intent(in) :: field_b
type(scalar_field) :: field_b_c
type(mesh_type) :: mesh_b_c
type(vector_field) :: positions_c_remap
! Allocate the supermesh field
assert(ele_count(field_b) > 0)
mesh_b_c = make_mesh(positions_c%mesh, ele_shape(field_b, 1), continuity = -1)
call allocate(field_b_c, mesh_b_c, name = trim(field_b%name) // "Supermesh")
call deallocate(mesh_b_c)
! We need the "target" positions handed to linear_interpolation to share its
! mesh with the supermesh field
if(positions_c%mesh == mesh_b_c) then
positions_c_remap = positions_c
call incref(positions_c_remap)
else
call allocate(positions_c_remap, positions_c%dim, mesh_b_c, name = "CoordinateRemap")
call remap_field(positions_c, positions_c_remap)
end if
! Project - consistent interpolation onto the supermesh is lossless
assert(ele_count(mesh_b_c) > 0)
call linear_interpolation(field_b, positions_b, field_b_c, positions_c_remap, map = spread(ele_b, 1, ele_count(mesh_b_c) * ele_loc(mesh_b_c, 1)))
! Cleanup
call deallocate(positions_c_remap)
end function project_target_field_to_supermesh_scalar
subroutine construct_supermesh_ele_single_state(ele_b, positions_a, positions_b, map_ba, &
& state_a, shape_mesh_b, &
& state_c, positions_c, shapes_c, &
& form_dn, single_mesh_state)
integer, intent(in) :: ele_b
type(vector_field), intent(in) :: positions_a
type(vector_field), intent(in) :: positions_b
type(ilist), intent(in) :: map_ba
type(state_type), intent(in) :: state_a
type(mesh_type), intent(in) :: shape_mesh_b
type(state_type), intent(out) :: state_c
type(vector_field), intent(out) :: positions_c
type(element_type), dimension(:), allocatable, intent(out) :: shapes_c
! If present and .false., do not form the shape function derivatives
logical, optional, intent(in) :: form_dn
! If present and .true., assume state_a contains fields all on the same mesh
logical, optional, intent(in) :: single_mesh_state
type(state_type), dimension(1) :: states_a, states_c
states_a = (/state_a/)
call construct_supermesh_ele(ele_b, positions_a, positions_b, map_ba, &
& states_a, shape_mesh_b, &
& states_c, positions_c, shapes_c, &
& form_dn = form_dn, mesh_sorted_states = single_mesh_state)
state_c = states_c(1)
end subroutine construct_supermesh_ele_single_state
subroutine construct_supermesh_ele_multiple_states(ele_b, positions_a, positions_b, map_ba, &
& states_a, shape_mesh_b, &
& states_c, positions_c, shapes_c, &
& form_dn, mesh_sorted_states)
integer, intent(in) :: ele_b
type(vector_field), intent(in) :: positions_a
type(vector_field), intent(in) :: positions_b
type(ilist), intent(in) :: map_ba
type(state_type), dimension(:), intent(in) :: states_a
type(mesh_type), intent(in) :: shape_mesh_b
type(state_type), dimension(size(states_a)), intent(out) :: states_c
type(vector_field), intent(out) :: positions_c
type(element_type), dimension(:), allocatable, intent(out) :: shapes_c
! If present and .false., do not form the shape function derivatives
logical, optional, intent(in) :: form_dn
! If present and .true., assume states_a is sorted by meshes
logical, optional, intent(in) :: mesh_sorted_states
integer :: i, j, stat
integer, dimension(:), allocatable :: map
type(element_type), pointer :: shape_c
type(mesh_type) :: mesh_c
type(mesh_type), pointer :: mesh_a
type(scalar_field), pointer :: s_field_a
type(scalar_field) :: s_field_c
type(state_type), dimension(:), allocatable :: sorted_states_a, sorted_states_c
type(tensor_field), pointer :: t_field_a
type(tensor_field) :: t_field_c
type(vector_field), pointer :: v_field_a
type(vector_field) :: v_field_c
! Supermesh
shape_c => ele_shape(positions_b, ele_b)
call construct_supermesh(positions_b, ele_b, positions_a, map_ba, shape_c, positions_c)
call insert(states_c, positions_c, "Coordinate")
call insert(states_c, positions_c%mesh, "CoordinateMesh")
! Generate the supermesh shape functions. These are the shape functions of
! the target mesh projected onto the supermesh.
call project_target_shape_to_supermesh(ele_b, &
& positions_b, shape_mesh_b, positions_c, &
& shapes_c, form_dn = form_dn)
! Generate the supermesh fields. These are the fields of the donor mesh
! projected onto the supermesh.
if(present_and_true(mesh_sorted_states)) then
do i = 1, size(states_a)
mesh_a => single_state_mesh(states_a(i), stat = stat)
if(stat /= 0) cycle
assert(ele_count(mesh_a) > 0)
shape_c => ele_shape(mesh_a, 1)
mesh_c = make_mesh(positions_c%mesh, shape_c, continuity = -1, name = mesh_a%name)
call insert(states_c(i), mesh_c, mesh_c%name)
do j = 1, scalar_field_count(states_a(i))
s_field_a => extract_scalar_field(states_a(i), j)
! We set all fields to have type FIELD_TYPE_NORMAL to keep the
! interpolation routines happy. Alternatively, we could modify the
! linear interpolation code to handle FIELD_TYPE_CONSTANT fields.
call allocate(s_field_c, mesh_c, s_field_a%name, field_type = FIELD_TYPE_NORMAL)
call insert(states_c(i), s_field_c, s_field_c%name)
call deallocate(s_field_c)
end do
do j = 1, vector_field_count(states_a(i))
v_field_a => extract_vector_field(states_a(i), j)
if(trim(v_field_a%name) == "Coordinate") cycle
call allocate(v_field_c, v_field_a%dim, mesh_c, v_field_a%name, field_type = FIELD_TYPE_NORMAL)
call insert(states_c(i), v_field_c, v_field_c%name)
call deallocate(v_field_c)
end do
do j = 1, tensor_field_count(states_a(i))
t_field_a => extract_tensor_field(states_a(i), j)
call allocate(t_field_c, mesh_c, t_field_a%name, field_type = FIELD_TYPE_NORMAL)
call insert(states_c(i), t_field_c, t_field_c%name)
call deallocate(t_field_c)
end do
call generate_supermesh_node_ownership(positions_c, mesh_c, map)
call linear_interpolation(states_a(i), states_c(i), map = map)
deallocate(map)
call deallocate(mesh_c)
end do
else
do i = 1, size(states_a)
do j = 1, mesh_count(states_a(i))
mesh_a => extract_mesh(states_a(i), j)
assert(ele_count(mesh_a) > 0)
shape_c => ele_shape(mesh_a, 1)
mesh_c = make_mesh(positions_c%mesh, shape_c, continuity = -1, name = mesh_a%name)
call insert(states_c(i), mesh_c, mesh_c%name)
call deallocate(mesh_c)
end do
do j = 1, scalar_field_count(states_a(i))
s_field_a => extract_scalar_field(states_a(i), j)
mesh_c = extract_mesh(states_c(i), s_field_a%mesh%name)
call allocate(s_field_c, mesh_c, s_field_a%name, field_type = FIELD_TYPE_NORMAL)
call insert(states_c(i), s_field_c, s_field_c%name)
call deallocate(s_field_c)
end do
do j = 1, vector_field_count(states_a(i))
v_field_a => extract_vector_field(states_a(i), j)
if(trim(v_field_a%name) == "Coordinate") cycle
mesh_c = extract_mesh(states_c(i), v_field_a%mesh%name)
call allocate(v_field_c, v_field_a%dim, mesh_c, v_field_a%name, field_type = FIELD_TYPE_NORMAL)
call insert(states_c(i), v_field_c, v_field_c%name)
call deallocate(v_field_c)
end do
do j = 1, tensor_field_count(states_a(i))
t_field_a => extract_tensor_field(states_a(i), j)
mesh_c = extract_mesh(states_c(i), t_field_a%mesh%name)
call allocate(t_field_c, mesh_c, t_field_a%name, field_type = FIELD_TYPE_NORMAL)
call insert(states_c(i), t_field_c, t_field_c%name)
call deallocate(t_field_c)
end do
end do
call sort_states_by_mesh(states_a, sorted_states_a)
call sort_states_by_mesh(states_c, sorted_states_c)
do i = 1, size(sorted_states_c)
mesh_c = single_state_mesh(sorted_states_c(i), stat = stat)
if(stat == 0) then
call generate_supermesh_node_ownership(positions_c, mesh_c, map)
call linear_interpolation(sorted_states_a(i), sorted_states_c(i), map = map)
deallocate(map)
end if
call deallocate(sorted_states_a(i))
call deallocate(sorted_states_c(i))
end do
deallocate(sorted_states_a)
deallocate(sorted_states_c)
end if
end subroutine construct_supermesh_ele_multiple_states
function single_state_mesh(state, stat) result(mesh)
type(state_type), intent(in) :: state
integer, optional, intent(out) :: stat
type(mesh_type), pointer :: mesh
type(scalar_field), pointer :: s_field
type(vector_field), pointer :: v_field
type(tensor_field), pointer :: t_field
if(present(stat)) stat = 0
if(scalar_field_count(state) > 0) then
s_field => extract_scalar_field(state, 1)
mesh => s_field%mesh
else if(vector_field_count(state) > 0) then
v_field => extract_vector_field(state, 1)
mesh => v_field%mesh
else if(tensor_field_count(state) > 0) then
t_field => extract_tensor_field(state, 1)
mesh => t_field%mesh
else
if(present(stat)) then
stat = 1
return
else
ewrite(-1, *) "For state " // trim(state%name)
FLAbort("No mesh found")
end if
end if
end function single_state_mesh
subroutine galerkin_projection_scalars(states_a, positions_a, states_b, positions_b)
type(state_type), dimension(:), intent(in) :: states_a
type(vector_field), intent(in) :: positions_a
type(state_type), dimension(size(states_a)), intent(inout) :: states_b
type(vector_field), intent(in) :: positions_b
integer :: ele_b, ele_c, field_count, i, j
type(csr_matrix), pointer :: mass_matrix
type(element_type), dimension(:), allocatable :: shapes_c
type(ilist), dimension(ele_count(positions_b)) :: map_ba
type(mesh_type), pointer :: mesh_b
type(scalar_field), dimension(:), allocatable :: rhs
type(scalar_field), pointer :: s_field_b
type(state_type) :: state_c
type(vector_field) :: positions_c
call intersector_set_dimension(positions_b%dim)
map_ba = intersection_finder(positions_b, positions_a)
do i = 1, size(states_b)
field_count = scalar_field_count(states_b(i))
if(field_count == 0) cycle
s_field_b => extract_scalar_field(states_b(i), 1)
mesh_b => s_field_b%mesh
select case(mesh_b%continuity)
case(0)
mass_matrix => get_mass_matrix(states_b(i), mesh_b)
allocate(rhs(scalar_field_count(states_b(i))))
do j = 1, field_count
call allocate(rhs(j), mesh_b, "GalerkinProjectionRHS" // int2str(j))
call zero(rhs(j))
end do
do ele_b = 1, ele_count(positions_b)
call construct_supermesh_ele(ele_b, positions_a, positions_b, map_ba(ele_b), &
& states_a(i), mesh_b, &
& state_c, positions_c, shapes_c, &
& form_dn = .false., single_mesh_state = .true.)
do ele_c = 1, ele_count(positions_c)
call assemble_galerkin_projection_scalars_ele(ele_c, ele_b, positions_c, state_c, shapes_c(ele_c), rhs)
end do
call deallocate(state_c)
call deallocate(positions_c)
do j = 1, size(shapes_c)
call deallocate(shapes_c(j))
end do
deallocate(shapes_c)
end do
do j = 1, field_count
s_field_b => extract_scalar_field(states_b(i), j)
call petsc_solve(s_field_b, mass_matrix, rhs(j), &
& option_path = trim(complete_field_path(s_field_b%option_path)) // "/galerkin_projection/continuous")
call deallocate(rhs(j))
end do
deallocate(rhs)
case(-1)
do ele_b = 1, ele_count(positions_b)
call construct_supermesh_ele(ele_b, positions_a, positions_b, map_ba(ele_b), &
& states_a(i), mesh_b, &
& state_c, positions_c, shapes_c, &
& form_dn = .false., single_mesh_state = .true.)
call solve_galerkin_projection_scalars_dg_ele(ele_b, positions_b, positions_c, mesh_b, states_b(i), state_c, shapes_c)
call deallocate(state_c)
call deallocate(positions_c)
do j = 1, size(shapes_c)
call deallocate(shapes_c(j))
end do
deallocate(shapes_c)
end do
case default
ewrite(-1, "(a,i0)") "For mesh continuity ", mesh_b%continuity
FLAbort("Unrecognised mesh continuity")
end select
end do
do i = 1, size(map_ba)
call deallocate(map_ba(i))
end do
end subroutine galerkin_projection_scalars
subroutine assemble_galerkin_projection_scalars_ele(ele, ele_out, positions, state, shape, rhs)
integer, intent(in) :: ele
integer, intent(in) :: ele_out
type(vector_field), intent(in) :: positions
type(state_type), intent(in) :: state
type(element_type), intent(in) :: shape
type(scalar_field), intent(inout), dimension(:) :: rhs
integer :: field
real, dimension(ele_ngi(positions, ele)) :: detwei
type(scalar_field), pointer :: s_field
assert(size(rhs) == scalar_field_count(state))
call transform_to_physical(positions, ele, detwei = detwei)
do field = 1, size(rhs)
s_field => extract_scalar_field(state, field)
call addto(rhs(field), ele_nodes(rhs(field), ele_out), &
& shape_rhs(shape, detwei * ele_val_at_quad(s_field, ele)))
end do
end subroutine assemble_galerkin_projection_scalars_ele
subroutine solve_galerkin_projection_scalars_dg_ele(ele_b, positions_b, positions_c, mesh_b, state_b, state_c, shapes_c)
integer, intent(in) :: ele_b
type(vector_field), intent(in) :: positions_b
type(vector_field), intent(in) :: positions_c
type(mesh_type), intent(in) :: mesh_b
type(state_type), intent(in) :: state_b
type(state_type), intent(in) :: state_c
type(element_type), dimension(ele_count(positions_c)), intent(in) :: shapes_c
integer :: i, j
real, dimension(ele_loc(mesh_b, ele_b), scalar_field_count(state_c)) :: little_rhs
real, dimension(ele_ngi(positions_b, ele_b)) :: detwei
real, dimension(ele_loc(mesh_b, ele_b), ele_loc(mesh_b, ele_b)) :: little_mass
type(scalar_field), pointer :: s_field_b
call transform_to_physical(positions_b, ele_b, detwei = detwei)
little_mass = shape_shape(ele_shape(mesh_b, ele_b), ele_shape(mesh_b, ele_b), detwei)
little_rhs = 0.0
do i = 1, scalar_field_count(state_b)
do j = 1, ele_count(positions_c)
call assemble_galerkin_projection_scalars_dg_ele(j, positions_c, state_c, shapes_c(j), little_rhs)
end do
end do
call solve(little_mass, little_rhs)
do i = 1, scalar_field_count(state_b)
s_field_b => extract_scalar_field(state_b, i)
call set(s_field_b, ele_nodes(s_field_b, ele_b), little_rhs(:, i))
end do
end subroutine solve_galerkin_projection_scalars_dg_ele
subroutine assemble_galerkin_projection_scalars_dg_ele(ele, positions, state, shape, little_rhs)
integer, intent(in) :: ele
type(vector_field), intent(in) :: positions
type(state_type), intent(in) :: state
type(element_type), intent(in) :: shape
real, dimension(shape%loc, scalar_field_count(state)), intent(inout) :: little_rhs
integer :: i
real, dimension(ele_ngi(positions, ele)) :: detwei
type(scalar_field), pointer :: s_field
call transform_to_physical(positions, ele, detwei = detwei)
do i = 1, scalar_field_count(state)
s_field => extract_scalar_field(state, i)
little_rhs(:, i) = little_rhs(:, i) + shape_rhs(shape, detwei * ele_val_at_quad(s_field, ele))
end do
end subroutine assemble_galerkin_projection_scalars_dg_ele
function compute_inner_product_sa(positions_a, positions_b, a, b) result(val)
type(vector_field), intent(in) :: positions_a
type(vector_field), intent(in) :: positions_b
type(scalar_field), intent(in) :: a
type(scalar_field), intent(in) :: b
real :: val
integer :: ele_b, ele_c
type(ilist), dimension(ele_count(positions_b)) :: map_ba
type(scalar_field) :: a_c, b_c
type(vector_field) :: positions_c
val = 0.0
call intersector_set_dimension(positions_a%dim)
map_ba = intersection_finder(positions_b, positions_a)
do ele_b = 1, ele_count(positions_b)
! Supermesh
call construct_supermesh(positions_b, ele_b, positions_a, map_ba(ele_b), ele_shape(positions_b, ele_b), positions_c)
if(ele_count(positions_c) == 0) then
call deallocate(positions_c)
cycle
end if
! Project a onto the supermesh
a_c = project_donor_field_to_supermesh(positions_a, positions_c, a)
! Project b onto the supermesh
b_c = project_target_field_to_supermesh(ele_b, positions_b, positions_c, b)
do ele_c = 1, ele_count(positions_c)
! Compute the contribution to the inner product
call add_inner_product_ele(ele_c, positions_c, a_c, b_c, val)
end do
! Cleanup
call deallocate(positions_c)
call deallocate(a_c)
call deallocate(b_c)
end do
do ele_b = 1, ele_count(positions_b)
call deallocate(map_ba(ele_b))
end do
end function compute_inner_product_sa
subroutine add_inner_product_ele(ele, positions, a, b, val)
integer, intent(in) :: ele
type(vector_field), intent(in) :: positions
type(scalar_field), intent(in) :: a
type(scalar_field), intent(in) :: b
real, intent(inout) :: val
real, dimension(ele_ngi(positions, ele)) :: detwei
call transform_to_physical(positions, ele, detwei = detwei)
val = val + dot_product(ele_val(a, ele), matmul(&
& shape_shape(ele_shape(a, ele), ele_shape(b, ele), detwei), ele_val(b, ele)))
end subroutine add_inner_product_ele
end module supermesh_assembly
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