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|
/*@@
@file AHFinder.F
@date April 1998
@author Miguel Alcubierre
@desc
Find an apparent horizon using a spherical harmonic
expansion and either a minimization or Gundlach's
fast flow algorithm.
Cactus4 by Lars Nerger / Gerd Lanfermann
@enddesc
@version $Header$
@@*/
#include "cctk.h"
#include "cctk_Parameters.h"
#include "cctk_Arguments.h"
#include "cctk_Functions.h"
subroutine AHFinder(CCTK_ARGUMENTS)
use AHFinder_dat
implicit none
DECLARE_CCTK_ARGUMENTS
DECLARE_CCTK_PARAMETERS
DECLARE_CCTK_FUNCTIONS
logical status,horizon,gauss,ahfconformal
logical giveup,report
integer handle,x_index,y_index,z_index,ierror
integer ahfso,ahfafter
integer i,j,l,m
integer NN
integer mtype
integer getoutpfx
integer istat
integer nhorizon
CCTK_REAL atime
CCTK_REAL rmx,r0
CCTK_REAL intexp_h,intexp2_h,intarea_h
CCTK_REAL aux,expin,expout,small1,small2
CCTK_REAL c0_temp(0:18)
CCTK_REAL maxval(3),minval(3)
CCTK_REAL rhor
CCTK_REAL, parameter :: zero = 0.0D0
CCTK_REAL, parameter :: half = 0.5D0
CCTK_REAL, parameter :: one = 1.0D0
CCTK_REAL, dimension (1:3) :: ahfmass
CCTK_INT :: save_conformal_state
character(200) logf
save ahfafter,ahfso,atime
! Description of variables:
!
! status Surface found?
!
! horizon Horizon found?
!
! gauss Output Gaussian curvature?
!
! ahfso How often we want to find a horizon?
! ahfafter After how many iterations start looking for horizons?
!
! i,l,m Counters.
!
! NN Total number of terms in expansion.
!
! rmx Radius of largest sphere that fits in the grid.
!
! mtype Type of surface:
! 0. No surface found.
! 1. Integral of H^2 is positive out and negative in.
! 2. Integral of H^2 is negative out and positive in.
! 3. Integral of H^2 is negative out and in.
! 4. Integral of H^2 is positive out and in.
!
! nhorizon Number of horizons to look for.
! ***************************
! *** INITIALIZE MASK ***
! ***************************
! Initialize mask to one, but only on first iteration.
! Notice that I do this even if we do not want to find
! a horizon from the very beginning. This is to make
! sure that the mask is 1 and not 0 in case some other
! thorn wants to use it.
if (cctk_iteration.eq.0 .or. CCTK_EQUALS(ahf_mask, "off")) then
ahmask = one
end if
! ***********************************************************
! *** CHECK IF WE WANT TO FIND A HORIZON AT THIS TIME ***
! ***********************************************************
atime = ahf_findaftertime
if (atime.le.zero) then
ahfafter = ahf_findafter
if (cctk_iteration.lt.ahfafter) return
else
if (cctk_time.lt.atime) return
if (ahf_ncall.eq.0) ahfafter = cctk_iteration
end if
ahfso = ahf_findevery
if (mod(int(cctk_iteration-ahfafter),ahfso).ne.0) return
! *******************************************
! *** ADD TO COUNT OF CALLS TO FINDER ***
! *******************************************
! Add to count of calls to finder. Notice that this counter was
! initialized to zero, so it must be increased on first call to 1.
ahf_ncall = ahf_ncall + 1
! *********************************************************
! *** FIND OUT IF WE WANT TO FIND A TRAPPED SURFACE ***
! *********************************************************
if (ahf_trapped_surface.ne.0) then
find_trapped_surface = .true.
else
find_trapped_surface = .false.
end if
! ***************************
! *** GRID PARAMETERS ***
! ***************************
nx = cctk_lsh(1)
ny = cctk_lsh(2)
nz = cctk_lsh(3)
dx = cctk_delta_space(1)
dy = cctk_delta_space(2)
dz = cctk_delta_space(3)
! *********************************************
! *** SET SYMMETRIES FOR GRID FUNCTIONS ***
! *********************************************
call AHFinder_SetSym(CCTK_ARGUMENTS)
! **********************************************
! *** FIND OUT ON WHICH PROCESSOR WE ARE ***
! **********************************************
myproc = CCTK_MyProc(cctkGH)
! *******************************************
! *** FIND {xmn,xmx,ymn,ymx,zmn,zmx} ***
! *******************************************
call CCTK_CoordRange(ierr,cctkGH,xmn,xmx,-1,"x","cart3d")
call CCTK_CoordRange(ierr,cctkGH,ymn,ymx,-1,"y","cart3d")
call CCTK_CoordRange(ierr,cctkGH,zmn,zmx,-1,"z","cart3d")
! **************************************************
! *** TRANSFORM CONFORMAL TO PHYSICAL METRIC ***
! **************************************************
ahfconformal = .false.
! The horizon finding routines know nothing about conformal
! metrics, so we need to make sure that we are working with
! the physical metric. I change not only the metric, but
! also the "conformal state" flag to make sure that any
! macros I use have always the physical metric. However,
! I need to remember the original value of the flag to change
! it back at the end if necesary.
if ( CCTK_Equals(metric_type,"static conformal") == 1 ) then
ahfconformal = .true.
save_conformal_state = conformal_state
conformal_state = 0
call ConfToPhysInPlace (nx,ny,nz,psi,
& gxx,gxy,gxz,gyy,gyz,gzz)
end if
! ************************
! *** FIND {lmax} ***
! ************************
lmax = ahf_lmax
if (lmax.ge.20) then
write(*,*)
write(*,*) 'ahf_lmax must be smaller than 20.'
write(*,*) 'STOPPED IN AHFinder.F'
write(*,*)
call CCTK_WARN(0,"ahf_lmax must be smaller than 20.")
end if
! ***********************************************
! *** CHECK IF WE WANT TO FIND 3 HORIZONS ***
! ***********************************************
if (ahf_find3.eq.0) then
find3 = .false.
nhorizon = 1
else
find3 = .true.
nhorizon = 3
end if
! ***************************************************
! *** ALLOCATE STORAGE FOR COEFFICIENT ARRAYS ***
! ***************************************************
if (ahf_ncall.eq.1) then
allocate(c0(0:lmax),c0_old(0:lmax))
allocate(cc(lmax,lmax),cc_old(lmax,lmax))
allocate(cs(lmax,lmax),cs_old(lmax,lmax))
c0 = zero
cc = zero
cs = zero
c0_old = zero
cc_old = zero
cs_old = zero
allocate(c0_0(0:lmax),c0_1(0:lmax),c0_2(0:lmax))
allocate(cc_0(lmax,lmax),cc_1(lmax,lmax),cc_2(lmax,lmax))
allocate(cs_0(lmax,lmax),cs_1(lmax,lmax),cs_2(lmax,lmax))
c0_0 = zero
cc_0 = zero
cs_0 = zero
c0_1 = zero
cc_1 = zero
cs_1 = zero
c0_2 = zero
cc_2 = zero
cs_2 = zero
end if
! ***************************************************
! *** START LOOP TO LOOK FOR SEVERAL HORIZONS ***
! ***************************************************
! IMPORTANT: This is the point where we start the loop
! to look for more than one horizon. Because of this,
! anything that is likely to be different for the different
! horizons should NOT be initialized until after this point!
ahfmass = 0.0D0
do mfind=1,nhorizon
! Say what we are doing.
if (nhorizon.gt.1) then
if (mfind.eq.1) then
write(*,*)
write(*,*)
write(*,*) 'AHFinder: MULTIPLE HORIZON MODE!'
end if
write(*,*)
write(*,*) 'Searching for horizon ',mfind-1
else
write(*,*)
write(*,*)
write(*,*) 'AHFinder: SINGLE HORIZON MODE!'
write(*,*)
write(*,*) 'Searching for horizon'
end if
! ********************************
! *** INITIALIZE {status} ***
! ********************************
status = .false.
! *********************************
! *** INITIALIZE FIRSTCALLS ***
! *********************************
firstleg = .true.
firstint = .true.
! ***************************************
! *** FIND OUT THE TYPE OF OUTPUT ***
! ***************************************
call CCTK_FortranString(nfile,out_dir,filestr)
if (ahf_logfile.ne.0) then
logfile = .true.
logf = filestr(1:nfile)//"/ahf_logfile"
if (find3) then
logf = trim(logf) // "_" // char(ichar('0') + mfind - 1)
end if
else
logfile = .false.
end if
if (ahf_verbose.ne.0) then
verbose = .true.
else
verbose = .false.
end if
if (ahf_veryverbose.ne.0) then
veryver = .true.
else
veryver = .false.
end if
if (ahf_guessverbose.ne.0) then
guessverbose = .true.
else
guessverbose = .false.
end if
if (logfile.and.(myproc.eq.0)) then
if (logfile) then
if (myproc.eq.0) then
open(11,file=logf,form='formatted',status='replace')
write(11,*)
write(11,*) 'LOG FILE FOR APPARENT HORIZON FINDER'
write(11,*)
write(11,*) 'Note: During an evolution, this file will only'
write(11,*) 'contain information about the last time that the'
write(11,*) 'finder was called.'
write(11,*)
close(11)
end if
end if
end if
! **********************************
! *** INITIALIZE {xc,yc,zc} ***
! **********************************
if (find3) then
if (mfind.eq.1) then
xc = ahf_xc_0
yc = ahf_yc_0
zc = ahf_zc_0
else if (mfind.eq.2) then
xc = ahf_xc_1
yc = ahf_yc_1
zc = ahf_zc_1
else
xc = ahf_xc_2
yc = ahf_yc_2
zc = ahf_zc_2
end if
else
xc = ahf_xc
yc = ahf_yc
zc = ahf_zc
end if
! Check if the center of the expansion is
! out of the grid. If it is, give up.
giveup = .false.
if ((xc.gt.xmx).or.(xc.lt.xmn)) then
write(*,*)
write(*,*) 'xc is out of the grid, giving up.'
giveup = .true.
end if
if ((yc.gt.ymx).or.(yc.lt.ymn)) then
write(*,*)
write(*,*) 'yc is out of the grid, giving up.'
giveup = .true.
end if
if ((zc.gt.zmx).or.(zc.lt.zmn)) then
write(*,*)
write(*,*) 'zc is out of the grid, giving up.'
giveup = .true.
end if
! The end of this if statement is very far down,
! it basically jumps all of the code. To find
! it look for the word "giveup" on a comment.
if (.not.giveup) then
! **************************
! *** FIND SYMMETRIES ***
! **************************
! Find out if we want to move the center.
if (ahf_offset.ne.0) then
offset = .true.
else
offset = .false.
end if
if (ahf_wander.ne.0) then
wander = .true.
else
wander = .false.
end if
if ((xc.ne.zero).or.(yc.ne.zero).or.(zc.ne.zero).or.
. (wander)) offset = .true.
! Find out if we are in non-axisymmetric mode.
if (ahf_phi.ne.0) then
nonaxi = .true.
else
nonaxi = .false.
end if
call AHFinder_SetReflections(CCTK_ARGUMENTS)
! Find the values of {stepx,stepy,stepz} depending
! on the symmetries.
stepx = 0
stepy = 0
stepz = 0
if (refx) stepx=1
if (refy) stepy=1
if (refz) stepz=1
if (CCTK_Equals(ahf_octant,"high").eq.1) stepx=3
! *******************************
! *** FIND {ntheta,nphi} ***
! *******************************
ntheta = ahf_ntheta
nphi = ahf_nphi
! For cartoon, I use only 2 points in the phi direction.
! I could use one, but using 2 minimizes the changes in
! the integration routine.
if (cartoon) then
nphi = 1
end if
! ********************************************************
! *** FIND TOTAL NUMBER OF TERMS IN EXPANSION {NN} ***
! ********************************************************
NN = 0
! Count {xc,yc,zc}.
if (wander) then
if (.not.refx) NN = NN + 1
if (.not.refy) NN = NN + 1
if (.not.refz) NN = NN + 1
end if
! Count c0(l).
do l=0,lmax,1+stepz
NN = NN + 1
end do
if (nonaxi) then
! Count cc(l,m).
do l=1,lmax
do m=1+stepx,l,1+stepx
if (stepz*mod(l-m,2).eq.0) NN = NN +1
end do
end do
! Count cs(l,m).
if (.not.refy) then
do l=1,lmax
do m=1,l,1+stepx
if (stepz*mod(l-m,2).eq.0) NN = NN + 1
end do
end do
end if
end if
! *****************************************
! *** FIND RADIUS OF INITIAL SPHERE ***
! *****************************************
! Find largest sphere that fits into the grid, taking
! into account the position of the center. Then multiply
! this number with 0.9 to leave a safety margin at the edge
! of the grid.
! Cartoon.
if (cartoon) then
xc = zero
yc = zero
rmx = min(xmx,zmx-zc,zc-zmn)
! Octant.
else if (CCTK_Equals(domain,"octant").eq.1) then
if ((xc.eq.zero).and.(yc.eq.zero).and.(zc.eq.zero)) then
rmx = min(xmx,ymx,zmx)
else if ((xc.eq.zero).and.(yc.eq.zero)) then
rmx = min(xmx,ymx,zmx-zc,zc)
else if ((xc.eq.zero).and.(zc.eq.zero)) then
rmx = min(xmx,ymx-yc,zmx,yc)
else if ((yc.eq.zero).and.(zc.eq.zero)) then
rmx = min(xmx-xc,ymx,zmx,xc)
else if (xc.eq.zero) then
rmx = min(xmx,ymx-yc,zmx-zc,yc,zc)
else if (yc.eq.zero) then
rmx = min(xmx-xc,ymx,zmx-zc,xc,zc)
else if (zc.eq.zero) then
rmx = min(xmx-xc,ymx-yc,zmx,xc,yc)
else
rmx = min(xmx-xc,ymx-yc,zmx-zc,xc,yc,zc)
end if
! Quadrant.
else if (CCTK_Equals(domain,"quadrant").eq.1) then
if ((xc.eq.zero).and.(yc.eq.zero)) then
rmx = min(xmx,ymx,zmx-zc,zc-zmn)
else if (xc.eq.zero) then
rmx = min(xmx,ymx-yc,zmx-zc,yc,zc-zmn)
else if (yc.eq.zero) then
rmx = min(xmx-xc,ymx,zmx-zc,xc,zc-zmn)
else
rmx = min(xmx-xc,ymx-yc,zmx-zc,xc,yc,zc-zmn)
end if
! Bitant.
else if (CCTK_Equals(domain,"bitant").eq.1) then
if (CCTK_Equals(bitant_plane,"xy").eq.1) then
if (zc.eq.zero) then
rmx = min(xmx-xc,ymx-yc,xc-xmn,yc-ymn,zmx)
else
rmx = min(xmx-xc,ymx-yc,xc-xmn,yc-ymn,zmx-zc,zc)
end if
else if (CCTK_Equals(bitant_plane,"xz").eq.1) then
if (yc.eq.zero) then
rmx = min(xmx-xc,zmx-zc,xc-xmn,zc-zmn,ymx)
else
rmx = min(xmx-xc,zmx-zc,xc-xmn,zc-zmn,ymx-yc,yc)
end if
else
if (xc.eq.zero) then
rmx = min(ymx-yc,zmx-zc,yc-ymn,zc-zmn,xmx)
else
rmx = min(ymx-yc,zmx-zc,yc-ymn,zc-zmn,xmx-xc,xc)
end if
end if
! Full.
else
rmx = min(xmx-xc,ymx-yc,zmx-zc,xc-xmn,yc-ymn,zc-zmn)
end if
rmx = 0.9*rmx
! Check if a special radius for the initial sphere
! has been forced by the parameter file.
if (find3) then
if (mfind.eq.1) then
r0 = ahf_r0_0
else if (mfind.eq.2) then
r0 = ahf_r0_1
else
r0 = ahf_r0_2
end if
else
r0 = ahf_r0
end if
if (r0.ne.zero) then
if (r0.le.rmx) then
rmx = r0
else
write (*,*)
write (*,*) 'ahf_r0 is too large, rescaling ...'
end if
end if
! *****************************
! *** GET INITIAL GUESS ***
! *****************************
! Initializing flags
sloppy = (ahf_sloppyguess.eq.1)
if (cartoon) sloppy = .true.
flow = (ahf_flow.eq.1)
inner = (ahf_inner.eq.1)
if (ahf_guessold.ne.0) then
guessold = .true.
else
guessold = .false.
end if
if (ahf_guess_absmin.ne.0) then
guess_absmin = .true.
else
guess_absmin = .false.
end if
if (ahf_manual_guess.ne.0) then
manual_guess = .true.
else
manual_guess = .false.
end if
if (ahf_minarea.ne.0) then
minarea = .true.
else
minarea = .false.
end if
! Get initial guess.
if (find3) then
if (mfind.eq.1) then
status_old = status_old_0
else if (mfind.eq.2) then
status_old = status_old_1
else
status_old = status_old_2
end if
end if
if (guessold.and.status_old) then
! Old horizon as initial guess.
if ((myproc.eq.0).and.verbose) then
write(*,*)
write(*,*) 'Using old horizon as initial guess'
end if
! If we are only looking for 1 horizon, then we are OK
! since the arrays (c0,cc,cs) where saved from the last
! call. If we are looking for 3 horizons, we saved all
! 3 sets of coefficients, but now we need to copy them
! back to the right place.
if (find3) then
if (mfind.eq.1) then
c0 = c0_0
cc = cc_0
cs = cs_0
else if (mfind.eq.2) then
c0 = c0_1
cc = cc_1
cs = cs_1
else
c0 = c0_2
cc = cc_2
cs = cs_2
end if
end if
else if (manual_guess) then
! Manual guess.
if ((myproc.eq.0).and.verbose) then
write(*,*)
write(*,*) 'Using manual initial guess'
end if
c0_temp(0) = ahf_l0_guess
c0_temp(2) = ahf_l2_guess
c0_temp(4) = ahf_l4_guess
c0_temp(6) = ahf_l6_guess
c0_temp(8) = ahf_l8_guess
c0_temp(10) = ahf_l10_guess
c0_temp(12) = ahf_l12_guess
c0_temp(14) = ahf_l14_guess
c0_temp(16) = ahf_l16_guess
c0_temp(18) = ahf_l18_guess
if (lmax.le.18) then
do i=0,lmax
c0(i) = c0_temp(i)
end do
else
do i=0,18
c0(i) = c0_temp(i)
end do
end if
else
! Standard initial guess.
if (.not.flow) then
! For minimization, call initial guess routine.
call AHFinder_initguess(CCTK_ARGUMENTS,rmx)
else
! For flow, take as initial guess a large sphere.
c0 = zero
cc = zero
cs = zero
c0_old = zero
cc_old = zero
cs_old = zero
if ((myproc.eq.0).and.verbose) then
write(*,*)
write(*,"(A35,ES11.3)") ' Initial guess sphere with radius: ',rmx
write(*,"(A13,3ES11.3)") ' centered on:',real(xc),real(yc),real(zc)
end if
c0(0) = rmx
end if
end if
! ***************************
! *** LOOK FOR HORIZON ***
! ***************************
if (.not.flow) then
! Minimization algorithm.
call AHFinder_min(CCTK_ARGUMENTS,NN,status,logf)
else
! Flow algorithm.
if ((ahf_ncall.eq.1).and.(mfind.eq.1)) then
allocate(hflow0(0:lmax),cflow0(0:lmax),nflow0(0:lmax))
allocate(hflowc(lmax,lmax),cflowc(lmax,lmax),nflowc(lmax,lmax))
allocate(hflows(lmax,lmax),cflows(lmax,lmax),nflows(lmax,lmax))
end if
call AHFinder_flow(CCTK_ARGUMENTS,rmx,status,logf)
flow = .false.
end if
! ***************************************
! *** WRITE MESSAGES AND LOG FILE ***
! ***************************************
if (find3) then
if (mfind.eq.1) then
status_old_0 = status
else if (mfind.eq.2) then
status_old_1 = status
else
status_old_2 = status
end if
else
status_old = status
end if
if (status) then
! Check if the expansion on the surface is small enough
! for a horizon. How small is small enough is of course
! pretty arbitrary, so to reduce the subjectivity I use
! three separate criteria:
!
! 1) The integral of the square of the expansion at the surface
! must be smaller than a given threshold (small1).
!
! 2) The mean value of the expansion on the surface must be
! smaller in absolute value than its standard deviation.
! This means that the mean value of the expansion is
! consistent with zero.
!
! 3) The integral of the square of the expansion at the surface
! must be smaller by a factor of "small2" than the same
! integral slightly outside and slightly inside.
horizon = .true.
small1 = 1.0D-2
small2 = 0.5D0
! Surface found.
call AHFinder_fun(CCTK_ARGUMENTS)
call AHFinder_exp(CCTK_ARGUMENTS)
call AHFinder_int(CCTK_ARGUMENTS)
if (ahf_gaussout.ne.0) then
call AHFinder_gau(CCTK_ARGUMENTS)
else
circ_eq = 0.0D0
meri_p1 = 0.0D0
meri_p2 = 0.0D0
end if
intexp_h = intexp
intexp2_h = intexp2
intarea_h = intarea
if (intexp2_h.gt.small1) horizon = .false.
! Find standard deviation: sqrt(<exp^2> - <exp>^2)
! The term inside the parenthesis is supposed to be positive,
! but may fail to be because of numerical errors in pathological
! situations, so be careful.
aux = intexp2_h/intarea_h - (intexp_h/intarea_h)**2
if (aux.ge.zero) then
aux = sqrt(aux)
if (abs(intexp_h/intarea_h)-aux.gt.zero) horizon = .false.
else
horizon = .false.
end if
! Surface slightly inside
aux = c0(0)
c0(0) = aux - half*min(dx,dy,dz)
call AHFinder_int(CCTK_ARGUMENTS)
expin = intexp
if (intexp2_h.gt.small2*intexp2) horizon = .false.
if (veryver) then
write(*,*)
write(*,*) 'Surface slightly inside the minimum surface: '
write(*,"(A21,ES14.6)") ' Integral of H =',intexp
write(*,"(A21,ES14.6)") ' Integral of H^2 =',intexp2
write(*,"(A21,ES14.6)") ' Mean value of H =',intexp/intarea
write(*,"(A21,ES14.6)") ' Mean value of H^2 =',intexp2/intarea
write(*,*) 'Number of interpolated points: ',
. inside_min_count
write(*,*) 'Number of those that are negative: ',
. inside_min_neg_count
endif
! Surface slightly outside.
c0(0) = aux + half*min(dx,dy,dz)
call AHFinder_int(CCTK_ARGUMENTS)
expout = intexp
if (intexp2_h.gt.small2*intexp2) horizon = .false.
if (veryver) then
write(*,*)
write(*,*) 'Surface slightly outside the minimum surface: '
write(*,"(A21,ES14.6)") ' Integral of H =',intexp
write(*,"(A21,ES14.6)") ' Integral of H^2 =',intexp2
write(*,"(A21,ES14.6)") ' Mean value of H =',intexp/intarea
write(*,"(A21,ES14.6)") ' Mean value of H^2 =',intexp2/intarea
write(*,*) 'Number of interpolated points: ',
. inside_min_count
write(*,*) 'Number of those that are negative: ',
. inside_min_neg_count
endif
c0(0) = aux
! What kind of horizon?
if ((expin.le.zero).and.(expout.ge.zero)) then
mtype = 1
else if ((expin.ge.zero).and.(expout.le.zero)) then
mtype = 2
else if ((expin.le.zero).and.(expout.le.zero)) then
mtype = 3
else
mtype = 4
end if
! Messages to screen and logfile
if (ahf_ReportAlways.eq.1) then
report = .true.
else
report = mtype.eq.1
end if
! Report on the details of the surface.
if (report.and.(myproc.eq.0)) then
! Open logfile.
if (logfile) then
open(11,file=logf,form='formatted',
. status='old',position='append')
end if
! Find inverse of area. Be carefull not to divide by zero!
! Also, a value of 1.0D10 indicates an error in the integration
! routine, and all integrals end up with the same value.
! So do not divide by it or I will be confused later.
if ((intarea_h.ne.zero).and.(intarea.lt.1.0D10)) then
aux = one/intarea_h
else
aux = one
end if
! Surface information. Notice that here I define the
! surface "mass" as:
!
! M = sqrt( A / (16 pi) ) = 0.141047396 sqrt(A)
ahfmass(mfind) = 0.141047396D0*sqrt(intarea_h)
write(*,*)
write(*,*) 'Surface found, details below.'
write(*,*)
write(*,"(A21,ES14.6)") ' Surface area =',intarea_h
write(*,"(A21,ES14.6)") ' Surface mass =',
. 0.141047396D0*sqrt(intarea_h)
write(*,"(A21,ES14.6)") ' Mean value of H =',aux*intexp_h
write(*,"(A21,ES14.6)") ' Mean value of H^2 =',aux*intexp2_h
write(*,"(A21,ES14.6)") ' Standard deviation =',
. sqrt(abs(aux*intexp2_h - (aux*intexp_h)**2))
write(*,*)
if (ahf_gaussout.ne.0) then
write(*,"(A11,ES14.6)") ' circ_eq =',circ_eq
write(*,"(A11,ES14.6)") ' meri_p1 =',meri_p1
write(*,"(A11,ES14.6)") ' meri_p2 =',meri_p2
write(*,*)
end if
if (logfile) then
write(11,*)
write(11,*) 'Surface found, details below'
write(11,*)
write(11,"(A21,ES14.6)") ' Surface area =',intarea_h
write(11,"(A21,ES14.6)") ' Surface mass =',
. 0.141047396D0*sqrt(intarea_h)
write(11,"(A21,ES14.6)") ' Mean value of H =',aux*intexp_h
write(11,"(A21,ES14.6)") ' Mean value of H^2 =',aux*intexp2_h
write(11,"(A21,ES14.6)") ' Standard deviation =',
. sqrt(abs(aux*intexp2_h - (aux*intexp_h)**2))
write(11,*)
if (ahf_gaussout.ne.0) then
write(11,"(A11,ES14.6)") ' circ_eq =',circ_eq
write(11,"(A11,ES14.6)") ' meri_p1 =',meri_p1
write(11,"(A11,ES14.6)") ' meri_p2 =',meri_p2
write(11,*)
end if
end if
if (mtype.eq.1) then
if (horizon) then
write(*,*) 'The surface seems to be an outer horizon.'
if (logfile) then
write(11,*) 'The surface seems to be an outer horizon.'
end if
else
write(*,*) 'The surface is probably an outer horizon, but'
write(*,*) 'the mean of the square of the expansion is'
write(*,*) 'not small enough. Try a larger lmax, or a'
write(*,*) 'smaller grid size.'
if (logfile) then
write(11,*) 'The surface is probably an outer horizon, but'
write(11,*) 'the mean of the square of the expansion is'
write(11,*) 'not small enough. Try a larger lmax, or a'
write(11,*) 'smaller grid size.'
end if
end if
else if (mtype.eq.2) then
if (horizon) then
write(*,*) 'The surface seems to be an inner horizon.'
if (logfile) then
write(11,*) 'The surface seems to be an inner horizon.'
end if
else
write(*,*) 'The surface is probably an inner horizon, but'
write(*,*) 'the mean of the square of the expansion is'
write(*,*) 'not small enough. Try a larger lmax, or a'
write(*,*) 'smaller grid size.'
if (logfile) then
write(11,*) 'The surface is probably an inner horizon, but'
write(11,*) 'the mean of the square of the expansion is'
write(11,*) 'not small enough. Try a larger lmax, or a'
write(11,*) 'smaller grid size.'
end if
end if
else if (mtype.eq.3)then
if (horizon) then
write(*,*) 'The surface seems to be a marginal horizon'
write(*,*) '(the integral of the expansion is negative'
write(*,*) 'on both sides.)'
if (logfile) then
write(11,*) 'The surface seems to be a marginal horizon'
write(11,*) '(the integral of the expansion is negative'
write(11,*) 'on both sides.)'
end if
else
write(*,*) 'The surface seems to be a trapped surface.'
if (logfile) then
write(11,*) 'The surface seems to be a trapped surface.'
end if
end if
else if (mtype.eq.4)then
if (horizon) then
write(*,*) 'The surface seems to be a marginal horizon'
write(*,*) '(the integral of the expansion is positive'
write(*,*) 'on both sides.)'
if (logfile) then
write(11,*) 'The surface seems to be a marginal horizon'
write(11,*) '(the integral of the expansion is positive'
write(11,*) 'on both sides.)'
end if
else
write(*,*) 'The surface does not seem to be a horizon.'
if (logfile) then
write(11,*) 'The surface does not seem to be a horizon.'
end if
end if
end if
! Shape.
if (verbose) then
write(*,*)
write(*,*) 'Shape coefficients:'
if (offset) then
write(*,*)
write(*,"(A6,ES14.6)") ' xc =',xc
write(*,"(A6,ES14.6)") ' yc =',yc
write(*,"(A6,ES14.6)") ' zc =',zc
end if
write(*,*)
write(*,"(A4,I2,A3,ES14.6)") ' c0(',0,') =',c0(0)
do l=1+stepz,lmax,1+stepz
write(*,"(A4,I2,A3,ES14.6)") ' c0(',l,') =',c0(l)
end do
end if
if (logfile) then
write(11,*)
write(11,*) 'Shape coefficients:'
if (offset) then
write(11,*)
write(11,"(A6,ES14.6)") ' xc =',xc
write(11,"(A6,ES14.6)") ' yc =',yc
write(11,"(A6,ES14.6)") ' zc =',zc
end if
write(11,*)
write(11,"(A4,I2,A3,ES14.6)") ' c0(',0,') =',c0(0)
do l=1+stepz,lmax,1+stepz
write(11,"(A4,I2,A3,ES14.6)") ' c0(',l,') =',c0(l)
end do
end if
if (nonaxi) then
if (.not.refy) then
if (verbose) then
write(*,*)
do l=1,lmax
do m=1,l
if (stepz*mod(l-m,2).eq.0) then
write(*,"(A4,I2,A1,I2,A4,ES14.6)") ' cc(',
. l,',',m,') =',cc(l,m)
end if
end do
end do
write(*,*)
do l=1,lmax
do m=1,l
if (stepz*mod(l-m,2).eq.0) then
write(*,"(A4,I2,A1,I2,A4,ES14.6)") ' cs(',
. l,',',m,') =',cs(l,m)
end if
end do
end do
end if
if (logfile) then
write(11,*)
do l=1,lmax
do m=1,l
if (stepz*mod(l-m,2).eq.0) then
write(11,"(A4,I2,A1,I2,A4,ES14.6)") ' cc(',
. l,',',m,') =',cc(l,m)
end if
end do
end do
write(11,*)
do l=1,lmax
do m=1,l
if (stepz*mod(l-m,2).eq.0) then
write(11,"(A4,I2,A1,I2,A4,ES14.6)") ' cs(',
. l,',',m,') =',cs(l,m)
end if
end do
end do
end if
else
if (verbose) then
write(*,*)
do l=1,lmax
do m=1,l
if (stepz*mod(l-m,2).eq.0) then
write(*,"(A4,I2,A1,I2,A4,ES14.6)") ' cc(',
. l,',',m,') =',cc(l,m)
end if
end do
end do
end if
if (logfile) then
write(11,*)
do l=1,lmax
do m=1,l
if (stepz*mod(l-m,2).eq.0) then
write(11,"(A4,I2,A1,I2,A4,ES14.6)") ' cc(',
. l,',',m,') =',cc(l,m)
end if
end do
end do
end if
end if
end if
! Close logfile
write(*,*)
if (logfile) then
write(11,*)
write(11,*) 'END OF LOG FILE'
write(11,*)
close(11)
end if
! If we found a surface that is not a horizon and we
! do not want to report all its details, just say that
! we did not find a horizon.
else if (myproc.eq.0) then
! Open logfile.
if (logfile) then
open(11,file=logf,form='formatted',
. status='old',position='append')
end if
! Write messages.
write(*,*)
write(*,*) 'No horizon found.'
if (logfile) then
write(11,*)
write(11,*) 'No horizon found.'
write(11,*)
end if
! Close logfile
write(*,*)
if (logfile) then
write(11,*)
write(11,*) 'END OF LOG FILE'
write(11,*)
close(11)
end if
end if
! No surface found.
else
mtype = 0
report = .false.
if (myproc.eq.0) then
! Open logfile.
if (logfile) then
open(11,file=logf,form='formatted',
. status='old',position='append')
end if
! Write messages.
write(*,*)
write(*,*) 'No horizon found.'
if (logfile) then
write(11,*)
write(11,*) 'No horizon found.'
write(11,*)
end if
! Close logfile
write(*,*)
if (logfile) then
write(11,*)
write(11,*) 'END OF LOG FILE'
write(11,*)
close(11)
end if
end if
end if
! ******************************************************
! *** PREPARING {ahfgrid3,ahf_exp3} FOR OUTPUT ***
! ******************************************************
if (find3) then
call AHFinder_find3(CCTK_ARGUMENTS,mtype)
end if
! ****************************
! *** WRITE DATA FILES ***
! ****************************
call AHFinder_Output(CCTK_ARGUMENTS,report,status,horizon,mtype,intarea_h)
! ****************
! *** MASK ***
! ****************
! Initialize the sides of the excised region to the center
! of the expansion.
if (ahf_ncall.eq.1) then
if (find3) then
if (mfind.eq.1) then
dhole1_xmin = xc
dhole1_ymin = yc
dhole1_zmin = zc
dhole1_xmax = xc
dhole1_ymax = yc
dhole1_zmax = zc
else if (mfind.eq.2) then
dhole2_xmin = xc
dhole2_ymin = yc
dhole2_zmin = zc
dhole2_xmax = xc
dhole2_ymax = yc
dhole2_zmax = zc
else
dhole3_xmin = xc
dhole3_ymin = yc
dhole3_zmin = zc
dhole3_xmax = xc
dhole3_ymax = yc
dhole3_zmax = zc
end if
else
dhole1_xmin = xc
dhole1_ymin = yc
dhole1_zmin = zc
dhole1_xmax = xc
dhole1_ymax = yc
dhole1_zmax = zc
end if
end if
! The mask should only be different from 1 inside a horizon.
! I therefore need to check first if I do have a horizon, and
! also if the mask is desired.
if ((horizon.and.(CCTK_EQUALS(ahf_mask,'strong'))).or.
. (status.and.(mtype.eq.1).and.(CCTK_EQUALS(ahf_mask,'weak')))) then
rhor = 0.0D0
if (find3) then
if ((mfind.eq.1).and.(ahf_mask_0.eq.1)) then
call AHFinder_mask(CCTK_ARGUMENTS,rhor)
else if ((mfind.eq.2).and.(ahf_mask_1.eq.1)) then
call AHFinder_mask(CCTK_ARGUMENTS,rhor)
else if ((mfind.eq.3).and.(ahf_mask_2.eq.1)) then
call AHFinder_mask(CCTK_ARGUMENTS,rhor)
end if
else
call AHFinder_mask(CCTK_ARGUMENTS,rhor)
end if
! Here I alter the parameters for SimpleExcision. Notice that at
! the moment, I only allow the excised cube to grow, and never
! to shrink. Also, notice that the sides of the cube have been
! set to 0.57*rhor. This is because if we want the corners of
! the cube to touch a sphere of radius rhor, we need to make the
! sides equal to 1/sqrt(3), which is roughly 0.57. If you worry
! that this is too close to the horizon, remember that rhor in fact
! has already been shrunk by a safety margin.
aux = 0.57D0*rhor
if (find3) then
if (mfind.eq.1) then
! First hole.
if (dhole1_xmin.gt.(xc-aux)) dhole1_xmin = xc-aux
if (dhole1_ymin.gt.(yc-aux)) dhole1_ymin = yc-aux
if (dhole1_zmin.gt.(zc-aux)) dhole1_zmin = zc-aux
if (dhole1_xmax.lt.(xc+aux)) dhole1_xmax = xc+aux
if (dhole1_ymax.lt.(yc+aux)) dhole1_ymax = yc+aux
if (dhole1_zmax.lt.(zc+aux)) dhole1_zmax = zc+aux
else if (mfind.eq.2) then
! Second hole.
if (dhole2_xmin.gt.(xc-aux)) dhole2_xmin = xc-aux
if (dhole2_ymin.gt.(yc-aux)) dhole2_ymin = yc-aux
if (dhole2_zmin.gt.(zc-aux)) dhole2_zmin = zc-aux
if (dhole2_xmax.lt.(xc+aux)) dhole2_xmax = xc+aux
if (dhole2_ymax.lt.(yc+aux)) dhole2_ymax = yc+aux
if (dhole2_zmax.lt.(zc+aux)) dhole2_zmax = zc+aux
else
! Third hole.
if (dhole3_xmin.gt.(xc-aux)) dhole3_xmin = xc-aux
if (dhole3_ymin.gt.(yc-aux)) dhole3_ymin = yc-aux
if (dhole3_zmin.gt.(zc-aux)) dhole3_zmin = zc-aux
if (dhole3_xmax.lt.(xc+aux)) dhole3_xmax = xc+aux
if (dhole3_ymax.lt.(yc+aux)) dhole3_ymax = yc+aux
if (dhole3_zmax.lt.(zc+aux)) dhole3_zmax = zc+aux
end if
else
if (dhole1_xmin.gt.(xc-aux)) dhole1_xmin = xc-aux
if (dhole1_ymin.gt.(yc-aux)) dhole1_ymin = yc-aux
if (dhole1_zmin.gt.(zc-aux)) dhole1_zmin = zc-aux
if (dhole1_xmax.lt.(xc+aux)) dhole1_xmax = xc+aux
if (dhole1_ymax.lt.(yc+aux)) dhole1_ymax = yc+aux
if (dhole1_zmax.lt.(zc+aux)) dhole1_zmax = zc+aux
end if
end if
! ********************************************************
! *** END OF LOOP FOR LOOKING FOR SEVERAL HORIZONS ***
! ********************************************************
! End of "giveup" if statement.
end if
! If we are looking for 3 horizons, save values of coefficients.
if (find3) then
if (mfind.eq.1) then
c0_0 = c0
cc_0 = cc
cs_0 = cs
else if (mfind.eq.2) then
c0_1 = c0
cc_1 = cc
cs_1 = cs
else
c0_2 = c0
cc_2 = cc
cs_2 = cs
end if
end if
write (*,*)
end do
! *******************************************************
! *** CALCULATE PROPER DISTANCES BETWEEN HORIZONS ***
! *******************************************************
if (find3) then
call AHFinder_dis(CCTK_ARGUMENTS)
end if
! **************************************************
! *** TRANSFORM PHYSICAL TO CONFORMAL METRIC ***
! **************************************************
! If necesary, change back the metric to conformal
! and change back the "conformal_state" flag.
if (ahfconformal) then
conformal_state = save_conformal_state
call PhysToConfInPlace (nx,ny,nz,psi,
& gxx,gxy,gxz,gyy,gyz,gzz)
end if
! ***************
! *** END ***
! ***************
end subroutine AHFinder
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