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#ifndef OMIT_F90
!!$ -*-Fortran-*-
#include "cctk.h"
!!$ This routine performs "WENO" prolongation. It is intended to be used
!!$ with GFs that are not expected to be smooth, particularly those
!!$ that must also obey certain constraints. The obvious example is the
!!$ density in hydrodynamics, which may be discontinuous yet must be
!!$ strictly positive.
!!$
!!$ To ensure that this prolongation method is used you should add the
!!$ tag
!!$
!!$ tags='Prolongation="WENO"'
!!$
!!$ to the interface.ccl on the appropriate group.
!!$
!!$ This applies WENO2 type limiting to the slope, checking over the
!!$ entire coarse grid cell for the least oscillatory quadratic in each
!!$ direction. If the slope changes sign over the extrema, linear
!!$ interpolation is used instead.
function weno1d(q)
implicit none
CCTK_REAL8 :: weno1d
CCTK_REAL8 :: q(5)
CCTK_REAL8 :: zero, one, two, three, four, five, eight, ten, eleven, &
thirteen, fifteen, nineteen, twentyfive, thirtyone, epsilon
parameter (zero = 0)
parameter (one = 1)
parameter (two = 2)
parameter (three = 3)
parameter (four = 4)
parameter (five = 5)
parameter (eight = 8)
parameter (ten = 10)
parameter (eleven = 11)
parameter (thirteen = 13)
parameter (fifteen = 15)
parameter (nineteen = 19)
parameter (twentyfive = 25)
parameter (thirtyone = 31)
parameter (epsilon = 0.000000001)
CCTK_REAL8, dimension(0:2,0:2) :: c
CCTK_REAL8 :: wtildesum, qmax, qmin
CCTK_REAL8, dimension(0:2) :: d, beta, wtilde, w, vr
logical, dimension(0:2) :: hacked
integer :: j, k
!!$ Linear weights
d(0) = three / ten
d(1) = three / five
d(2) = one / ten
c(0,0) = three / eight
c(0,1) = three / four
c(0,2) = -one / eight
c(1,0) = -one / eight
c(1,1) = three / four
c(1,2) = three / eight
c(2,0) = three / eight
c(2,1) = -five / four
c(2,2) = fifteen / eight
!!$ Substencils
do j = 0, 2
vr(j) = 0.d0
do k = 0, 2
vr(j) = vr(j) + c(j, k) * q(3 - j + k)
end do
end do
!!$ Nonlinear weights
beta(0) = (ten * q(3)**2 - &
thirtyone * q(3) * q(4) + &
twentyfive * q(4)**2 + &
eleven * q(3) * q(5) - &
nineteen * q(4) * q(5) + &
four * q(5)**2) / three
beta(1) = (four * q(2)**2 - &
thirteen * q(2) * q(3) + &
thirteen * q(3)**2 + &
five * q(2) * q(4) - &
thirteen * q(3) * q(4) + &
four * q(4)**2) / three
beta(2) = (four * q(1)**2 - &
nineteen * q(1) * q(2) + &
twentyfive * q(2)**2 + &
eleven * q(1) * q(3) - &
thirtyone * q(2) * q(3) + &
ten * q(3)**2) / three
do j = 0, 2
wtilde(j) = d(j) / (epsilon + beta(j))**2
end do
!!$ Hack the weights if outside the range
qmax = maxval(q)
qmin = minval(q)
do j = 0, 2
hacked(j) = .false.
if ( (qmax - vr(j)) * (vr(j) - qmin) < 0.d0 ) then
wtilde(j) = 0.d0
hacked(j) = .true.
end if
end do
!!$ If all weights were hacked we cannot get a good interpolant;
!!$ drop to linear interpolation
if (hacked(0).and.hacked(1).and.hacked(2)) then
!!$ Linear interpolation
weno1d = 0.5d0 * (q(3) + q(4))
else
wtildesum = wtilde(0) + wtilde(1) + wtilde(2)
w = wtilde / wtildesum
weno1d = 0.d0
do j = 0, 2
weno1d = weno1d + w(j) * vr(j)
end do
end if
!!$ if (.not.( (weno1d .ge. 0.d0 ).or.(weno1d .le. 0.d0) ) ) then
!!$ write(*,*) 'Error?', weno1d
!!$ write(*,*) 'Done weno1d', weno1d, hacked
!!$ write(*,*) 'Substencil',vr
!!$ write(*,*) 'Weights', w
!!$ write(*,*) 'Indicators', beta
!!$ write(*,*) 'Input', q
!!$ end if
!!$ write(*,*) 'Done weno1d', weno1d, hacked
!!$ write(*,*) 'Substencil',vr
!!$ write(*,*) 'Weights', w
!!$ write(*,*) 'Indicators', beta
!!$ write(*,*) 'Input', q
end function weno1d
subroutine prolongate_3d_real8_weno ( &
src, srcipadext, srcjpadext, srckpadext, srciext, srcjext, srckext, &
dst, dstipadext, dstjpadext, dstkpadext, dstiext, dstjext, dstkext, &
srcbbox, dstbbox, regbbox)
implicit none
CCTK_REAL8 one
parameter (one = 1)
integer srcipadext, srcjpadext, srckpadext
integer srciext, srcjext, srckext
CCTK_REAL8 src(srcipadext,srcjpadext,srckpadext)
integer dstipadext, dstjpadext, dstkpadext
integer dstiext, dstjext, dstkext
CCTK_REAL8 dst(dstipadext,dstjpadext,dstkpadext)
!!$ bbox(:,1) is lower boundary (inclusive)
!!$ bbox(:,2) is upper boundary (inclusive)
!!$ bbox(:,3) is stride
integer srcbbox(3,3), dstbbox(3,3), regbbox(3,3)
integer offsetlo, offsethi
integer regiext, regjext, regkext
integer dstifac, dstjfac, dstkfac
integer srcioff, srcjoff, srckoff
integer dstioff, dstjoff, dstkoff
integer i, j, k
integer i0, j0, k0
integer fi, fj, fk
integer ii, jj, kk
integer d
CCTK_REAL8, dimension(0:4,0:4) :: tmp1
CCTK_REAL8, dimension(0:4) :: tmp2
external weno1d
CCTK_REAL8 weno1d
CCTK_REAL8 half, zero
parameter (half = 0.5)
parameter (zero = 0)
do d=1,3
if (srcbbox(d,3).eq.0 .or. dstbbox(d,3).eq.0 &
.or. regbbox(d,3).eq.0) then
call CCTK_WARN (0, "Internal error: stride is zero")
end if
if (srcbbox(d,3).le.regbbox(d,3) &
.or. dstbbox(d,3).ne.regbbox(d,3)) then
call CCTK_WARN (0, "Internal error: strides disagree")
end if
if (mod(srcbbox(d,3), dstbbox(d,3)).ne.0) then
call CCTK_WARN (0, "Internal error: destination strides are not integer multiples of the source strides")
end if
if (mod(srcbbox(d,1), srcbbox(d,3)).ne.0 &
.or. mod(dstbbox(d,1), dstbbox(d,3)).ne.0 &
.or. mod(regbbox(d,1), regbbox(d,3)).ne.0) then
call CCTK_WARN (0, "Internal error: array origins are not integer multiples of the strides")
end if
if (regbbox(d,1).gt.regbbox(d,2)) then
!!$ This could be handled, but is likely to point to an error elsewhere
call CCTK_WARN (0, "Internal error: region extent is empty")
end if
regkext = (regbbox(d,2) - regbbox(d,1)) / regbbox(d,3) + 1
dstkfac = srcbbox(d,3) / dstbbox(d,3)
srckoff = (regbbox(d,1) - srcbbox(d,1)) / dstbbox(d,3)
offsetlo = regbbox(d,3)
if (mod(srckoff + 0, dstkfac).eq.0) then
offsetlo = 0
if (regkext.gt.1) then
offsetlo = regbbox(d,3)
end if
end if
offsethi = regbbox(d,3)
if (mod(srckoff + regkext-1, dstkfac).eq.0) then
offsethi = 0
if (regkext.gt.1) then
offsethi = regbbox(d,3)
end if
end if
if (regbbox(d,1)-offsetlo.lt.srcbbox(d,1) &
.or. regbbox(d,2)+offsethi.gt.srcbbox(d,2) &
.or. regbbox(d,1).lt.dstbbox(d,1) &
.or. regbbox(d,2).gt.dstbbox(d,2)) then
call CCTK_WARN (0, "Internal error: region extent is not contained in array extent")
end if
end do
if (srciext.ne.(srcbbox(1,2)-srcbbox(1,1))/srcbbox(1,3)+1 &
.or. srcjext.ne.(srcbbox(2,2)-srcbbox(2,1))/srcbbox(2,3)+1 &
.or. srckext.ne.(srcbbox(3,2)-srcbbox(3,1))/srcbbox(3,3)+1 &
.or. dstiext.ne.(dstbbox(1,2)-dstbbox(1,1))/dstbbox(1,3)+1 &
.or. dstjext.ne.(dstbbox(2,2)-dstbbox(2,1))/dstbbox(2,3)+1 &
.or. dstkext.ne.(dstbbox(3,2)-dstbbox(3,1))/dstbbox(3,3)+1) then
call CCTK_WARN (0, "Internal error: array sizes don't agree with bounding boxes")
end if
regiext = (regbbox(1,2) - regbbox(1,1)) / regbbox(1,3) + 1
regjext = (regbbox(2,2) - regbbox(2,1)) / regbbox(2,3) + 1
regkext = (regbbox(3,2) - regbbox(3,1)) / regbbox(3,3) + 1
dstifac = srcbbox(1,3) / dstbbox(1,3)
dstjfac = srcbbox(2,3) / dstbbox(2,3)
dstkfac = srcbbox(3,3) / dstbbox(3,3)
srcioff = (regbbox(1,1) - srcbbox(1,1)) / dstbbox(1,3)
srcjoff = (regbbox(2,1) - srcbbox(2,1)) / dstbbox(2,3)
srckoff = (regbbox(3,1) - srcbbox(3,1)) / dstbbox(3,3)
dstioff = (regbbox(1,1) - dstbbox(1,1)) / dstbbox(1,3)
dstjoff = (regbbox(2,1) - dstbbox(2,1)) / dstbbox(2,3)
dstkoff = (regbbox(3,1) - dstbbox(3,1)) / dstbbox(3,3)
!!$ Loop over fine region
!$omp parallel do collapse(3) private(i,j,k, i0,fi,j0,fj,k0,fk, tmp1,tmp2, ii,jj,kk)
do k = 0, regkext-1
do j = 0, regjext-1
do i = 0, regiext-1
i0 = (srcioff + i) / dstifac
fi = mod(srcioff + i, dstifac)
j0 = (srcjoff + j) / dstjfac
fj = mod(srcjoff + j, dstjfac)
k0 = (srckoff + k) / dstkfac
fk = mod(srckoff + k, dstkfac)
!!$ Where is the fine grid point w.r.t the coarse grid?
select case (fi + 10*fj + 100*fk)
case (0)
!!$ On a coarse grid point exactly!
dst (dstioff+i+1, dstjoff+j+1, dstkoff+k+1) = &
src(i0+1,j0+1,k0+1)
case (1)
!!$ Interpolate only in x
dst (dstioff+i+1, dstjoff+j+1, dstkoff+k+1) = &
weno1d(src(i0-1:i0+3,j0+1,k0+1))
case (10)
!!$ Interpolate only in y
dst (dstioff+i+1, dstjoff+j+1, dstkoff+k+1) = &
weno1d(src(i0+1,j0-1:j0+3,k0+1))
case (11)
!!$ Interpolate only in x and y
do jj = 0, 4
tmp2(jj) = weno1d(src(i0-1:i0+3,j0+jj-1,k0+1))
end do
dst (dstioff+i+1, dstjoff+j+1, dstkoff+k+1) = &
weno1d(tmp2(0:4))
case (100)
!!$ Interpolate only in z
dst (dstioff+i+1, dstjoff+j+1, dstkoff+k+1) = &
weno1d(src(i0+1,j0+1,k0-1:k0+3))
case (101)
!!$ Interpolate only in x and z
do kk = 0, 4
tmp2(kk) = weno1d(src(i0-1:i0+3,j0+1,k0+kk-1))
end do
dst (dstioff+i+1, dstjoff+j+1, dstkoff+k+1) = &
weno1d(tmp2(0:4))
case (110)
!!$ Interpolate only in y and z
do kk = 0, 4
tmp2(kk) = weno1d(src(i0+1,j0-1:j0+3,k0+kk-1))
end do
dst (dstioff+i+1, dstjoff+j+1, dstkoff+k+1) = &
weno1d(tmp2(0:4))
case (111)
!!$ Interpolate in all of x, y, and z
do jj = 0, 4
do kk = 0, 4
tmp1(jj,kk) = weno1d(src(i0-1:i0+3,j0+jj-1,k0+kk-1))
end do
end do
do ii = 0, 4
tmp2(ii) = weno1d(tmp1(0:4,ii))
end do
dst (dstioff+i+1, dstjoff+j+1, dstkoff+k+1) = &
weno1d(tmp2(0:4))
case default
call CCTK_ERROR("Internal error in WENO prolongation. Should only be used with refinement factor 2!")
end select
end do
end do
end do
end subroutine prolongate_3d_real8_weno
#endif /* !OMIT_F90 */
|
