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!=== COPYRIGHT AND LICENSE STATEMENT ===
!
! This file is part of the TensorProductMultigrid code.
!
! (c) The copyright relating to this work is owned jointly by the
! Crown, Met Office and NERC [2014]. However, it has been created
! with the help of the GungHo Consortium, whose members are identified
! at https://puma.nerc.ac.uk/trac/GungHo/wiki .
!
! Main Developer: Eike Mueller
!
! TensorProductMultigrid 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, either version 3 of the
! License, or (at your option) any later version.
!
! TensorProductMultigrid 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 TensorProductMultigrid (see files COPYING and COPYING.LESSER).
! If not, see <http://www.gnu.org/licenses/>.
!
!=== COPYRIGHT AND LICENSE STATEMENT ===
!==================================================================
!
! Discretisation module of the model problem
!
!
! -omega2 * (d^2/dx^2 + d^2/dy^2 + lambda2 * d^2/dz^2 ) u
! + delta u = RHS
! [Cartesian]
!
! or
!
! -omega2 * (laplace_{2d} + lambda2/r^2 d/dr (r^2 d/dr)) u
! + delta u = RHS
! [Spherical]
!
! We use a cell centered finite volume discretisation with
! The equation is discretised either in a unit cube or on 1/6th
! of a cubed sphere grid.
!
! The vertical grid spacing is not necessarily uniform and can
! be chosen by specifying the vertical grid in a vector.
!
! The following boundary conditions are used:
!
! * Dirichlet in the horizontal
! * Neumann in the vertical
!
! For delta = 0 the operator reduces to the Poisson operator.
!
! Eike Mueller, University of Bath, Feb 2012
!
!==================================================================
module discretisation
use parameters
use messages
use datatypes
use communication
use mpi
implicit none
private
type model_parameters
real(kind=rl) :: omega2 ! omega^2
real(kind=rl) :: lambda2 ! lambda^2
real(kind=rl) :: delta ! delta
end type model_parameters
! --- Stencil ---
!
! Grid traversal direction in SOR
integer, parameter :: DIRECTION_FORWARD = 1
integer, parameter :: DIRECTION_BACKWARD = 2
! Ordering in SOR
! Lexicographic ordering
integer, parameter :: ORDERING_LEX = 1
! Red-black ordering
integer, parameter :: ORDERING_RB = 2
type smoother_parameters
! smoother
integer :: smoother
! relaxation parameter
real(kind=rl) :: rho
! ordering of degrees of freedom
integer :: ordering
end type smoother_parameters
! Allowed smoothers
integer, parameter :: SMOOTHER_LINE_SOR = 3
integer, parameter :: SMOOTHER_LINE_SSOR = 4
integer, parameter :: SMOOTHER_LINE_JAC = 6
! Number of levels
integer :: nlev
! Grid parameters
type(grid_parameters) :: grid_param
! Model parameters
type(model_parameters) :: model_param
! Smoother parameters
type(smoother_parameters) :: smoother_param
! Arrays for measuring the residual reduction
real(kind=rl), allocatable :: log_resreduction(:)
integer, allocatable :: nsmooth_total(:)
! Data structure for storing the vertical discretisation
type vertical_coefficients
real(kind=rl), allocatable :: a(:)
real(kind=rl), allocatable :: b(:)
real(kind=rl), allocatable :: c(:)
real(kind=rl), allocatable :: d(:)
end type vertical_coefficients
! Stoarge for vertical coefficients
type(vertical_coefficients) :: vert_coeff
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public::discretisation_initialise_mnh
public::discretisation_initialise
public::discretisation_finalise
public::smooth
public::line_SOR
public::line_SSOR
public::line_jacobi
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public::calculate_residual_mnh
public::calculate_residual
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public::apply_mnh
public::apply
public::model_parameters
public::smoother_parameters
public::volume_of_element
public::SMOOTHER_LINE_SOR
public::SMOOTHER_LINE_SSOR
public::SMOOTHER_LINE_JAC
public::DIRECTION_FORWARD
public::DIRECTION_BACKWARD
public::ORDERING_LEX
public::ORDERING_RB
contains
!==================================================================
! Initialise module
!==================================================================
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subroutine discretisation_initialise_mnh(grid_param_in, &
model_param_in, &
smoother_param_in, &
nlev_in)
implicit none
type(grid_parameters), intent(in) :: grid_param_in
type(model_parameters), intent(in) :: model_param_in
type(smoother_parameters), intent(in) :: smoother_param_in
integer, intent(in) :: nlev_in
integer :: k
grid_param = grid_param_in
model_param = model_param_in
smoother_param = smoother_param_in
nlev = nlev_in
allocate(log_resreduction(nlev))
allocate(nsmooth_total(nlev))
log_resreduction(:) = 0.0_rl
nsmooth_total(:) = 0
allocate(r_grid(grid_param%nz+1))
if (grid_param%graded) then
do k=1,grid_param%nz+1
r_grid(k) = grid_param%H*(1.0_rl*(k-1.0_rl)/grid_param%nz)**2
end do
else
do k=1,grid_param%nz+1
r_grid(k) = grid_param%H*(1.0_rl*(k-1.0_rl)/grid_param%nz)
end do
end if
#ifdef CARTESIANGEOMETRY
#else
r_grid(:) = 1.0_rl + r_grid(:)
#endif
! Allocate arrays for vertical discretisation matrices
! and calculate matrix entries
allocate(vert_coeff%a(grid_param%nz))
allocate(vert_coeff%b(grid_param%nz))
allocate(vert_coeff%c(grid_param%nz))
allocate(vert_coeff%d(grid_param%nz))
call construct_vertical_coeff_mnh()
end subroutine discretisation_initialise_mnh
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subroutine discretisation_initialise(grid_param_in, &
model_param_in, &
smoother_param_in, &
nlev_in)
implicit none
type(grid_parameters), intent(in) :: grid_param_in
type(model_parameters), intent(in) :: model_param_in
type(smoother_parameters), intent(in) :: smoother_param_in
integer, intent(in) :: nlev_in
integer :: k
grid_param = grid_param_in
model_param = model_param_in
smoother_param = smoother_param_in
nlev = nlev_in
allocate(log_resreduction(nlev))
allocate(nsmooth_total(nlev))
log_resreduction(:) = 0.0_rl
nsmooth_total(:) = 0
allocate(r_grid(grid_param%nz+1))
if (grid_param%graded) then
do k=1,grid_param%nz+1
r_grid(k) = grid_param%H*(1.0_rl*(k-1.0_rl)/grid_param%nz)**2
end do
else
do k=1,grid_param%nz+1
r_grid(k) = grid_param%H*(1.0_rl*(k-1.0_rl)/grid_param%nz)
end do
end if
#ifdef CARTESIANGEOMETRY
#else
r_grid(:) = 1.0_rl + r_grid(:)
#endif
! Allocate arrays for vertical discretisation matrices
! and calculate matrix entries
allocate(vert_coeff%a(grid_param%nz))
allocate(vert_coeff%b(grid_param%nz))
allocate(vert_coeff%c(grid_param%nz))
allocate(vert_coeff%d(grid_param%nz))
call construct_vertical_coeff()
end subroutine discretisation_initialise
!==================================================================
! Finalise module
!==================================================================
subroutine discretisation_finalise()
implicit none
integer :: level
real(kind=rl) :: rho_avg
#ifdef MEASURESMOOTHINGRATE
if (i_am_master_mpi) then
write(STDOUT,'("Average smoothing rates:")')
do level=nlev,1,-1
if (nsmooth_total(level) > 0) then
rho_avg = exp(log_resreduction(level)/nsmooth_total(level))
else
rho_avg = 1.0_rl
end if
write(STDOUT,'("rho_{avg}(",I3,") = ",E10.4," ( ",I5," x )")') &
level, rho_avg, nsmooth_total(level)
end do
end if
#endif
deallocate(log_resreduction)
deallocate(nsmooth_total)
deallocate(r_grid)
! Deallocate storage for vertical discretisation matrices
deallocate(vert_coeff%a)
deallocate(vert_coeff%b)
deallocate(vert_coeff%c)
deallocate(vert_coeff%d)
end subroutine discretisation_finalise
!==================================================================
! Construct alpha_{i',j'} and |T_{ij}| needed for the
! horizontal stencil
! ( alpha_{i+1,j},
! alpha_{i-1,j},
! alpha_{i,j+1},
! alpha_{i,j-1},
! alpha_{ij})
! (ix,iy) are LOCAL indices of the grid boxes, which are
! converted to global indices
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!==================================================================
subroutine construct_alpha_T_mnh(grid_param,ix,iy,alpha_T,Tij)
implicit none
type(grid_parameters), intent(in) :: grid_param
integer, intent(in) :: ix
integer, intent(in) :: iy
real(kind=rl), intent(inout), dimension(5) :: alpha_T
real(kind=rl), intent(out) :: Tij
real(kind=rl) :: h, rho_i, sigma_j
#ifdef CARTESIANGEOMETRY
h = grid_param%L/grid_param%n
! Cartesian coefficients
Tij = h**2
if (ix == grid_param%n) then
alpha_T(1) = 2.0_rl
else
alpha_T(1) = 1.0_rl
end if
if (ix == 1) then
alpha_T(2) = 2.0_rl
else
alpha_T(2) = 1.0_rl
end if
if (iy == grid_param%n) then
alpha_T(3) = 2.0_rl
else
alpha_T(3) = 1.0_rl
end if
if (iy == 1) then
alpha_T(4) = 2.0_rl
else
alpha_T(4) = 1.0_rl
end if
#else
! Coefficients in cubed sphere geometry
! (rho_i,sigma_j) \in [-1,1] x [-1,1] are the coordinates of the
! cubed sphere segment
h = 2.0_rl/grid_param%n
Tij = volume_of_element(ix,iy,grid_param)
rho_i = 2.0_rl*(1.0_rl*ix-0.5_rl)/grid_param%n-1.0_rl
sigma_j = 2.0_rl*(1.0_rl*iy-0.5_rl)/grid_param%n-1.0_rl
! alpha_{i+1,j}
if (ix == grid_param%n) then
alpha_T(1) = 2.0_rl*DSQRT((1.0_rl+(rho_i+0.25_rl*h)**2)/(1.0_rl+sigma_j**2))
else
alpha_T(1) = DSQRT((1.0_rl+(rho_i+0.5_rl*h)**2)/(1.0_rl+sigma_j**2))
end if
! alpha_{i-1,j}
if (ix == 1) then
alpha_T(2) = 2.0_rl*DSQRT((1.0_rl+(rho_i-0.25_rl*h)**2)/(1.0_rl+sigma_j**2))
else
alpha_T(2) = DSQRT((1.0_rl+(rho_i-0.5_rl*h)**2)/(1.0_rl+sigma_j**2))
end if
! alpha_{i,j+1}
if (iy == grid_param%n) then
alpha_T(3) = 2.0_rl*DSQRT((1.0_rl+(sigma_j+0.25_rl*h)**2)/(1.0_rl+rho_i**2))
else
alpha_T(3) = DSQRT((1.0_rl+(sigma_j+0.5_rl*h)**2)/(1.0_rl+rho_i**2))
end if
! alpha_{i,j-1}
if (iy == 1) then
alpha_T(4) = 2.0_rl*DSQRT((1.0_rl+(sigma_j-0.25_rl*h)**2)/(1.0_rl+rho_i**2))
else
alpha_T(4) = DSQRT((1.0_rl+(sigma_j-0.5_rl*h)**2)/(1.0_rl+rho_i**2))
end if
#endif
alpha_T(5) = alpha_T(1) + alpha_T(2) + alpha_T(3) + alpha_T(4)
end subroutine construct_alpha_T_mnh
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!==================================================================
subroutine construct_alpha_T(grid_param,ix,iy,alpha_T,Tij)
implicit none
type(grid_parameters), intent(in) :: grid_param
integer, intent(in) :: ix
integer, intent(in) :: iy
real(kind=rl), intent(inout), dimension(5) :: alpha_T
real(kind=rl), intent(out) :: Tij
real(kind=rl) :: h, rho_i, sigma_j
#ifdef CARTESIANGEOMETRY
h = grid_param%L/grid_param%n
! Cartesian coefficients
Tij = h**2
if (ix == grid_param%n) then
alpha_T(1) = 2.0_rl
else
alpha_T(1) = 1.0_rl
end if
if (ix == 1) then
alpha_T(2) = 2.0_rl
else
alpha_T(2) = 1.0_rl
end if
if (iy == grid_param%n) then
alpha_T(3) = 2.0_rl
else
alpha_T(3) = 1.0_rl
end if
if (iy == 1) then
alpha_T(4) = 2.0_rl
else
alpha_T(4) = 1.0_rl
end if
#else
! Coefficients in cubed sphere geometry
! (rho_i,sigma_j) \in [-1,1] x [-1,1] are the coordinates of the
! cubed sphere segment
h = 2.0_rl/grid_param%n
Tij = volume_of_element(ix,iy,grid_param)
rho_i = 2.0_rl*(1.0_rl*ix-0.5_rl)/grid_param%n-1.0_rl
sigma_j = 2.0_rl*(1.0_rl*iy-0.5_rl)/grid_param%n-1.0_rl
! alpha_{i+1,j}
if (ix == grid_param%n) then
alpha_T(1) = 2.0_rl*DSQRT((1.0_rl+(rho_i+0.25_rl*h)**2)/(1.0_rl+sigma_j**2))
else
alpha_T(1) = DSQRT((1.0_rl+(rho_i+0.5_rl*h)**2)/(1.0_rl+sigma_j**2))
end if
! alpha_{i-1,j}
if (ix == 1) then
alpha_T(2) = 2.0_rl*DSQRT((1.0_rl+(rho_i-0.25_rl*h)**2)/(1.0_rl+sigma_j**2))
else
alpha_T(2) = DSQRT((1.0_rl+(rho_i-0.5_rl*h)**2)/(1.0_rl+sigma_j**2))
end if
! alpha_{i,j+1}
if (iy == grid_param%n) then
alpha_T(3) = 2.0_rl*DSQRT((1.0_rl+(sigma_j+0.25_rl*h)**2)/(1.0_rl+rho_i**2))
else
alpha_T(3) = DSQRT((1.0_rl+(sigma_j+0.5_rl*h)**2)/(1.0_rl+rho_i**2))
end if
! alpha_{i,j-1}
if (iy == 1) then
alpha_T(4) = 2.0_rl*DSQRT((1.0_rl+(sigma_j-0.25_rl*h)**2)/(1.0_rl+rho_i**2))
else
alpha_T(4) = DSQRT((1.0_rl+(sigma_j-0.5_rl*h)**2)/(1.0_rl+rho_i**2))
end if
#endif
alpha_T(5) = alpha_T(1) + alpha_T(2) + alpha_T(3) + alpha_T(4)
end subroutine construct_alpha_T
!==================================================================
! Construct coefficients of tridiagonal matrix A_T
! describing the coupling in the vertical direction and the
! diagonal matrix diag(d)
!==================================================================
Juan Escobar
committed
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subroutine construct_vertical_coeff_mnh()
implicit none
real(kind=rl) :: a_k_tmp, b_k_tmp, c_k_tmp, d_k_tmp
real(kind=rl) :: omega2, lambda2, delta, vol_r, surface_k, surface_kp1
integer :: k
omega2 = model_param%omega2
lambda2 = model_param%lambda2
delta = model_param%delta
do k = 1, grid_param%nz
#ifdef CARTESIANGEOMETRY
vol_r = r_grid(k+1)-r_grid(k)
surface_k = 1.0_rl
surface_kp1 = 1.0_rl
#else
vol_r = (r_grid(k+1)**3 - r_grid(k)**3)/3.0_rl
surface_k = r_grid(k)**2
surface_kp1 = r_grid(k+1)**2
#endif
! Diagonal element
a_k_tmp = delta*vol_r
! off diagonal elements
! Boundary conditions
! Top
if (k == grid_param%nz) then
if (grid_param%vertbc == VERTBC_DIRICHLET) then
b_k_tmp = - 2.0_rl * omega2*lambda2 &
* surface_kp1/(r_grid(k+1)-r_grid(k))
else
b_k_tmp = 0.0_rl
end if
else
b_k_tmp = - 2.0_rl*omega2*lambda2 &
* surface_kp1/(r_grid(k+2)-r_grid(k))
end if
! Bottom
if (k == 1) then
if (grid_param%vertbc == VERTBC_DIRICHLET) then
c_k_tmp = - 2.0_rl * omega2*lambda2 &
* surface_k/(r_grid(k+1)-r_grid(k))
else
c_k_tmp = 0.0_rl
end if
else
c_k_tmp = - 2.0_rl * omega2 * lambda2 &
* surface_k/(r_grid(k+1)-r_grid(k-1))
end if
! Diagonal matrix d_k
d_k_tmp = - omega2 * (r_grid(k+1)-r_grid(k))
vert_coeff%a(k) = a_k_tmp/d_k_tmp
vert_coeff%b(k) = b_k_tmp/d_k_tmp
vert_coeff%c(k) = c_k_tmp/d_k_tmp
vert_coeff%d(k) = d_k_tmp
end do
end subroutine construct_vertical_coeff_mnh
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subroutine construct_vertical_coeff()
implicit none
real(kind=rl) :: a_k_tmp, b_k_tmp, c_k_tmp, d_k_tmp
real(kind=rl) :: omega2, lambda2, delta, vol_r, surface_k, surface_kp1
integer :: k
omega2 = model_param%omega2
lambda2 = model_param%lambda2
delta = model_param%delta
do k = 1, grid_param%nz
#ifdef CARTESIANGEOMETRY
vol_r = r_grid(k+1)-r_grid(k)
surface_k = 1.0_rl
surface_kp1 = 1.0_rl
#else
vol_r = (r_grid(k+1)**3 - r_grid(k)**3)/3.0_rl
surface_k = r_grid(k)**2
surface_kp1 = r_grid(k+1)**2
#endif
! Diagonal element
a_k_tmp = delta*vol_r
! off diagonal elements
! Boundary conditions
! Top
if (k == grid_param%nz) then
if (grid_param%vertbc == VERTBC_DIRICHLET) then
b_k_tmp = - 2.0_rl * omega2*lambda2 &
* surface_kp1/(r_grid(k+1)-r_grid(k))
else
b_k_tmp = 0.0_rl
end if
else
b_k_tmp = - 2.0_rl*omega2*lambda2 &
* surface_kp1/(r_grid(k+2)-r_grid(k))
end if
! Bottom
if (k == 1) then
if (grid_param%vertbc == VERTBC_DIRICHLET) then
c_k_tmp = - 2.0_rl * omega2*lambda2 &
* surface_k/(r_grid(k+1)-r_grid(k))
else
c_k_tmp = 0.0_rl
end if
else
c_k_tmp = - 2.0_rl * omega2 * lambda2 &
* surface_k/(r_grid(k+1)-r_grid(k-1))
end if
! Diagonal matrix d_k
d_k_tmp = - omega2 * (r_grid(k+1)-r_grid(k))
vert_coeff%a(k) = a_k_tmp/d_k_tmp
vert_coeff%b(k) = b_k_tmp/d_k_tmp
vert_coeff%c(k) = c_k_tmp/d_k_tmp
vert_coeff%d(k) = d_k_tmp
end do
end subroutine construct_vertical_coeff
!==================================================================
! Calculate local residual r = b - A.u
!==================================================================
Juan Escobar
committed
subroutine calculate_residual_mnh(level,m,b,u,r)
implicit none
integer, intent(in) :: level
integer, intent(in) :: m
type(scalar3d), intent(in) :: b
type(scalar3d), intent(inout) :: u
type(scalar3d), intent(inout) :: r
integer :: ix,iy,iz
! r <- A.u
call apply_mnh(u,r)
! r <- b - r = b - A.u
do ix=u%icompx_min,u%icompx_max
do iy=u%icompy_min,u%icompy_max
do iz=1,u%grid_param%nz
r%s(iz,iy,ix) = b%s(iz,iy,ix) - r%s(iz,iy,ix)
end do
end do
end do
end subroutine calculate_residual_mnh
subroutine calculate_residual(level,m,b,u,r)
implicit none
integer, intent(in) :: level
integer, intent(in) :: m
type(scalar3d), intent(in) :: b
type(scalar3d), intent(inout) :: u
type(scalar3d), intent(inout) :: r
integer :: ix,iy,iz
! r <- A.u
call apply(u,r)
! r <- b - r = b - A.u
do ix=u%icompx_min,u%icompx_max
do iy=u%icompy_min,u%icompy_max
do iz=1,u%grid_param%nz
r%s(iz,iy,ix) = b%s(iz,iy,ix) - r%s(iz,iy,ix)
end do
end do
end do
end subroutine calculate_residual
!==================================================================
! Apply operator v = A.u
!==================================================================
Juan Escobar
committed
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subroutine apply_mnh(u,v)
implicit none
type(scalar3d), intent(in) :: u
type(scalar3d), intent(inout) :: v
real(kind=rl), dimension(5) :: alpha_T
real(kind=rl) :: Tij
real(kind=rl) :: a_k, b_k, c_k, d_k
integer :: ix,iy,iz
real(kind=rl) :: tmp
do ix=u%icompx_min,u%icompx_max
do iy=u%icompy_min,u%icompy_max
! Construct horizontal part of stencil
call construct_alpha_T_mnh(u%grid_param, &
ix+u%ix_min-1, &
iy+u%iy_min-1, &
alpha_T,Tij)
do iz=1,u%grid_param%nz
a_k = vert_coeff%a(iz)
b_k = vert_coeff%b(iz)
c_k = vert_coeff%c(iz)
d_k = vert_coeff%d(iz)
tmp = ((a_k-b_k-c_k)*Tij - alpha_T(5)) * u%s(iz,iy,ix)
if (iz < grid_param%nz) then
tmp = tmp + b_k*Tij * u%s(iz+1,iy,ix)
end if
if (iz > 1) then
tmp = tmp + c_k*Tij * u%s(iz-1,iy,ix)
end if
tmp = tmp + alpha_T(1) * u%s(iz, iy ,ix+1) &
+ alpha_T(2) * u%s(iz, iy ,ix-1) &
+ alpha_T(3) * u%s(iz, iy+1,ix ) &
+ alpha_T(4) * u%s(iz, iy-1,ix )
v%s(iz,iy,ix) = d_k*tmp
end do
end do
end do
end subroutine apply_mnh
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subroutine apply(u,v)
implicit none
type(scalar3d), intent(in) :: u
type(scalar3d), intent(inout) :: v
real(kind=rl), dimension(5) :: alpha_T
real(kind=rl) :: Tij
real(kind=rl) :: a_k, b_k, c_k, d_k
integer :: ix,iy,iz
real(kind=rl) :: tmp
do ix=u%icompx_min,u%icompx_max
do iy=u%icompy_min,u%icompy_max
! Construct horizontal part of stencil
call construct_alpha_T(u%grid_param, &
ix+u%ix_min-1, &
iy+u%iy_min-1, &
alpha_T,Tij)
do iz=1,u%grid_param%nz
a_k = vert_coeff%a(iz)
b_k = vert_coeff%b(iz)
c_k = vert_coeff%c(iz)
d_k = vert_coeff%d(iz)
tmp = ((a_k-b_k-c_k)*Tij - alpha_T(5)) * u%s(iz,iy,ix)
if (iz < grid_param%nz) then
tmp = tmp + b_k*Tij * u%s(iz+1,iy,ix)
end if
if (iz > 1) then
tmp = tmp + c_k*Tij * u%s(iz-1,iy,ix)
end if
tmp = tmp + alpha_T(1) * u%s(iz, iy ,ix+1) &
+ alpha_T(2) * u%s(iz, iy ,ix-1) &
+ alpha_T(3) * u%s(iz, iy+1,ix ) &
+ alpha_T(4) * u%s(iz, iy-1,ix )
v%s(iz,iy,ix) = d_k*tmp
end do
end do
end do
end subroutine apply
!==================================================================
!==================================================================
!
! S M O O T H E R S
!
!==================================================================
!==================================================================
!==================================================================
! Perform nsmooth smoother iterations
!==================================================================
subroutine smooth(level,m,nsmooth,direction,b,u)
implicit none
integer, intent(in) :: level
integer, intent(in) :: m
integer, intent(in) :: nsmooth ! Number of smoothing steps
integer, intent(in) :: direction ! Direction
type(scalar3d), intent(inout) :: b ! RHS
type(scalar3d), intent(inout) :: u ! solution vector
integer :: i
real(kind=rl) :: log_res_initial, log_res_final
type(scalar3d) :: r
integer :: halo_size
integer :: nlocal, nz
#ifdef MEASURESMOOTHINGRATE
r%ix_min = u%ix_min
r%ix_max = u%ix_max
r%iy_min = u%iy_min
r%iy_max = u%iy_max
r%icompx_min = u%icompx_min
r%icompx_max = u%icompx_max
r%icompy_min = u%icompy_min
r%icompy_max = u%icompy_max
r%halo_size = u%halo_size
r%isactive = u%isactive
r%grid_param = u%grid_param
nlocal = r%ix_max-r%ix_min+1
halo_size = r%halo_size
nz = r%grid_param%nz
allocate(r%s(0:nz+1, &
1-halo_size:nlocal+halo_size, &
1-halo_size:nlocal+halo_size))
call calculate_residual(level,m,b,u,r)
log_res_initial = log(l2norm(r))
#endif
! Carry out nsmooth iterations of the smoother
if (smoother_param%smoother == SMOOTHER_LINE_SOR) then
do i=1,nsmooth
call line_SOR(level,m,direction,b,u)
end do
else if (smoother_param%smoother == SMOOTHER_LINE_SSOR) then
do i=1,nsmooth
call line_SSOR(level,m,direction,b,u)
end do
else if (smoother_param%smoother == SMOOTHER_LINE_JAC) then
do i=1,nsmooth
call line_jacobi(level,m,b,u)
end do
end if
#ifdef MEASURESMOOTHINGRATE
call calculate_residual(level,m,b,u,r)
log_res_final = log(l2norm(r))
log_resreduction(level) = log_resreduction(level) &
+ (log_res_final - log_res_initial)
nsmooth_total(level) = nsmooth_total(level) + nsmooth
deallocate(r%s)
#endif
end subroutine smooth
!==================================================================
! SOR line smoother
!==================================================================
subroutine line_SOR(level,m,direction,b,u)
implicit none
integer, intent(in) :: level
integer, intent(in) :: m
integer, intent(in) :: direction
type(scalar3d), intent(in) :: b
type(scalar3d), intent(inout) :: u
real(kind=rl), allocatable :: r(:)
integer :: nz, nlocal
real(kind=rl), allocatable :: c(:), utmp(:)
integer :: ixmin(5), ixmax(5), dix
integer :: iymin(5), iymax(5), diy
integer :: color
integer :: nsweeps, isweep
integer :: ordering
real(kind=rl) :: rho
integer, dimension(4) :: send_requests, recv_requests
integer :: tmp, ierr
integer :: iblock
logical :: overlap_comms
ordering = smoother_param%ordering
rho = smoother_param%rho
nz = u%grid_param%nz
! Create residual vector
allocate(r(nz))
! Allocate memory for auxiliary vectors for Thomas algorithm
allocate(c(nz))
allocate(utmp(nz))
nlocal = u%ix_max-u%ix_min+1
#ifdef OVERLAPCOMMS
overlap_comms = (nlocal > 2)
#else
overlap_comms = .false.
#endif
! Block 1 (N)
ixmin(1) = 1
ixmax(1) = nlocal
iymin(1) = 1
iymax(1) = 1
! Block 2 (S)
ixmin(2) = 1
ixmax(2) = nlocal
iymin(2) = nlocal
iymax(2) = nlocal
! Block 3 (W)
ixmin(3) = 1
ixmax(3) = 1
iymin(3) = 2
iymax(3) = nlocal-1
! Block 4 (E)
ixmin(4) = nlocal
ixmax(4) = nlocal
iymin(4) = 2
iymax(4) = nlocal-1
! Block 5 (INTERIOR)
if (overlap_comms) then
ixmin(5) = 2
ixmax(5) = nlocal-1
iymin(5) = 2
iymax(5) = nlocal-1
else
! If there are no interior cells, do not overlap
! communications and calculations, just loop over interior cells
ixmin(5) = 1
ixmax(5) = nlocal
iymin(5) = 1
iymax(5) = nlocal
end if
dix = +1
diy = +1
color = 1
! When iteration backwards over the grid, reverse the direction
if (direction == DIRECTION_BACKWARD) then
do iblock = 1, 5
tmp = ixmax(iblock)
ixmax(iblock) = ixmin(iblock)
ixmin(iblock) = tmp
tmp = iymax(iblock)
iymax(iblock) = iymin(iblock)
iymin(iblock) = tmp
end do
dix = -1
diy = -1
color = 0
end if
nsweeps = 1
if (ordering == ORDERING_LEX) then
nsweeps = 1
else if (ordering == ORDERING_RB) then
nsweeps = 2
end if
do isweep = 1, nsweeps
if (overlap_comms) then
! Loop over cells next to boundary (iblock = 1,...,4)
do iblock = 1, 4
call loop_over_grid(iblock)
end do
! Initiate halo exchange
call ihaloswap(level,m,u,send_requests,recv_requests)
end if
! Loop over INTERIOR cells
iblock = 5
call loop_over_grid(iblock)
if (overlap_comms) then
if (m > 0) then
call mpi_waitall(4,recv_requests, MPI_STATUSES_IGNORE, ierr)
end if
else
call haloswap(level,m,u)
end if
color = 1-color
end do
! Free memory again
deallocate(r)
deallocate(c)
deallocate(utmp)
contains
!------------------------------------------------------------------
! Loop over grid, for a given block
!------------------------------------------------------------------
subroutine loop_over_grid(iblock)
implicit none
integer, intent(in) :: iblock
integer :: ix,iy,iz
do ix=ixmin(iblock),ixmax(iblock),dix
do iy=iymin(iblock),iymax(iblock),diy
if (ordering == ORDERING_RB) then
if (mod((ix+u%ix_min)+(iy+u%iy_min),2) .ne. color) cycle
end if
call apply_tridiag_solve(ix,iy,r,c,b, &
u%s(1:nz,iy ,ix+1), &
u%s(1:nz,iy ,ix-1), &
u%s(1:nz,iy+1,ix ), &
u%s(1:nz,iy-1,ix ), &
utmp)
! Add to field with overrelaxation-factor
do iz=1,nz
u%s(iz,iy,ix) = (1.0_rl-rho)*u%s(iz,iy,ix) + rho*utmp(iz)
end do
end do
end do
end subroutine loop_over_grid
end subroutine line_SOR
!==================================================================
! SSOR line smoother
!==================================================================
subroutine line_SSOR(level,m,direction,b,u)
implicit none
integer, intent(in) :: level
integer, intent(in) :: m
integer, intent(in) :: direction
type(scalar3d), intent(in) :: b
type(scalar3d), intent(inout) :: u
if (direction == DIRECTION_FORWARD) then
call line_SOR(level,m,DIRECTION_FORWARD,b,u)
call line_SOR(level,m,DIRECTION_BACKWARD,b,u)
else
call line_SOR(level,m,DIRECTION_BACKWARD,b,u)
call line_SOR(level,m,DIRECTION_FORWARD,b,u)
end if
end subroutine line_SSOR
!==================================================================
! Jacobi line smoother
!==================================================================
subroutine line_Jacobi(level,m,b,u)
implicit none
integer, intent(in) :: level
integer, intent(in) :: m
type(scalar3d), intent(in) :: b
type(scalar3d), intent(inout) :: u
real(kind=rl), allocatable :: r(:)
integer :: ix,iy,iz, nz
real(kind=rl), dimension(5) :: alpha_T
real(kind=rl), allocatable :: c(:), utmp(:)
real(kind=rl), allocatable :: u0(:,:,:)
integer :: nlocal, halo_size
real(kind=rl) :: rho
logical :: overlap_comms
integer, dimension(4) :: send_requests, recv_requests
integer :: ixmin(5), ixmax(5)
integer :: iymin(5), iymax(5)
integer :: iblock, ierr
! Set optimal smoothing parameter on each level
rho = 2.0_rl/(2.0_rl+4.0_rl*model_param%omega2*u%grid_param%n**2/(1.0_rl+4.0_rl*model_param%omega2*u%grid_param%n**2))
nz = u%grid_param%nz
nlocal = u%ix_max -u%ix_min + 1
halo_size = u%halo_size
#ifdef OVERLAPCOMMS
overlap_comms = (nlocal > 2)
#else
overlap_comms = .false.
#endif
! Block 1 (N)
ixmin(1) = 1
ixmax(1) = nlocal
iymin(1) = 1
iymax(1) = 1
! Block 2 (S)
ixmin(2) = 1
ixmax(2) = nlocal
iymin(2) = nlocal
iymax(2) = nlocal
! Block 3 (W)
ixmin(3) = 1
ixmax(3) = 1
iymin(3) = 2
iymax(3) = nlocal-1
! Block 4 (E)
ixmin(4) = nlocal
ixmax(4) = nlocal
iymin(4) = 2
iymax(4) = nlocal-1
! Block 5 (INTERIOR)
if (overlap_comms) then
ixmin(5) = 2
ixmax(5) = nlocal-1
iymin(5) = 2
iymax(5) = nlocal-1
else
! If there are no interior cells, do not overlap
! communications and calculations, just loop over interior cells
ixmin(5) = 1
ixmax(5) = nlocal
iymin(5) = 1
iymax(5) = nlocal
end if
! Temporary vector
allocate(u0(0:u%grid_param%nz+1, &
1-halo_size:nlocal+halo_size, &
1-halo_size:nlocal+halo_size) )
u0(:,:,:) = u%s(:,:,:)
! Create residual vector
allocate(r(nz))
! Allocate memory for auxiliary vectors for Thomas algorithm
allocate(c(nz))
allocate(utmp(nz))
! Loop over grid
if (overlap_comms) then
! Loop over cells next to boundary (iblock = 1,...,4)
do iblock = 1, 4
call loop_over_grid(iblock)
end do
! Initiate halo exchange
call ihaloswap(level,m,u,send_requests,recv_requests)
end if
! Loop over INTERIOR cells
iblock = 5
call loop_over_grid(iblock)
if (overlap_comms) then
if (m > 0) then
call mpi_waitall(4,recv_requests, MPI_STATUSES_IGNORE, ierr)