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pinit2lib.f
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c-----------------------------------------------------------------------
c 2d parallel PIC library for initialization
c pinit2lib.f contains procedures to initialize particle
c co-ordinates:
c PISTR2 initializes x, y and vx, vy co-ordinates for 2d code, with
c uniform distribution in space, and distributed data.
c PVISTR2 initializes x, y and vx, vy co-ordinates for 2d code, with
c uniform distribution in space, and distributed data. Uses
c parallel random number generator.
c PISTR2H initializes x, y and vx, vy, vz co-ordinates for magnetized
c 2-1/2d codes, with uniform distribution in space, and
c distributed data.
c PVISTR2H initializes x, y and vx, vy, vz co-ordinates for magnetized
c 2-1/2d codes, with uniform distribution in space, and
c distributed data. Uses parallel random number generator.
c PLDISTR2 initializes x, y co-ordinates for 2d code, with bi-linear
c distribution in space, and distributed data.
c PFDISTR2 initializes x, y co-ordinates for 2d code, with general
c distribution in space, and distributed data.
c PRDISTR2 randomizes x, y co-ordinates for 2d code, with general
c distribution in space previously calculated by FDISTR2.
c PVRDISTR2 initializes and randomizes x, y co-ordinates for 2d code,
c with general distribution in space, and distributed data.
c Uses parallel random number generator.
c PVDISTR2 initializes vx, vy co-ordinates for 2d code, with maxwellian
c velocity distribution with drift, and distributed data.
c PVVISTR2 initializes vx, vy co-ordinates for 2d code, with maxwellian
c velocity distribution with drift, and distributed data.
c Uses parallel random number generator.
c PVDISTR2H initializes vx, vy, vz co-ordinates for 2-1/2d code, with
c maxwellian velocity distribution with drift, and distributed
c data.
c PVVISTR2H initializes vx, vy, vz co-ordinates for 2-1/2d code, with
c maxwellian velocity distribution with drift, and distributed
c data. Uses parallel random number generator.
c PGBDISTR2L calculates guiding centers for magnetized 2-1/2d codes,
c with distributed data.
c PGBZDISTR2L calculates guiding centers for magnetized 2d codes, with
c distributed data.
c PGRBDISTR2L calculates guiding centers for relativistic, magnetized
c 2-1/2d codes, with distributed data.
c PGRBZDISTR2L calculates guiding centers for relativistic, magnetized
c 2d codes, with distributed data.
c FEDGES2 = finds new partitions boundaries (edges,noff,nyp)
c from analytic general density profile.
c ranorm = generates gaussian random numbers.
c randum = generates uniform random numbers.
c pranorm = generates gaussian random numbers in parallel.
c prandom = generates uniform random numbers in parallel.
c written by viktor k. decyk, ucla
c copyright 1995, regents of the university of california
c update: may 24, 2013
c-----------------------------------------------------------------------
subroutine PISTR2(part,edges,npp,nps,vtx,vty,vdx,vdy,npx,npy,nx,ny
1,idimp,npmax,nblok,idps,ipbc,ierr)
c for 2d code, this subroutine calculates initial particle co-ordinates
c and velocities with uniform density and maxwellian velocity with drift
c for distributed data.
c part(1,n,l) = position x of particle n in partition l
c part(2,n,l) = position y of particle n in partition l
c part(3,n,l) = velocity vx of particle n in partition l
c part(4,n,l) = velocity vy of particle n in partition l
c edges(1,l) = lower boundary of particle partition l
c edges(2,l) = upper boundary of particle partition l
c npp(l) = number of particles in partition l
c nps(l) = starting address of particles in partition l
c vtx/vty = thermal velocity of electrons in x/y direction
c vdx/vdy = drift velocity of beam electrons in x/y direction
c npx/npy = initial number of particles distributed in x/y direction
c nx/ny = system length in x/y direction
c idimp = size of phase space = 4
c npmax = maximum number of particles in each partition
c nblok = number of particle partitions.
c idps = number of partition boundaries
c ipbc = particle boundary condition = (0,1,2,3) =
c (none,2d periodic,2d reflecting,mixed reflecting/periodic)
c ierr = (0,1) = (no,yes) error condition exists
c ranorm = gaussian random number with zero mean and unit variance
c with spatial decomposition
c integer*8 npxy
double precision dnpx, dnpxy, dt1
double precision ranorm
double precision sum0, sum1, sum3, work3
dimension part(idimp,npmax,nblok)
dimension edges(idps,nblok), npp(nblok), nps(nblok)
dimension sum3(3), work3(3)
ierr = 0
c particle distribution constant
dnpx = dble(npx)
c set boundary values
edgelx = 0.
edgely = 0.
at1 = float(nx)/float(npx)
at2 = float(ny)/float(npy)
if (ipbc.eq.2) then
edgelx = 1.
edgely = 1.
at1 = float(nx-2)/float(npx)
at2 = float(ny-2)/float(npy)
else if (ipbc.eq.3) then
edgelx = 1.
edgely = 0.
at1 = float(nx-2)/float(npx)
at2 = float(ny)/float(npy)
endif
do 30 k = 1, npy
yt = edgely + at2*(float(k) - .5)
do 20 j = 1, npx
c uniform density profile
xt = edgelx + at1*(float(j) - .5)
c maxwellian velocity distribution
vxt = vtx*ranorm()
vyt = vty*ranorm()
do 10 l = 1, nblok
if ((yt.ge.edges(1,l)).and.(yt.lt.edges(2,l))) then
npt = npp(l) + 1
if (npt.le.npmax) then
part(1,npt,l) = xt
part(2,npt,l) = yt
part(3,npt,l) = vxt
part(4,npt,l) = vyt
npp(l) = npt
else
ierr = ierr + 1
endif
endif
10 continue
20 continue
30 continue
npxyp = 0
c add correct drift
sum3(1) = 0.0d0
sum3(2) = 0.0d0
do 50 l = 1, nblok
sum0 = 0.0d0
sum1 = 0.0d0
do 40 j = nps(l), npp(l)
npxyp = npxyp + 1
sum0 = sum0 + part(3,j,l)
sum1 = sum1 + part(4,j,l)
40 continue
sum3(1) = sum3(1) + sum0
sum3(2) = sum3(2) + sum1
50 continue
sum3(3) = npxyp
call PDSUM(sum3,work3,3,1)
dnpxy = sum3(3)
call PIMAX(ierr,iwork,1,1)
dt1 = 1.0d0/dnpxy
sum3(1) = dt1*sum3(1) - vdx
sum3(2) = dt1*sum3(2) - vdy
do 70 l = 1, nblok
do 60 j = nps(l), npp(l)
part(3,j,l) = part(3,j,l) - sum3(1)
part(4,j,l) = part(4,j,l) - sum3(2)
60 continue
70 continue
c process errors
if (ierr.gt.0) then
write (2,*) 'particle overflow error, ierr = ', ierr
else if (dnpxy.ne.(dnpx*dble(npy))) then
ierr = dnpxy - dnpx*dble(npy)
write (2,*) 'particle distribution truncated, np = ', dnpxy
endif
return
end
c-----------------------------------------------------------------------
subroutine PVISTR2(part,npp,nps,vtx,vty,vdx,vdy,npx,npy,nx,ny,idim
1p,npmax,nblok,ipbc,vranx,vrany,kstrt,nvp,ndv,nvrp,ierr)
c for 2d code, this subroutine calculates initial particle co-ordinates
c and velocities with uniform density and maxwellian velocity with drift
c for distributed data. on input, the array npp contains the number of
c particles already stored in part, normally zero. on output, contains
c the number of particles stored in part.
c the total number of particles should be a multiple of ndv, if the
c number of processors is <= ndv, or else a multiple of the number of
c processors.
c part(1,n,l) = position x of particle n in partition l
c part(2,n,l) = position y of particle n in partition l
c part(3,n,l) = velocity vx of particle n in partition l
c part(4,n,l) = velocity vy of particle n in partition l
c npp(l) = number of particles in partition l
c nps(l) = starting address of particles in partition l
c vtx/vty = thermal velocity of electrons in x/y direction
c vdx/vdy = drift velocity of beam electrons in x/y direction
c npx/npy = initial number of particles distributed in x/y direction
c nx/ny = system length in x/y direction
c idimp = size of phase space = 4
c npmax = maximum number of particles in each partition
c nblok = number of particle partitions.
c ipbc = particle boundary condition = (0,1,2,3) =
c (none,2d periodic,2d reflecting,mixed reflecting/periodic)
c vranx, vrany = output arrays for parallel gaussian random numbers,
c with zero mean and unit variance
c kstrt = starting data block number
c nvp = number of real or virtual processors
c ndv = total maximum number of random seeds, currently 256
c nvrp = number of parallel seeds per processor
c ierr = (0,1) = (no,yes) error condition exists
c npx*npy should be a multiple of nvrp*nvp
c with spatial decomposition
c integer*8 npxy, ipp, nppv, koff, nng
double precision vranx, vrany
double precision dnpx, dnpxy, dnppv, dkoff, dnng, dt1
double precision sum0, sum1, sum3, work3
dimension part(idimp,npmax,nblok)
dimension npp(nblok), nps(nblok)
dimension vranx(nvrp,nblok), vrany(nvrp,nblok)
dimension sum3(3), work3(3)
ierr = 0
c particle distribution constants
ks = kstrt - 2
dnpx = dble(npx)
dnpxy = dnpx*dble(npy)
c npd = total number of seeds used
npd = nvrp*nvp
c ipp = number of particles per seed
ipp = dnpxy/dble(npd)
c nppv = number of particles per processor
nppv = nvrp*ipp
dnppv = dble(nppv)
c adjacent mdp processors share the same seed
mdp = nvp/min0(nvp,ndv)
if (dnpxy.ne.(dble(ipp)*dble(npd))) ierr = 1
call PIMAX(ierr,iwork,1,1)
if (ierr.gt.0) then
if (kstrt.eq.1) then
write (2,*) 'number of seeds not multiple of particle number',
1,npd, dnpxy
endif
return
endif
c set boundary values
edgelx = 0.
edgely = 0.
at1 = float(nx)/float(npx)
at2 = float(ny)/float(npy)
if (ipbc.eq.2) then
edgelx = 1.
edgely = 1.
at1 = float(nx-2)/float(npx)
at2 = float(ny-2)/float(npy)
else if (ipbc.eq.3) then
edgelx = 1.
edgely = 0.
at1 = float(nx-2)/float(npx)
at2 = float(ny)/float(npy)
endif
c outer loop over processor blocks which share the same seed
do 40 ii = 1, mdp
c particles in each block get random numbers from the same seed
do 30 n = 1, ipp
call pranorm(vranx,kstrt,nvp,nvrp,nd,nvrp,nblok)
call pranorm(vrany,kstrt,nvp,nvrp,nd,nvrp,nblok)
c inner loop over independent seeds
do 20 l = 1, nblok
id = (l + ks)/mdp
is = l + ks - id*mdp + 1
dkoff = dnppv*dble(l + ks)
do 10 jj = 1, nvrp
c i = local particle number belonging to jj seed
i = n + ipp*(jj - 1)
c nng = global particle number
dnng = dble(i) + dkoff
c j, k = used to determine spatial location of this particle
k = (dnng - 1.0d0)/dnpx
j = dnng - dnpx*dble(k)
k = k + 1
vxt = vtx*vranx(jj,l)
vyt = vty*vrany(jj,l)
c nth group keeps nth block of random numbers
if (ii.eq.is) then
npt = nps(l) + i - 1
if (npt.le.npmax) then
c uniform density profile
part(1,npt,l) = edgelx + at1*(float(j) - .5)
part(2,npt,l) = edgely + at2*(float(k) - .5)
c maxwellian velocity distribution
part(3,npt,l) = vxt
part(4,npt,l) = vyt
else
ierr = ierr + 1
endif
endif
10 continue
c update particle number
if (ii.eq.is) npp(l) = npp(l) + nvrp
20 continue
30 continue
40 continue
npxyp = 0
c add correct drift
sum3(1) = 0.0d0
sum3(2) = 0.0d0
do 60 l = 1, nblok
sum0 = 0.0d0
sum1 = 0.0d0
do 50 j = nps(l), npp(l)
npxyp = npxyp + 1
sum0 = sum0 + part(3,j,l)
sum1 = sum1 + part(4,j,l)
50 continue
sum3(1) = sum3(1) + sum0
sum3(2) = sum3(2) + sum1
60 continue
sum3(3) = npxyp
call PDSUM(sum3,work3,3,1)
dnpxy = sum3(3)
call PISUM(ierr,iwork,1,1)
dt1 = 1.0d0/dnpxy
sum3(1) = dt1*sum3(1) - vdx
sum3(2) = dt1*sum3(2) - vdy
do 80 l = 1, nblok
do 70 j = nps(l), npp(l)
part(3,j,l) = part(3,j,l) - sum3(1)
part(4,j,l) = part(4,j,l) - sum3(2)
70 continue
80 continue
c process errors
if (ierr.gt.0) then
if (kstrt.eq.1) then
write (2,*) 'particle overflow error, ierr = ', ierr
endif
else if (dnpxy.ne.(dnpx*dble(npy))) then
ierr = dnpxy - dnpx*dble(npy)
if (kstrt.eq.1) then
write (2,*) 'particle distribution truncated, np = ', dnpxy
endif
endif
return
end
c-----------------------------------------------------------------------
subroutine PISTR2H(part,edges,npp,nps,vtx,vty,vtz,vdx,vdy,vdz,npx,
1npy,nx,ny,idimp,npmax,nblok,idps,ipbc,ierr)
c for 2-1/2d code, this subroutine calculates initial particle
c co-ordinates and velocities with uniform density and maxwellian
c velocity with drift for distributed data.
c part(1,n,l) = position x of particle n in partition l
c part(2,n,l) = position y of particle n in partition l
c part(3,n,l) = velocity vx of particle n in partition l
c part(4,n,l) = velocity vy of particle n in partition l
c part(5,n,l) = velocity vz of particle n in partition l
c edges(1,l) = lower boundary of particle partition l
c edges(2,l) = upper boundary of particle partition l
c npp(l) = number of particles in partition l
c nps(l) = starting address of particles in partition l
c vtx/vty/vtz = thermal velocity of electrons in x/y/z direction
c vdx/vdy/vdz = drift velocity of beam electrons in x/y/z direction
c npx/npy = initial number of particles distributed in x/y direction
c nx/ny = system length in x/y direction
c idimp = size of phase space = 5
c npmax = maximum number of particles in each partition
c nblok = number of particle partitions.
c idps = number of partition boundaries
c ipbc = particle boundary condition = (0,1,2,3) =
c (none,2d periodic,2d reflecting,mixed reflecting/periodic)
c ierr = (0,1) = (no,yes) error condition exists
c ranorm = gaussian random number with zero mean and unit variance
c with spatial decomposition
c integer*8 npxy
double precision dnpx, dnpxy, dt1
double precision ranorm
double precision sum0, sum1, sum2, sum4, work4
dimension part(idimp,npmax,nblok)
dimension edges(idps,nblok), npp(nblok), nps(nblok)
dimension sum4(4), work4(4)
ierr = 0
c particle distribution constant
dnpx = dble(npx)
c set boundary values
edgelx = 0.
edgely = 0.
at1 = float(nx)/float(npx)
at2 = float(ny)/float(npy)
if (ipbc.eq.2) then
edgelx = 1.
edgely = 1.
at1 = float(nx-2)/float(npx)
at2 = float(ny-2)/float(npy)
else if (ipbc.eq.3) then
edgelx = 1.
edgely = 0.
at1 = float(nx-2)/float(npx)
at2 = float(ny)/float(npy)
endif
do 30 k = 1, npy
yt = edgely + at2*(float(k) - .5)
do 20 j = 1, npx
c uniform density profile
xt = edgelx + at1*(float(j) - .5)
c maxwellian velocity distribution
vxt = vtx*ranorm()
vyt = vty*ranorm()
vzt = vtz*ranorm()
do 10 l = 1, nblok
if ((yt.ge.edges(1,l)).and.(yt.lt.edges(2,l))) then
npt = npp(l) + 1
if (npt.le.npmax) then
part(1,npt,l) = xt
part(2,npt,l) = yt
part(3,npt,l) = vxt
part(4,npt,l) = vyt
part(5,npt,l) = vzt
npp(l) = npt
else
ierr = ierr + 1
endif
endif
10 continue
20 continue
30 continue
npxyp = 0
c add correct drift
sum4(1) = 0.0d0
sum4(2) = 0.0d0
sum4(3) = 0.0d0
do 50 l = 1, nblok
sum0 = 0.0d0
sum1 = 0.0d0
sum2 = 0.0d0
do 40 j = nps(l), npp(l)
npxyp = npxyp + 1
sum0 = sum0 + part(3,j,l)
sum1 = sum1 + part(4,j,l)
sum2 = sum2 + part(5,j,l)
40 continue
sum4(1) = sum4(1) + sum0
sum4(2) = sum4(2) + sum1
sum4(3) = sum4(3) + sum2
50 continue
sum4(4) = npxyp
call PDSUM(sum4,work4,4,1)
dnpxy = sum4(4)
call PIMAX(ierr,iwork,1,1)
dt1 = 1.0d0/dnpxy
sum4(1) = dt1*sum4(1) - vdx
sum4(2) = dt1*sum4(2) - vdy
sum4(3) = dt1*sum4(3) - vdz
do 70 l = 1, nblok
do 60 j = nps(l), npp(l)
part(3,j,l) = part(3,j,l) - sum4(1)
part(4,j,l) = part(4,j,l) - sum4(2)
part(5,j,l) = part(5,j,l) - sum4(3)
60 continue
70 continue
c process errors
if (ierr.gt.0) then
write (2,*) 'particle overflow error, ierr = ', ierr
else if (dnpxy.ne.(dnpx*dble(npy))) then
ierr = dnpxy - dnpx*dble(npy)
write (2,*) 'particle distribution truncated, np = ', dnpxy
endif
return
end
c-----------------------------------------------------------------------
subroutine PVISTR2H(part,npp,nps,vtx,vty,vtz,vdx,vdy,vdz,npx,npy,n
1x,ny,idimp,npmax,nblok,ipbc,vranx,vrany,vranz,kstrt,nvp,ndv,nvrp,i
2err)
c for 2-1/2d code, this subroutine calculates initial particle
c co-ordinates and velocities with uniform density and maxwellian
c velocity with drift for distributed data.
c on input, the array npp contains the number of particles already
c stored in part, normally zero.
c on output, contains the number of particles stored in part.
c the total number of particles should be a multiple of ndv, if the
c number of processors is <= ndv, or else a multiple of the number of
c processors.
c part(1,n,l) = position x of particle n in partition l
c part(2,n,l) = position y of particle n in partition l
c part(3,n,l) = velocity vx of particle n in partition l
c part(4,n,l) = velocity vy of particle n in partition l
c part(5,n,l) = velocity vz of particle n in partition l
c npp(l) = number of particles in partition l
c nps(l) = starting address of particles in partition l
c vtx/vty/vtz = thermal velocity of electrons in x/y/z direction
c vdx/vdy/vdz = drift velocity of beam electrons in x/y/z direction
c npx/npy = initial number of particles distributed in x/y direction
c nx/ny = system length in x/y direction
c idimp = size of phase space = 5
c npmax = maximum number of particles in each partition
c nblok = number of particle partitions.
c ipbc = particle boundary condition = (0,1,2,3) =
c (none,2d periodic,2d reflecting,mixed reflecting/periodic)
c vranx,vrany,vranz = output arrays for parallel gaussian random numbers
c with zero mean and unit variance
c kstrt = starting data block number
c nvp = number of real or virtual processors
c ndv = total maximum number of random seeds, currently 256
c nvrp = number of parallel seeds per processor
c ierr = (0,1) = (no,yes) error condition exists
c npx*npy should be a multiple of nvrp*nvp
c with spatial decomposition
c integer*8 npxy, ipp, nppv, koff, nng
double precision vranx, vrany, vranz
double precision dnpx, dnpxy, dnppv, dkoff, dnng, dt1
double precision sum0, sum1, sum4, work4
dimension part(idimp,npmax,nblok)
dimension npp(nblok), nps(nblok)
dimension vranx(nvrp,nblok), vrany(nvrp,nblok), vranz(nvrp,nblok)
dimension sum4(4), work4(4)
ierr = 0
c particle distribution constants
ks = kstrt - 2
dnpx = dble(npx)
dnpxy = dnpx*dble(npy)
c npd = total number of seeds used
npd = nvrp*nvp
c ipp = number of particles per seed
ipp = dnpxy/dble(npd)
c nppv = number of particles per processor
nppv = nvrp*ipp
dnppv = dble(nppv)
c adjacent mdp processors share the same seed
mdp = nvp/min0(nvp,ndv)
if (dnpxy.ne.(dble(ipp)*dble(npd))) ierr = 1
call PIMAX(ierr,iwork,1,1)
if (ierr.gt.0) then
if (kstrt.eq.1) then
write (2,*) 'number of seeds not multiple of particle number',
1,npd, dnpxy
endif
return
endif
c set boundary values
edgelx = 0.
edgely = 0.
at1 = float(nx)/float(npx)
at2 = float(ny)/float(npy)
if (ipbc.eq.2) then
edgelx = 1.
edgely = 1.
at1 = float(nx-2)/float(npx)
at2 = float(ny-2)/float(npy)
else if (ipbc.eq.3) then
edgelx = 1.
edgely = 0.
at1 = float(nx-2)/float(npx)
at2 = float(ny)/float(npy)
endif
c outer loop over processor blocks which share the same seed
do 40 ii = 1, mdp
c particles in each block get random numbers from the same seed
do 30 n = 1, ipp
call pranorm(vranx,kstrt,nvp,nvrp,nd,nvrp,nblok)
call pranorm(vrany,kstrt,nvp,nvrp,nd,nvrp,nblok)
call pranorm(vranz,kstrt,nvp,nvrp,nd,nvrp,nblok)
c inner loop over independent seeds
do 20 l = 1, nblok
id = (l + ks)/mdp
is = l + ks - id*mdp + 1
dkoff = dnppv*dble(l + ks)
do 10 jj = 1, nvrp
c i = local particle number belonging to jj seed
i = n + ipp*(jj - 1)
c nng = global particle number
dnng = dble(i) + dkoff
c j, k = used to determine spatial location of this particle
k = (dnng - 1.0d0)/dnpx
j = dnng - dnpx*dble(k)
k = k + 1
vxt = vtx*vranx(jj,l)
vyt = vty*vrany(jj,l)
vzt = vtz*vranz(jj,l)
c nth group keeps nth block of random numbers
if (ii.eq.is) then
npt = nps(l) + i - 1
if (npt.le.npmax) then
c uniform density profile
part(1,npt,l) = edgelx + at1*(float(j) - .5)
part(2,npt,l) = edgely + at2*(float(k) - .5)
c maxwellian velocity distribution
part(3,npt,l) = vxt
part(4,npt,l) = vyt
part(5,npt,l) = vzt
else
ierr = ierr + 1
endif
endif
10 continue
c update particle number
if (ii.eq.is) npp(l) = npp(l) + nvrp
20 continue
30 continue
40 continue
npxyp = 0
c add correct drift
sum4(1) = 0.0d0
sum4(2) = 0.0d0
sum4(3) = 0.0d0
do 60 l = 1, nblok
sum0 = 0.0d0
sum1 = 0.0d0
sum2 = 0.0d0
do 50 j = nps(l), npp(l)
npxyp = npxyp + 1
sum0 = sum0 + part(3,j,l)
sum1 = sum1 + part(4,j,l)
sum2 = sum2 + part(5,j,l)
50 continue
sum4(1) = sum4(1) + sum0
sum4(2) = sum4(2) + sum1
sum4(3) = sum4(3) + sum2
60 continue
sum4(4) = npxyp
call PDSUM(sum4,work4,4,1)
dnpxy = sum4(4)
call PISUM(ierr,iwork,1,1)
dt1 = 1./dnpxy
sum4(1) = dt1*sum4(1) - vdx
sum4(2) = dt1*sum4(2) - vdy
sum4(3) = dt1*sum4(3) - vdz
do 80 l = 1, nblok
do 70 j = nps(l), npp(l)
part(3,j,l) = part(3,j,l) - sum4(1)
part(4,j,l) = part(4,j,l) - sum4(2)
part(5,j,l) = part(5,j,l) - sum4(3)
70 continue
80 continue
c process errors
if (ierr.gt.0) then
if (kstrt.eq.1) then
write (2,*) 'particle overflow error, ierr = ', ierr
endif
else if (dnpxy.ne.(dnpx*dble(npy))) then
ierr = dnpxy - dnpx*dble(npy)
if (kstrt.eq.1) then
write (2,*) 'particle distribution truncated, np = ', dnpxy
endif
endif
return
end
c-----------------------------------------------------------------------
subroutine PLDISTR2(part,nps,anlx,anly,npx,npy,nx,ny,idimp,npmax,n
1blok,kstrt,nvp,ipbc,ierr)
c for 2d code, this subroutine calculates initial particle co-ordinates
c with the following bi-linear density profile:
c n(x,y) = n(x)*n(y), where n(x) = n0x*(1. + anlx*(x/nx - .5)) and
c n(y) = n0y*(1. + anly*(y/ny - .5)) and where
c n0x = npx/(nx - 2*edgelx) and n0y = npy/(ny - 2*edgely)
c for distributed data.
c particles are not necessarily in the correct processor.
c part(1,n,l) = position x of particle n in partition l
c part(2,n,l) = position y of particle n in partition l
c nps(l) = starting address of particles in partition l
c anlx/anly = initial linear density weight in x/y direction
c npx/npy = initial number of particles distributed in x/y direction
c nx/ny = system length in x/y direction
c idimp = size of phase space = 4
c npmax = maximum number of particles in each partition
c nblok = number of particle partitions
c kstrt = starting data block number
c nvp = number of real or virtual processors
c ipbc = particle boundary condition = (0,1,2,3) =
c (none,2d periodic,2d reflecting,mixed reflecting/periodic)
c ierr = (0,1) = (no,yes) error condition exists
c with spatial decomposition
implicit none
integer npx, npy, nx, ny, idimp, npmax, nblok, kstrt, nvp, ipbc
integer ierr, nps
real anlx, anly
real part
dimension part(idimp,npmax,nblok)
dimension nps(nblok)
c local data
c integer*8 npxy, nppv, koff, nng
double precision dnpxy, dnpx, dnppv, dkoff, dnng
integer nppv, ks, j, k, l, n, noff, iwork
real edgelx, edgely, at1, at2, bt1, bt2, antx, anty, xt, yt
ierr = 0
c particle distribution constants
ks = kstrt - 2
dnpx = dble(npx)
nppv = dnpx*dble(npy)/dble(nvp)
nppv = min(nppv,npmax)
dnppv = dble(nppv)
dnpxy = dnppv*dble(nvp)
c check for errors
if (dnpxy.ne.(dnpx*dble(npy))) ierr = 1
call PISUM(ierr,iwork,1,1)
if (ierr.gt.0) then
ierr = dnpxy - dnpx*dble(npy)
write (2,*) 'particle distribution truncated, np = ', dnpxy
return
endif
c set boundary values
edgelx = 0.
edgely = 0.
at1 = float(nx)/float(npx)
at2 = float(ny)/float(npy)
if (ipbc.eq.2) then
edgelx = 1.
edgely = 1.
at1 = float(nx-2)/float(npx)
at2 = float(ny-2)/float(npy)
else if (ipbc.eq.3) then
edgelx = 1.
edgely = 0.
at1 = float(nx-2)/float(npx)
at2 = float(ny)/float(npy)
endif
if (anly.ne.0.) then
anty = anly/float(ny)
at2 = 2.*anty*at2
bt2 = 1. - .5*anty*(float(ny) - 2.*edgely)
endif
if (anlx.ne.0.) then
antx = anlx/float(nx)
at1 = 2.*antx*at1
bt1 = 1. - .5*antx*(float(nx) - 2.*edgelx)
endif
c uniform density profile
do 20 l = 1, nblok
dkoff = dnppv*dble(l + ks)
noff = nps(l) - 1
do 10 n = 1, nppv
c j, k = used to determine spatial location of this particle
dnng = dble(n) + dkoff
k = (dnng - 1.0d0)/dnpx
j = dnng - dnpx*dble(k)
k = k + 1
c linear density in x
if (anlx.ne.0.) then
xt = edgelx + (sqrt(bt1*bt1 + at1*(float(j) - .5)) - bt1)/antx
c uniform density in x
else
xt = edgelx + at1*(float(j) - .5)
endif
c linear density in y
if (anly.ne.0.) then
yt = edgely + (sqrt(bt2*bt2 + at2*(float(k) - .5)) - bt2)/anty
c uniform density in y
else
yt = edgely + at2*(float(k) - .5)
endif
part(1,n+noff,l) = xt
part(2,n+noff,l) = yt
10 continue
20 continue
return
end
c-----------------------------------------------------------------------
subroutine PFDISTR2(part,nps,fnx,argx1,argx2,argx3,fny,argy1,argy2
1,argy3,npx,npy,nx,ny,idimp,npmax,nblok,kstrt,nvp,ipbc,ierr)
c for 2d code, this subroutine calculates initial particle co-ordinates
c with general density profile n(x,y) = n(x)*n(y),
c where density in x is given by n(x) = fnx(x,argx1,argx2,argx3,0)
c and integral of the density is given by = fnx(x,argx1,argx2,argx3,1)
c and where density in y is given by n(y) = fny(y,argy1,argy2,argy3,0)
c and integral of the density is given by = fny(y,argy1,argy2,argy3,1)
c for distributed data.
c particles are not necessarily in the correct processor.
c part(1,n,l) = position x of particle n in partition l
c part(2,n,l) = position y of particle n in partition l
c nps(l) = starting address of particles in partition l
c fnx/fny = density and density integral function in x/y direction
c argx1,argx2,argx3 = arguments to fnx
c argy1,argy2,argy3 = arguments to fny
c npx/npy = initial number of particles distributed in x/y direction
c nx/ny = system length in x/y direction
c idimp = size of phase space = 4 or 5
c npmax = maximum number of particles in each partition
c nblok = number of particle partitions
c kstrt = starting data block number
c nvp = number of real or virtual processors
c ipbc = particle boundary condition = (0,1,2,3) =
c (none,2d periodic,2d reflecting,mixed reflecting/periodic)
c ierr = (0,1) = (no,yes) error condition exists
c with spatial decomposition
implicit none
integer npx, npy, nx, ny, idimp, npmax, nblok, kstrt, nvp, ipbc
integer ierr, nps
real argx1, argx2, argx3, argy1, argy2, argy3
real part
dimension part(idimp,npmax,nblok)
dimension nps(nblok)
real fnx, fny
external fnx, fny
c local data
c integer*8 npxy, nppv, koff, nng
double precision dnpxy, dnpx, dnppv, dkoff, dnng
integer nppv, ks, kc, jc, i, j, k, l, n, nn, noff
integer imax, iwork
real edgelx, edgely, anx, any, bnx, bny, xt, yt, xt0, yt0, x0, y0
real xn, yn, eps, big, f, fp
ierr = 0
c particle distribution constants
ks = kstrt - 2
dnpx = dble(npx)
nppv = dnpx*dble(npy)/dble(nvp)
nppv = min(nppv,npmax)
dnppv = dble(nppv)
dnpxy = dnppv*dble(nvp)
c eps = convergence criterion
imax = max(nx,ny)
eps = 0.0001
big = 0.5
c check for errors
if (dnpxy.ne.(dnpx*dble(npy))) ierr = 1
call PIMAX(ierr,iwork,1,1)
if (ierr.gt.0) then
ierr = dnpxy - dnpx*dble(npy)
write (2,*) 'particle distribution truncated, np = ', dnpxy
return
endif
c set boundary values
edgelx = 0.
edgely = 0.
if (ipbc.eq.2) then
edgelx = 1.
edgely = 1.
else if (ipbc.eq.3) then
edgelx = 1.
edgely = 0.
endif
c find normalization for function
anx = float(nx) - edgelx
any = float(ny) - edgely
x0 = fnx(edgelx,argx1,argx2,argx3,1)
y0 = fny(edgely,argy1,argy2,argy3,1)
bnx = float(npx)/(fnx(anx,argx1,argx2,argx3,1) - x0)
bny = float(npy)/(fny(any,argy1,argy2,argy3,1) - y0)
x0 = bnx*x0 - .5
y0 = bny*y0 - .5
c calculate density profile
do 90 l = 1, nblok
dkoff = dnppv*dble(l + ks)
noff = nps(l) - 1
c integrate to find starting point in y
kc = dkoff/dnpx
yt0 = edgely
yt = yt0
fp = bny*fny(yt,argy1,argy2,argy3,0)
if (fp.eq.0.0) fp = 0.5
yt = yt + 1.0/fp
do 20 k = 1, kc
yn = float(k) + y0
c guess next value for yt
if (k.gt.1) then
fp = bny*fny(yt,argy1,argy2,argy3,0)
if (fp.eq.0.0) fp = 1.0
yt = yt + 1.0/fp
endif
yt = max(edgely,min(yt,any))
i = 0
10 f = bny*fny(yt,argy1,argy2,argy3,1) - yn
c find improved value for yt
if (abs(f).ge.eps) then
fp = bny*fny(yt,argy1,argy2,argy3,0)
c newton's method
if ((abs(f).lt.big).and.(fp.gt.0.0)) then
yt0 = yt
yt = yt - f/fp
yt = max(edgely,min(yt,any))
c bisection method
else if (f.gt.0.) then
fp = .5*(yt - yt0)
yt = yt0 + fp
else
fp = yt - yt0
yt0 = yt
yt = yt + fp
endif
i = i + 1
if (i.lt.imax) go to 10
write (2,*) 'newton iteration max exceeded, yt = ', yt
ierr = ierr + 1
endif
yt0 = yt
20 continue
c quit if error
if (ierr.ne.0) return
c integrate to find starting point in x
jc = dkoff - dnpx*dble(kc)
xt0 = edgelx
xt = xt0
fp = bnx*fnx(xt,argx1,argx2,argx3,0)
if (fp.gt.0.0) xt = xt + 0.5/fp
do 40 j = 1, jc
xn = float(j) + x0
c guess next value for xt
if (j.gt.1) then
fp = bnx*fnx(xt,argx1,argx2,argx3,0)
if (fp.eq.0.0) fp = 1.0
xt = xt + 1.0/fp
endif
xt = max(edgelx,min(xt,anx))
i = 0
30 f = bnx*fnx(xt,argx1,argx2,argx3,1) - xn
c find improved value for xt
if (abs(f).ge.eps) then
fp = bnx*fnx(xt,argx1,argx2,argx3,0)
c newton's method
if ((abs(f).lt.big).and.(fp.gt.0.0)) then
xt0 = xt
xt = xt - f/fp
xt = max(edgelx,min(xt,anx))
c bisection method
else if (f.gt.0.) then
fp = .5*(xt - xt0)
xt = xt0 + fp
else
fp = xt - xt0
xt0 = xt
xt = xt + fp
endif
i = i + 1
if (i.lt.imax) go to 30
write (2,*) 'newton iteration max exceeded, xt = ', xt
ierr = ierr + 1
endif
xt0 = xt
40 continue
c quit if error
if (ierr.ne.0) return
c density profile in x
kc = kc + 1
do 60 n = 1, min(npx,nppv)
c j, k = used to determine spatial location of this particle
dnng = dble(n) + dkoff
k = (dnng - 1.0d0)/dnpx
j = dnng - dnpx*dble(k)
k = k + 1
xn = float(j) + x0
c guess next value for xt
if (j.eq.1) then
xt0 = edgelx
xt = xt0
fp = bnx*fnx(xt,argx1,argx2,argx3,0)
if (fp.eq.0.0) fp = 0.5
xt = xt + 0.5/fp
else
fp = bnx*fnx(xt,argx1,argx2,argx3,0)
if (fp.eq.0.0) fp = 1.0
xt = xt + 1.0/fp
endif
xt = max(edgelx,min(xt,anx))
i = 0
50 f = bnx*fnx(xt,argx1,argx2,argx3,1) - xn
c find improved value for xt
if (abs(f).ge.eps) then
fp = bnx*fnx(xt,argx1,argx2,argx3,0)
c newton's method
if ((abs(f).lt.big).and.(fp.gt.0.0)) then
xt0 = xt
xt = xt - f/fp
xt = max(edgelx,min(xt,anx))
c bisection method
else if (f.gt.0.) then
fp = .5*(xt - xt0)
xt = xt0 + fp
else
fp = xt - xt0
xt0 = xt
xt = xt + fp
endif
i = i + 1
if (i.lt.imax) go to 50
write (2,*) 'newton iteration max exceeded, xt = ', xt
ierr = ierr + 1
endif
part(1,n+noff,l) = xt
xt0 = xt
60 continue
c quit if error
if (ierr.ne.0) return
c density profile in y
do 80 n = 1, nppv
c j, k = used to determine spatial location of this particle
dnng = dble(n) + dkoff
k = (dnng - 1.0d0)/dnpx
j = dnng - dnpx*dble(k)
k = k + 1
nn = (dble(n) - 1.0d0)/dnpx
nn = dble(n) - dble(nn)*dnpx
if (k.eq.kc) then
yn = float(k) + y0
c guess next value for yt
if (k.gt.1) then
fp = bny*fny(yt,argy1,argy2,argy3,0)
if (fp.eq.0.0) fp = 1.0
yt = yt + 1.0/fp
endif
yt = max(edgely,min(yt,any))
i = 0
70 f = bny*fny(yt,argy1,argy2,argy3,1) - yn
c find improved value for yt
if (abs(f).ge.eps) then
fp = bny*fny(yt,argy1,argy2,argy3,0)
c newton's method
if ((abs(f).lt.big).and.(fp.gt.0.0)) then
yt0 = yt
yt = yt - f/fp
yt = max(edgely,min(yt,any))
c bisection method
else if (f.gt.0.) then
fp = .5*(yt - yt0)
yt = yt0 + fp
else
fp = yt - yt0
yt0 = yt