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#include "cctk.h"
!!$ This routine performs "ENO" 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="ENO"'
!!$
!!$ to the interface.ccl on the appropriate group.
!!$
!!$ This applies ENO2 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 eno1d(q)
implicit none
CCTK_REAL8 :: eno1d
CCTK_REAL8, INTENT(IN) :: q(4)
CCTK_REAL8 :: zero, one, two, three, six, half, eighth
parameter (zero = 0)
parameter (two = 2)
parameter (one = 1)
parameter (three = 3)
parameter (six = 6)
parameter (eighth = one / 8)
parameter (half = one / two)
CCTK_REAL8 :: diffleft, diffright
!!$ Directly find the second undivided differences
!!$ We need to pick between discrete values at
!!$ 1 2 3 4 for the interpolation between 2 and 3.
diffleft = q(1) + q(3) - two * q(2)
diffright = q(2) + q(4) - two * q(3)
if ( abs(diffleft) .lt. abs(diffright) ) then
!!$ Apply the left quadratic
eno1d = eighth * (-q(1) + six * q(2) + three * q(3))
else
!!$ Apply the right quadratic
eno1d = eighth * (three * q(2) + six * q(3) - q(4))
end if
!!$ Check that the quadratic is reasonable:
!!$ Check 1: interpolated value between
!!$ values at interpolation points
!!$ Check 2: sign of the curvature of the interpolating
!!$ polynomial does not change.
if ( ((eno1d-q(2)) * (q(3)-eno1d) .lt. zero) &
.or. &
(diffleft*diffright .le. zero) ) then
!!$ Not reasonable. Linear interpolation
eno1d = half * (q(2) + q(3))
end if
end function eno1d
subroutine prolongate_3d_real8_eno (src, srciext, srcjext, &
srckext, dst, dstiext, dstjext, dstkext, srcbbox, &
dstbbox, regbbox)
implicit none
CCTK_REAL8 one
parameter (one = 1)
integer srciext, srcjext, srckext
CCTK_REAL8 src(srciext,srcjext,srckext)
integer dstiext, dstjext, dstkext
CCTK_REAL8 dst(dstiext,dstjext,dstkext)
!!$ 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(0:3,0:3) :: tmp1
CCTK_REAL8, dimension(0:3) :: tmp2
external eno1d
CCTK_REAL8 eno1d
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
do k = 0, regkext-1
k0 = (srckoff + k) / dstkfac
fk = mod(srckoff + k, dstkfac)
do j = 0, regjext-1
j0 = (srcjoff + j) / dstjfac
fj = mod(srcjoff + j, dstjfac)
do i = 0, regiext-1
i0 = (srcioff + i) / dstifac
fi = mod(srcioff + i, dstifac)
!!$ 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) = &
eno1d(src(i0:i0+3,j0+1,k0+1))
case (10)
!!$ Interpolate only in y
dst (dstioff+i+1, dstjoff+j+1, dstkoff+k+1) = &
eno1d(src(i0+1,j0:j0+3,k0+1))
case (11)
!!$ Interpolate only in x and y
do jj = 0, 3
tmp2(jj) = eno1d(src(i0:i0+3,j0+jj,k0+1))
end do
dst (dstioff+i+1, dstjoff+j+1, dstkoff+k+1) = &
eno1d(tmp2(0:3))
case (100)
!!$ Interpolate only in z
dst (dstioff+i+1, dstjoff+j+1, dstkoff+k+1) = &
eno1d(src(i0+1,j0+1,k0:k0+3))
case (101)
!!$ Interpolate only in x and z
do kk = 0, 3
tmp2(kk) = eno1d(src(i0:i0+3,j0+1,k0+kk))
end do
dst (dstioff+i+1, dstjoff+j+1, dstkoff+k+1) = &
eno1d(tmp2(0:3))
case (110)
!!$ Interpolate only in y and z
do kk = 0, 3
tmp2(kk) = eno1d(src(i0+1,j0:j0+3,k0+kk))
end do
dst (dstioff+i+1, dstjoff+j+1, dstkoff+k+1) = &
eno1d(tmp2(0:3))
case (111)
!!$ Interpolate in all of x, y, and z
do jj = 0, 3
do kk = 0, 3
tmp1(jj,kk) = eno1d(src(i0:i0+3,j0+jj,k0+kk))
end do
end do
do ii = 0, 3
tmp2(ii) = eno1d(tmp1(0:3,ii))
end do
dst (dstioff+i+1, dstjoff+j+1, dstkoff+k+1) = &
eno1d(tmp2(0:3))
case default
call CCTK_WARN(0, "Internal error in ENO prolongation. Should only be used with refinement factor 2!")
end select
end do
end do
end do
end subroutine prolongate_3d_real8_eno
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