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filter_mod.f90
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filter_mod.f90
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module filter_mod
!
!.. Use Statements ..
use module_kind_types
!
use generic_types_mod, only : matrix
!
use ovar, only : Filter_Option,Limiter_Filter_Option
use ovar, only : Filter_etac, Limiter_Filter_etac
use ovar, only : Filter_Order, Limiter_Filter_Order
use ovar, only : Filter_Alpha, Limiter_Filter_Alpha
use ovar, only : Filter_eps, Limiter_Filter_eps
!
implicit none
!
private
!
!
! Module Public Procedures
!
public :: init_filter_matrices
public :: filter_usp
public :: filter_memory_usage
!
! Module public arrays
!
! filter_t : derived type that contains various types of filtering matrices
!
type, public :: filter_t
! exponential : matrix to filter a polynomial by multiplying the polynomial
! modes by an exponentially decreasing function
type(matrix), allocatable :: exponential
! limiter : filter matrix to use as a limiter for troubled cells
type(matrix), allocatable :: limiter
! cutoff : matrix to filter a polynomial by
! cutting-off (zeroing) higher modes
type(matrix), allocatable :: cutoff(:)
end type filter_t
!
! filter : filter matrices for all combinations of cell geometry and
! cell order that are possible in the current simulation
!
type(filter_t), public, save, target, allocatable :: filter(:,:)
!
! Cutoff_Filter_Option : method used to compute the cutoff filter matrices
! = 1 : use a tensor product of the 1D filter with the filter cutoff
! based on the order of the 1D polynomial
! = 2 : the filter cutoff is based on total polynomial order,
! i.e., for the polynomial (x^a * y^b * z*c),
! the total polynomial order = a+b+c
!
integer, parameter :: Cutoff_Filter_Option = 1
!integer, parameter :: Cutoff_Filter_Option = 2
!
contains
!
!###############################################################################
!
subroutine init_filter_matrices()
!
!.. Use Statements ..
use order_mod, only : geom_solpts
use order_mod, only : n_min_geom,n_max_geom
use order_mod, only : n_min_order,n_max_order
use quadrature_mod, only : geom_is_used
use vandermonde_mod, only : vand
!
!.. Local Scalars ..
integer :: ierr,gmin,gmax,omin,omax
integer :: this_geom,this_order,npts
integer :: cutoff_order
character(len=200) :: array_name
!
!.. Local Pointers ..
type(matrix), pointer :: filt
!real(wp), pointer, contiguous :: fmat(:,:)
real(wp), pointer :: fmat(:,:)
!real(wp), pointer, contiguous :: vmat(:,:)
real(wp), pointer :: vmat(:,:)
!real(wp), pointer, contiguous :: vmat_inv(:,:)
real(wp), pointer :: vmat_inv(:,:)
!
!.. Local Parameters ..
character(len=*), parameter :: pname = "init_filter_matrices"
!
continue
!
call debug_timer(entering_procedure,pname)
!
! Initialize the local pointers to disassociated
!
filt => null()
fmat => null()
vmat => null()
vmat_inv => null()
!
! Allocate the filter array
!
gmin = n_min_geom
gmax = n_max_geom
omin = n_min_order
omax = n_max_order
!
allocate ( filter(gmin:gmax,omin:omax) , stat=ierr , errmsg=error_message )
call alloc_error(pname,"filter",1,__LINE__,__FILE__,ierr,error_message)
!
geom_loop: do this_geom = gmin,gmax
!
if (.not. geom_is_used(this_geom)) cycle geom_loop
if (all(this_geom /= Geom_Valid)) cycle geom_loop
if (this_geom == Geom_Node) cycle geom_loop
!
order_loop: do this_order = omin,omax
!
! Get the number of solution points for this cell
!
npts = geom_solpts(this_geom,this_order)
!
! Assign local pointers as aliases to simplify the code
!
vmat => vand(this_geom,this_order)%modal2nodal%mat
vmat_inv => vand(this_geom,this_order)%nodal2modal%mat
!
! ###################################
! ##### 1. Exponential Filter #####
! ###################################
!
! Allocate the exponential filter matrix
!
allocate ( filter(this_geom,this_order)%exponential , &
stat=ierr , errmsg=error_message )
write (array_name,1) Geom_Name(this_geom),this_order,"exponential"
call alloc_error(pname,array_name,1,__LINE__,__FILE__,ierr,error_message)
!
! Assign local pointers as aliases to simplify the code
!
filt => filter(this_geom,this_order)%exponential
!
! Allocate the exponential filter matrix
!
allocate ( filt%mat(1:npts,1:npts) , &
source=zero , stat=ierr , errmsg=error_message )
write (array_name,1) Geom_Name(this_geom),this_order,"exponential%mat"
call alloc_error(pname,array_name,1,__LINE__,__FILE__,ierr,error_message)
!
! Assign local pointers as aliases to simplify the code
!
fmat => filt%mat
!
! Compute the filter matrices depending on geometry type
!
select case (this_geom)
case (Geom_Edge)
!
fmat = FilterMatrix_Edge( vmat , vmat_inv )
!
case (Geom_Tria)
!
fmat = FilterMatrix_Tria( vmat , vmat_inv )
!
case (Geom_Quad)
!
fmat = FilterMatrix_Quad( vmat , vmat_inv )
!
case (Geom_Tetr)
!
fmat = FilterMatrix_Tetr( vmat , vmat_inv )
!
case (Geom_Pyra)
!
fmat = FilterMatrix_Pyra( vmat , vmat_inv )
!
case (Geom_Pris)
!
fmat = FilterMatrix_Pris( vmat , vmat_inv )
!
case (Geom_Hexa)
!
fmat = FilterMatrix_Hexa( vmat , vmat_inv )
!
case default
!
write (error_message,100)
call stop_gfr(stop_mpi,pname,__LINE__,__FILE__,error_message)
!
end select
!
! Remove all associations of the local pointers before continuing
!
if (associated(fmat)) fmat => null()
if (associated(filt)) filt => null()
!
! ###############################
! ##### 2. Limiter Filter #####
! ###############################
!
! Allocate the limiter filter matrix
!
allocate ( filter(this_geom,this_order)%limiter , &
stat=ierr , errmsg=error_message )
write (array_name,1) Geom_Name(this_geom),this_order,"limiter"
call alloc_error(pname,array_name,1,__LINE__,__FILE__,ierr,error_message)
!
! Assign local pointers as aliases to simplify the code
!
filt => filter(this_geom,this_order)%limiter
!
! Allocate the limiter filter matrix
!
allocate ( filt%mat(1:npts,1:npts) , &
source=zero , stat=ierr , errmsg=error_message )
write (array_name,1) Geom_Name(this_geom),this_order,"limiter%mat"
call alloc_error(pname,array_name,1,__LINE__,__FILE__,ierr,error_message)
!
! Assign local pointers as aliases to simplify the code
!
fmat => filt%mat
!
! Compute the filter matrices depending on geometry type
!
select case (this_geom)
case (Geom_Edge)
!
fmat = FilterMatrix_Edge( vmat , vmat_inv , cutoff_order=-1 )
!
case (Geom_Tria)
!
fmat = FilterMatrix_Tria( vmat , vmat_inv , cutoff_order=-1 )
!
case (Geom_Quad)
!
fmat = FilterMatrix_Quad( vmat , vmat_inv , cutoff_order=-1 )
!
case (Geom_Tetr)
!
fmat = FilterMatrix_Tetr( vmat , vmat_inv , cutoff_order=-1 )
!
case (Geom_Pyra)
!
fmat = FilterMatrix_Pyra( vmat , vmat_inv , cutoff_order=-1 )
!
case (Geom_Pris)
!
fmat = FilterMatrix_Pris( vmat , vmat_inv , cutoff_order=-1 )
!
case (Geom_Hexa)
!
fmat = FilterMatrix_Hexa( vmat , vmat_inv , cutoff_order=-1 )
!
case default
!
write (error_message,100)
call stop_gfr(stop_mpi,pname,__LINE__,__FILE__,error_message)
!
end select
!
! Remove all associations of the local pointers before continuing
!
if (associated(fmat)) fmat => null()
if (associated(filt)) filt => null()
!
! ################################
! ##### 3. Cut-Off Filters #####
! ################################
!
! Allocate the cutoff filter matrix
!
allocate ( filter(this_geom,this_order)%cutoff(1:this_order) , &
stat=ierr , errmsg=error_message )
write (array_name,1) Geom_Name(this_geom),this_order,"cutoff"
call alloc_error(pname,array_name,1,__LINE__,__FILE__,ierr,error_message)
!
cutoff_loop: do cutoff_order = 1,this_order
!
! Assign local pointers as aliases to simplify the code
!
filt => filter(this_geom,this_order)%cutoff(cutoff_order)
!
! Allocate the cutoff filter matrix
!
allocate ( filt%mat(1:npts,1:npts) , &
source=zero , stat=ierr , errmsg=error_message )
write (array_name,1) Geom_Name(this_geom),this_order, &
"cutoff",cutoff_order
call alloc_error(pname,array_name,1,__LINE__,__FILE__, &
ierr,error_message)
!
! Assign local pointers as aliases to simplify the code
!
fmat => filt%mat
!
! Compute the filter matrices depending on geometry type
!
select case (this_geom)
case (Geom_Edge)
!
fmat = FilterMatrix_Edge( vmat , vmat_inv , cutoff_order )
!
case (Geom_Tria)
!
fmat = FilterMatrix_Tria( vmat , vmat_inv , cutoff_order )
!
case (Geom_Quad)
!
fmat = FilterMatrix_Quad( vmat , vmat_inv , cutoff_order )
!
case (Geom_Tetr)
!
fmat = FilterMatrix_Tetr( vmat , vmat_inv , cutoff_order )
!
case (Geom_Pyra)
!
fmat = FilterMatrix_Pyra( vmat , vmat_inv , cutoff_order )
!
case (Geom_Pris)
!
fmat = FilterMatrix_Pris( vmat , vmat_inv , cutoff_order )
!
case (Geom_Hexa)
!
fmat = FilterMatrix_Hexa( vmat , vmat_inv , cutoff_order )
!
case default
!
write (error_message,100)
call stop_gfr(stop_mpi,pname,__LINE__,__FILE__,error_message)
!
end select
!
! Remove all associations of the local pointers before continuing
!
if (associated(fmat)) fmat => null()
if (associated(filt)) filt => null()
!
end do cutoff_loop
!
! Remove all associations of the local pointers before continuing
!
if (associated(fmat)) fmat => null()
if (associated(filt)) filt => null()
if (associated(vmat)) vmat => null()
if (associated(vmat_inv)) vmat_inv => null()
!
end do order_loop
!
end do geom_loop
!
! Check for sparsity
!
do this_geom = gmin,gmax
do this_order = omin,omax
if (allocated(filter(this_geom,this_order)%exponential)) then
call filter(this_geom,this_order)%exponential%check_for_sparsity
end if
if (allocated(filter(this_geom,this_order)%limiter)) then
call filter(this_geom,this_order)%limiter%check_for_sparsity
end if
if (allocated(filter(this_geom,this_order)%cutoff)) then
call filter(this_geom,this_order)%cutoff%check_for_sparsity
end if
end do
end do
!
call debug_timer(leaving_procedure,pname)
!
! Format Statements
!
1 format ("filter(",a,",",i0,")%",a,:,"(",i0,")%mat")
100 format (" A grid cell of an unknown geometry type was found!")
!
end subroutine init_filter_matrices
!
!###############################################################################
!
subroutine filter_usp
!
!.. Use Statements ..
use geovar, only : ncell,cell
use flowvar, only : usp
!
!.. Local Scalars ..
integer :: n,n1,n2,m
integer :: this_geom,this_order
!
!.. Local Parameters ..
character(len=*), parameter :: pname = "filter_usp"
!
continue
!
!call debug_timer(entering_procedure,pname)
!
! Apply the filter to each cell
!
do n = 1,ncell
!
n1 = cell(n)%beg_sp
n2 = cell(n)%end_sp
!
this_geom = cell(n)%geom
this_order = cell(n)%order
!
do m = 1,size(usp,dim=1)
usp(m,n1:n2) = filter(this_geom,this_order)% &
exponential% &
mv_mult( usp(m,n1:n2) )
end do
!
end do
!
!call debug_timer(leaving_procedure,pname)
!
end subroutine filter_usp
!
!###############################################################################
!
pure function FilterMatrix_Edge(vand,vand_inv,cutoff_order) result(return_value)
!
! Routine to compute the spectral filter matrices
!
!.. Formal Arguments ..
real(wp), dimension(:,:), intent(in) :: vand
real(wp), dimension(:,:), intent(in) :: vand_inv
!
!.. Optional Arguments ..
integer, optional, intent(in) :: cutoff_order
!
!.. Function Return Value ..
real(wp), allocatable :: return_value(:,:)
!
!.. Local Scalars ..
integer :: i,nsp,order
integer :: Filter_Cutoff,ierr
integer :: local_Filter_Option
integer :: filt_order
real(qp) :: rd_qp,fetac_qp
real(qp) :: rn_qp,falpha_qp
real(qp) :: feps_qp
!
!.. Local Allocatable Arrays ..
real(qp), allocatable :: filter_1D_qp(:)
real(qp), allocatable :: fmat_qp(:,:)
!
continue
!
! Get the number of solution points
!
nsp = size(vand,dim=1)
order = nsp-1
!
! Covert Filter_Alpha and Filter_etac to quad precision
!
falpha_qp = real( Filter_Alpha , kind=qp )
!
filt_order = Filter_Order
!
if (present(cutoff_order)) then
if (cutoff_order >= 0) then
local_Filter_Option = Cutoff_Filter_Option
Filter_Cutoff = cutoff_order
fetac_qp = real(cutoff_order,kind=qp) / real(order,kind=qp)
feps_qp = qzero
else
fetac_qp = real( Limiter_Filter_etac , kind=qp )
Filter_Cutoff = nint( max(zero,min(one,Limiter_Filter_etac)) * &
real(order,kind=wp) )
local_Filter_Option = Limiter_Filter_Option
feps_qp = real( one - Limiter_Filter_eps , kind=qp )
falpha_qp = real( Limiter_Filter_Alpha , kind=qp )
filt_order = Limiter_Filter_Order
end if
else
fetac_qp = real( Filter_etac , kind=qp )
Filter_Cutoff = nint( max(zero,min(one,Filter_etac)) * real(order,kind=wp) )
local_Filter_Option = Filter_Option
feps_qp = real( one - Filter_eps , kind=qp )
end if
!
! Allocate the return array containing the working
! precision filter matrix
!
allocate ( return_value(1:nsp,1:nsp) , source=zero , stat=ierr )
!
! Create the filter matrix using quad precision
!
allocate ( fmat_qp(1:nsp,1:nsp) , source=qzero , stat=ierr )
!
! Initialize the local filter matrices to identity matrices
!
do i = 1,nsp
fmat_qp(i,i) = qone
end do
!
! Fill the diagonal of the filter matrix with the filter function
!
if (local_Filter_Option /= 0) then
!
do i = 0,order
if (i >= Filter_Cutoff) then
!
rn_qp = real(i,kind=qp)/real(order,kind=qp) - fetac_qp
rd_qp = max( qzero , qone - fetac_qp )
!
if (rd_qp == qzero) then
fmat_qp(i+1,i+1) = feps_qp
else
fmat_qp(i+1,i+1) = feps_qp*exp(-falpha_qp*(rn_qp/rd_qp)**filt_order)
end if
!
end if
end do
!
end if
!
! Compute the final filter matrix for quadrilaterals
!
fmat_qp = matmul( real(vand,kind=qp) , fmat_qp )
fmat_qp = matmul( fmat_qp , real(vand_inv,kind=qp) )
!
! Use the chop function to copy fmat_qp into return_value while also
! setting any values that are less than working machine epsilon to zero.
!
return_value = chop( fmat_qp )
!
end function FilterMatrix_Edge
!
!###############################################################################
!
pure &
function FilterMatrix_Quad(vand,vand_inv,cutoff_order) result(return_value)
!
! Routine to compute the spectral filter matrices
!
!.. Formal Arguments ..
real(wp), dimension(:,:), intent(in) :: vand
real(wp), dimension(:,:), intent(in) :: vand_inv
!
!.. Optional Arguments ..
integer, optional, intent(in) :: cutoff_order
!
!.. Function Return Value ..
real(wp), allocatable :: return_value(:,:)
!
!.. Local Scalars ..
integer :: i,j,k,np,nsp,order
integer :: Filter_Cutoff,ierr
integer :: local_Filter_Option
integer :: filt_order
real(qp) :: rd_qp,fetac_qp
real(qp) :: rn_qp,falpha_qp
real(qp) :: feps_qp
!
!.. Local Arrays ..
real(qp), allocatable :: filter_1D_qp(:)
real(qp), allocatable :: fmat_qp(:,:)
!
continue
!
! Get the number of solution points
!
nsp = size(vand,dim=1)
order = solpts2order_quad(nsp)
np = order+1
!np = nint( sqrt(real(nsp,kind=wp)) )
!order = np-1
!
! Covert Filter_Alpha and Filter_etac to quad precision
!
falpha_qp = real( Filter_Alpha , kind=qp )
!
filt_order = Filter_Order
!
if (present(cutoff_order)) then
if (cutoff_order >= 0) then
local_Filter_Option = Cutoff_Filter_Option
i = merge(2,1,local_Filter_Option==2)
Filter_Cutoff = i*cutoff_order
fetac_qp = real(Filter_Cutoff,kind=qp) / real(i*order,kind=qp)
feps_qp = qzero
else
fetac_qp = real( Limiter_Filter_etac , kind=qp )
Filter_Cutoff = nint( max(zero,min(one,Limiter_Filter_etac)) * &
real(order,kind=wp) )
local_Filter_Option = Limiter_Filter_Option
feps_qp = real( one - Limiter_Filter_eps , kind=qp )
falpha_qp = real( Limiter_Filter_Alpha , kind=qp )
filt_order = Limiter_Filter_Order
end if
else
fetac_qp = real( Filter_etac , kind=qp )
Filter_Cutoff = nint( max(zero,min(one,Filter_etac)) * real(order,kind=wp) )
local_Filter_Option = Filter_Option
feps_qp = real( one - Filter_eps , kind=qp )
end if
!
! Allocate the return array containing the working
! precision filter matrix
!
allocate ( return_value(1:nsp,1:nsp) , source=zero , stat=ierr )
!
! Create the filter matrix using quad precision
!
allocate ( fmat_qp(1:nsp,1:nsp) , source=qzero , stat=ierr )
!
! Initialize the local filter matrices to identity matrices
!
do i = 1,nsp
fmat_qp(i,i) = qone
end do
!
! Compute the filter diagonal for quadrilaterals
!
if (local_Filter_Option == 1) then
!
! Option 1 - Tensor product of the 1D filter
! (Equivalent to using a 1D filter in each direction)
!
! Allocate the 1D filter vector and set all its values to one
!
allocate ( filter_1D_qp(1:np) , source=qone , stat=ierr )
!
! First get the 1D filter diagonal
!
do i = 0,order
if (i >= Filter_Cutoff) then
!
rn_qp = real(i,kind=qp)/real(order,kind=qp) - fetac_qp
rd_qp = max( qzero , qone - fetac_qp )
!
if (rd_qp == qzero) then
filter_1D_qp(i+1) = feps_qp
else
filter_1D_qp(i+1) = feps_qp * &
exp(-falpha_qp * (rn_qp/rd_qp)**filt_order)
end if
!
end if
end do
!
! Now fill the filter diagonal for quads
!
do j = 0,order
do i = 0,order
!
k = np*j + i + 1
!
fmat_qp(k,k) = filter_1D_qp(i+1)*filter_1D_qp(j+1)
!
end do
end do
!
else if (local_Filter_Option == 2) then
!
! Option 2 - The quad basis functions actually contains cross polynomial
! terms up to order 2*p (as opposed to just 1*p for triangles).
! This filter applies the cut-off frequency based on 2*p as
! opposed to basing it on just p in 1D like Option 1.
!
do i = 0,order
do j = 0,order
!
if (i+j >= Filter_Cutoff) then
!
k = np*j + i + 1
!
rn_qp = real(i+j-Filter_Cutoff,kind=qp)
rd_qp = max( qzero , real(2*order-Filter_Cutoff,kind=qp) )
!
if (rd_qp == qzero) then
fmat_qp(k,k) = feps_qp
else
fmat_qp(k,k) = feps_qp*exp(-falpha_qp * (rn_qp/rd_qp)**filt_order)
end if
!
end if
!
end do
end do
!
end if
!
! Compute the final filter matrix for quadrilaterals
!
fmat_qp = matmul( real(vand,kind=qp) , fmat_qp )
fmat_qp = matmul( fmat_qp , real(vand_inv,kind=qp) )
!
! Use the chop function to copy fmat_qp into return_value while also
! setting any values that are less than working machine epsilon to zero.
!
return_value = chop( fmat_qp )
!
end function FilterMatrix_Quad
!
!###############################################################################
!
pure function FilterMatrix_Tria(vand,vand_inv,cutoff_order) result(return_value)
!
! Routine to compute the spectral filter matrices
!
!.. Formal Arguments ..
real(wp), dimension(:,:), intent(in) :: vand
real(wp), dimension(:,:), intent(in) :: vand_inv
!
!.. Optional Arguments ..
integer, optional, intent(in) :: cutoff_order
!
!.. Function Return Value ..
real(wp), allocatable :: return_value(:,:)
!
!.. Local Scalars ..
integer :: i,j,k,np,nsp,order
integer :: Filter_Cutoff,ierr
integer :: local_Filter_Option
integer :: filt_order
real(qp) :: rd_qp,fetac_qp
real(qp) :: rn_qp,falpha_qp
real(qp) :: feps_qp
!
!.. Local Allocatable Arrays ..
real(qp), allocatable :: fmat_qp(:,:)
!
continue
!
! Get the number of solution points
!
nsp = size(vand,dim=1)
order = solpts2order_tria(nsp)
np = order+1
!
! Covert Filter_Alpha and Filter_etac to quad precision
!
falpha_qp = real( Filter_Alpha , kind=qp )
!
filt_order = Filter_Order
!
if (present(cutoff_order)) then
if (cutoff_order >= 0) then
local_Filter_Option = Cutoff_Filter_Option
Filter_Cutoff = cutoff_order
fetac_qp = real(Filter_Cutoff,kind=qp) / real(order,kind=qp)
feps_qp = qzero
else
fetac_qp = real( Limiter_Filter_etac , kind=qp )
Filter_Cutoff = nint( max(zero,min(one,Limiter_Filter_etac)) * &
real(order,kind=wp) )
local_Filter_Option = Limiter_Filter_Option
feps_qp = real( one - Limiter_Filter_eps , kind=qp )
falpha_qp = real( Limiter_Filter_Alpha , kind=qp )
filt_order = Limiter_Filter_Order
end if
else
fetac_qp = real( Filter_etac , kind=qp )
Filter_Cutoff = nint( max(zero,min(one,Filter_etac)) * real(order,kind=wp) )
local_Filter_Option = Filter_Option
feps_qp = real( one - Filter_eps , kind=qp )
end if
!
! Allocate the return array containing the working
! precision filter matrix
!
allocate ( return_value(1:nsp,1:nsp) , source=zero , stat=ierr )
!
! Create the filter matrix using quad precision
!
allocate ( fmat_qp(1:nsp,1:nsp) , source=qzero , stat=ierr )
!
! Initialize the local filter matrices to identity matrices
!
do i = 1,nsp
fmat_qp(i,i) = qone
end do
!
! Compute the filter diagonal for triangles
!
if (local_Filter_Option /= 0) then
!
k = 1
do i = 0,order
do j = 0,order-i
!
if (i+j >= Filter_Cutoff) then
!
rn_qp = real(i,kind=qp)/real(order,kind=qp) - fetac_qp
rd_qp = max( qzero , qone - fetac_qp )
!
if (rd_qp == qzero) then
fmat_qp(k,k) = feps_qp
else
fmat_qp(k,k) = feps_qp*exp(-falpha_qp * (rn_qp/rd_qp)**filt_order)
end if
!
end if
!
k = k + 1
!
end do
end do
!
end if
!
! Compute the final filter matrix for triangles
!
fmat_qp = matmul( real(vand,kind=qp) , fmat_qp )
fmat_qp = matmul( fmat_qp , real(vand_inv,kind=qp) )
!
! Use the chop function to copy fmat_qp into return_value while also
! setting any values that are less than working machine epsilon to zero.
!
return_value = chop( fmat_qp )
!
end function FilterMatrix_Tria
!
!###############################################################################
!
pure function FilterMatrix_Tetr(vand,vand_inv,cutoff_order) result(return_value)
!
! Routine to compute the spectral filter matrices
!
!.. Formal Arguments ..
real(wp), dimension(:,:), intent(in) :: vand
real(wp), dimension(:,:), intent(in) :: vand_inv
!
!.. Optional Arguments ..
integer, optional, intent(in) :: cutoff_order
!
!.. Function Return Value ..
real(wp), allocatable :: return_value(:,:)
!
!.. Local Scalars ..
integer :: i,j,k,np,nsp,order
integer :: Filter_Cutoff,ierr
integer :: local_Filter_Option
integer :: filt_order
real(qp) :: rd_qp,fetac_qp
real(qp) :: rn_qp,falpha_qp
real(qp) :: feps_qp
!
!.. Local Allocatable Arrays ..
real(qp), allocatable :: fmat_qp(:,:)
!
continue
!
! Get the number of solution points
!
nsp = size(vand,dim=1)
order = solpts2order_tetr(nsp)
np = order+1
!
! Covert Filter_Alpha and Filter_etac to quad precision
!
falpha_qp = real( Filter_Alpha , kind=qp )
!
filt_order = Filter_Order
!
if (present(cutoff_order)) then
if (cutoff_order >= 0) then
local_Filter_Option = Cutoff_Filter_Option
Filter_Cutoff = cutoff_order
fetac_qp = real(Filter_Cutoff,kind=qp) / real(order,kind=qp)
feps_qp = qzero
else
fetac_qp = real( Limiter_Filter_etac , kind=qp )
Filter_Cutoff = nint( max(zero,min(one,Limiter_Filter_etac)) * &
real(order,kind=wp) )
local_Filter_Option = Limiter_Filter_Option
feps_qp = real( one - Limiter_Filter_eps , kind=qp )
falpha_qp = real( Limiter_Filter_Alpha , kind=qp )
filt_order = Limiter_Filter_Order
end if
else
fetac_qp = real( Filter_etac , kind=qp )
Filter_Cutoff = nint( max(zero,min(one,Filter_etac)) * real(order,kind=wp) )
local_Filter_Option = Filter_Option
feps_qp = real( one - Filter_eps , kind=qp )
end if
!
! Allocate the return array containing the working
! precision filter matrix
!
allocate ( return_value(1:nsp,1:nsp) , source=zero , stat=ierr )
!
! Create the filter matrix using quad precision
!
allocate ( fmat_qp(1:nsp,1:nsp) , source=qzero , stat=ierr )
!
! Initialize the local filter matrices to identity matrices
!
do i = 1,nsp
fmat_qp(i,i) = qone
end do
!
! Compute the filter diagonal for triangles
!
if (local_Filter_Option /= 0) then
!
k = 1
do i = 0,order
do j = 0,order-i
!
if (i+j >= Filter_Cutoff) then
!
rn_qp = real(i,kind=qp)/real(order,kind=qp) - fetac_qp
rd_qp = max( qzero , qone - fetac_qp )
!
if (rd_qp == qzero) then
fmat_qp(k,k) = feps_qp
else
fmat_qp(k,k) = feps_qp*exp(-falpha_qp * (rn_qp/rd_qp)**filt_order)
end if
!
end if
!
k = k + 1
!
end do
end do
!
end if
!
! Compute the final filter matrix for triangles
!
fmat_qp = matmul( real(vand,kind=qp) , fmat_qp )
fmat_qp = matmul( fmat_qp , real(vand_inv,kind=qp) )
!
! Use the chop function to copy fmat_qp into return_value while also
! setting any values that are less than working machine epsilon to zero.
!
return_value = chop( fmat_qp )
!
end function FilterMatrix_Tetr
!
!###############################################################################
!
pure function FilterMatrix_Pyra(vand,vand_inv,cutoff_order) result(return_value)
!
! Routine to compute the spectral filter matrices
!
!.. Formal Arguments ..
real(wp), dimension(:,:), intent(in) :: vand
real(wp), dimension(:,:), intent(in) :: vand_inv
!
!.. Optional Arguments ..
integer, optional, intent(in) :: cutoff_order
!
!.. Function Return Value ..
real(wp), allocatable :: return_value(:,:)
!
!.. Local Scalars ..
integer :: i,j,k,np,nsp,order
integer :: Filter_Cutoff,ierr
integer :: local_Filter_Option
integer :: filt_order
real(qp) :: rd_qp,fetac_qp
real(qp) :: rn_qp,falpha_qp
real(qp) :: feps_qp
!
!.. Local Allocatable Arrays ..
real(qp), allocatable :: fmat_qp(:,:)
!
continue
!
! Get the number of solution points
!
nsp = size(vand,dim=1)
order = solpts2order_pyra(nsp)
np = order+1
!
! Covert Filter_Alpha and Filter_etac to quad precision
!
falpha_qp = real( Filter_Alpha , kind=qp )
!
filt_order = Filter_Order
!
if (present(cutoff_order)) then
if (cutoff_order >= 0) then
local_Filter_Option = Cutoff_Filter_Option
Filter_Cutoff = cutoff_order
fetac_qp = real(Filter_Cutoff,kind=qp) / real(order,kind=qp)
feps_qp = qzero
else
fetac_qp = real( Limiter_Filter_etac , kind=qp )
Filter_Cutoff = nint( max(zero,min(one,Limiter_Filter_etac)) * &
real(order,kind=wp) )
local_Filter_Option = Limiter_Filter_Option
feps_qp = real( one - Limiter_Filter_eps , kind=qp )
falpha_qp = real( Limiter_Filter_Alpha , kind=qp )
filt_order = Limiter_Filter_Order
end if
else
fetac_qp = real( Filter_etac , kind=qp )
Filter_Cutoff = nint( max(zero,min(one,Filter_etac)) * real(order,kind=wp) )
local_Filter_Option = Filter_Option
feps_qp = real( one - Filter_eps , kind=qp )
end if
!
! Allocate the return array containing the working
! precision filter matrix
!
allocate ( return_value(1:nsp,1:nsp) , source=zero , stat=ierr )
!
! Create the filter matrix using quad precision