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c $Revision: 1.3 $
c $Date: 2009/09/30 23:29:59 $
c ----------------------------------------------------------------
c Example problem for FIDA: 2D heat equation, parallel, GMRES,
c IDABBDPRE.
c
c This example solves a discretized 2D heat equation problem.
c This version uses the Krylov solver IDASPGMR and BBD
c preconditioning.
c
c The DAE system solved is a spatial discretization of the PDE
c du/dt = d^2u/dx^2 + d^2u/dy^2
c on the unit square. The boundary condition is u = 0 on all edges.
c Initial conditions are given by u = 16 x (1 - x) y (1 - y). The
c PDE is treated with central differences on a uniform MX x MY
c grid. The values of u at the interior points satisfy ODEs, and
c equations u = 0 at the boundaries are appended, to form a DAE
c system of size N = MX * MY. Here MX = MY = 10.
c
c The system is actually implemented on submeshes, processor by
c processor, with an MXSUB by MYSUB mesh on each of NPEX * NPEY
c processors.
c
c The system is solved with FIDA using the Krylov linear solver
c IDASPGMR in conjunction with the preconditioner module IDABBDPRE.
c The preconditioner uses a tridiagonal approximation
c (half-bandwidths = 1). The constraints u >= 0 are posed for all
c components. Local error testing on the boundary values is
c suppressed. Output is taken at t = 0, .01, .02, .04, ..., 10.24.
c ----------------------------------------------------------------
c
program fidaHeat2D_kry_bbd_p
c
include "mpif.h"
c
c global variables
c
integer*4 nlocal, neq, npex, npey, mxsub, mysub, mx, my
integer*4 ixsub, jysub
integer thispe
integer mxsubg, mysubg, nlocalg
parameter (mxsubg = 5, mysubg = 5)
parameter (nlocalg = mxsubg*mysubg)
double precision dx, dy, coeffx, coeffy, coeffxy
double precision uext((mxsubg+2)*(mysubg+2))
c
c local variables
c
integer*4 mudq, mldq, mukeep, mlkeep
integer*4 iout(25), ipar
double precision rout(10), rpar
integer nout, ier
parameter (nout = 11)
integer npes, inopt, maxl, gstype, maxrs, itask, iatol
double precision t0, t1, tout, tret, dqrely, eplifac, dqincfac
double precision atol, rtol
double precision constr(nlocalg), uu(nlocalg), up(nlocalg)
double precision res(nlocalg), id(nlocalg)
c
data atol/1.0d-3/, rtol/0.0d0/
c
common /pcom/ dx, dy, coeffx, coeffy, coeffxy, uext,
& nlocal, neq, mx, my, mxsub, mysub, npey, npex,
& ixsub, jysub, thispe
c
c Initialize variables
c
npex = 2
npey = 2
mxsub = 5
mysub = 5
mx = npex*mxsub
my = npey*mysub
neq = mx*my
nlocal = mxsub*mysub
inopt = 1
t0 = 0.0d0
t1 = 0.01d0
mudq = mxsub
mldq = mxsub
mukeep = 1
mlkeep = 1
dqrely = 0.0d0
maxl = 0
gstype = 0
maxrs = 0
eplifac = 0.0d0
dqincfac = 0.0d0
itask = 1
iatol = 1
c
c Initialize MPI environment
c
call mpi_init(ier)
if (ier .ne. 0) then
write(*,2) ier
2 format(///' MPI_ERROR: MPI_INIT returned IER = ', i5)
stop
endif
c
call mpi_comm_size(mpi_comm_world, npes, ier)
if (ier .ne. 0) then
write(*,3) ier
3 format(///' MPI_ERROR: MPI_COMM_SIZE returned IER = ', i5)
call mpi_abort(mpi_comm_world, 1, ier)
stop
endif
c
call mpi_comm_rank(mpi_comm_world, thispe, ier)
if (ier .ne. 0) then
write(*,4) ier
4 format(///' MPI_ERROR: MPI_COMM_RANK returned IER = ', i5)
call mpi_abort(mpi_comm_world, 1, ier)
stop
endif
c
if (npes .ne. npex*npey) then
if (thispe .eq. 0) then
write(*,5) npes, npex*npey
5 format(///' MPI_ERROR: npes = ', i5, ' is not equal to ',
& 'NPEX*NPEY = ', i5)
call mpi_finalize(ier)
stop
endif
endif
c
call fnvinitp(mpi_comm_world, 2, nlocal, neq, ier)
if (ier .ne. 0) then
write(*,6) ier
6 format(///' SUNDIALS_ERROR: FNVINITP returned IER = ', i5)
call mpi_finalize(ier)
stop
endif
c
jysub = int(thispe/npex)
ixsub = thispe-jysub*npex
c
c Initialize problem data
c
call setinitprofile(uu, up, id, res, constr, ipar, rpar)
c
c Initialize IDA environment
c
call fidamalloc(t0, uu, up, iatol, rtol, atol,
& iout, rout, ipar, rpar, ier)
if (ier .ne. 0) then
write(*,7) ier
7 format(///' SUNDIALS_ERROR: FIDAMALLOC returned IER = ', i5)
call mpi_abort(mpi_comm_world, 1, ier)
stop
endif
c
c Set optional inputs
c
call fidasetiin('SUPPRESS_ALG', 1, ier)
call fidasetvin('ID_VEC', id, ier)
call fidasetvin('CONSTR_VEC', constr, ier)
c
c Initialize and attach BBDSPGMR module
c
call fidaspgmr(maxl, gstype, maxrs, eplifac, dqincfac, ier)
if (ier .ne. 0) then
write(*,9) ier
9 format(///' SUNDIALS_ERROR: FIDABBDSPGMR returned IER = ', i5)
call mpi_abort(mpi_comm_world, 1, ier)
stop
endif
c
call fidabbdinit(nlocal, mudq, mldq, mukeep, mlkeep, dqrely, ier)
if (ier .ne. 0) then
write(*,8) ier
8 format(///' SUNDIALS_ERROR: FIDABBDINIT returned IER = ', i5)
call mpi_abort(mpi_comm_world, 1, ier)
stop
endif
c
c Print header
c
if (thispe .eq. 0) then
call prntintro(rtol, atol)
call prntcase(1, mudq, mukeep)
endif
c
tout = t1
do 10 jout = 1, nout
c
call fidasolve(tout, tret, uu, up, itask, ier)
c
call prntoutput(tret, uu, iout, rout)
c
if (ier .ne. 0) then
write(*,11) ier
11 format(///' SUNDIALS_ERROR: FIDASOLVE returned IER = ', i5)
call fidafree
stop
endif
c
tout = tout*2.0d0
c
10 continue
c
c Print statistics
c
if (thispe .eq. 0) then
call prntfinalstats(iout)
endif
c
c Reinitialize variables and data for second problem
c
mudq = 1
mldq = 1
c
call setinitprofile(uu, up, id, res, constr, ipar, rpar)
c
call fidareinit(t0, uu, up, iatol, rtol, atol, ier)
if (ier .ne. 0) then
write(*,33) ier
33 format(///' SUNDIALS_ERROR: FIDAREINIT returned IER = ', i5)
endif
c
call fidabbdreinit(nlocal, mudq, mldq, dqrely, ier)
if (ier .ne. 0) then
write(*,34) ier
34 format(///' SUNDIALS_ERROR: FIDABBDREINIT returned IER = ', i5)
call fidafree
stop
endif
c
c Print header
c
if (thispe .eq. 0) then
call prntcase(2, mudq, mukeep)
endif
c
tout = t1
do 12 jout = 1, nout
c
call fidasolve(tout, tret, uu, up, itask, ier)
c
call prntoutput(tret, uu, iout, rout)
c
if (ier .ne. 0) then
write(*,13) ier
13 format(///' SUNDIALS_ERROR: FIDASOLVE returned IER = ', i5)
call fidafree
stop
endif
c
tout = tout*2.0d0
c
12 continue
c
c Print statistics
c
if (thispe .eq. 0) then
call prntfinalstats(iout)
endif
c
c Free memory
c
call fidafree
c
call mpi_finalize(ier)
c
stop
end
c
c ==========
c
subroutine setinitprofile(uu, up, id, res, constr, ipar, rpar)
c
c global variables
c
integer*4 nlocal, neq, npex, npey, mxsub, mysub, mx, my
integer*4 ixsub, jysub, ipar(*)
integer thispe
integer mxsubg, mysubg, nlocalg
parameter (mxsubg = 5, mysubg = 5)
parameter (nlocalg = mxsubg*mysubg)
double precision dx, dy, coeffx, coeffy, coeffxy, rpar(*)
double precision uext((mxsubg+2)*(mysubg+2))
c
c local variables
c
integer*4 i, iloc, j, jloc, offset, loc
integer*4 ixbegin, ixend, jybegin, jyend
integer reserr
double precision xfact, yfact
double precision uu(*), up(*), id(*), res(*), constr(*)
c
common /pcom/ dx, dy, coeffx, coeffy, coeffxy, uext,
& nlocal, neq, mx, my, mxsub, mysub, npey, npex,
& ixsub, jysub, thispe
c
c Initialize variables
c
dx = 1.0d0/dble(mx-1)
dy = 1.0d0/dble(my-1)
coeffx = 1.0d0/(dx*dx)
coeffy = 1.0d0/(dy*dy)
coeffxy = 2.0d0/(dx*dx)+2.0d0/(dy*dy)
ixbegin = mxsub*ixsub
ixend = mxsub*(ixsub+1)-1
jybegin = mysub*jysub
jyend = mysub*(jysub+1)-1
c
do 14 i = 1, nlocal
id(i) = 1.0d0
14 continue
c
jloc = 0
do 15 j = jybegin, jyend
yfact = dy*dble(j)
offset = jloc*mxsub
iloc = 0
do 16 i = ixbegin, ixend
xfact = dx*dble(i)
loc = offset+iloc
uu(loc+1) = 16.0d0*xfact*(1.0d0-xfact)*yfact*(1.0d0-yfact)
if (i .eq. 0 .or. i .eq. mx-1) then
id(loc+1) = 0.0d0
endif
if (j .eq. 0 .or. j .eq. my-1) then
id(loc+1) = 0.0d0
endif
iloc = iloc+1
16 continue
jloc = jloc+1
15 continue
c
do 17 i = 1, nlocal
up(i) = 0.0d0
constr(i) = 1.0d0
17 continue
c
call fidaresfun(0.0d0, uu, up, res, ipar, rpar, reserr)
c
do 18 i = 1, nlocal
up(i) = -1.0d0*res(i)
18 continue
c
return
end
c
c ==========
c
subroutine fidaresfun(tres, u, up, res, ipar, rpar, reserr)
c
c global variables
c
integer*4 nlocal, neq, npex, npey, mxsub, mysub, mx, my
integer*4 ixsub, jysub, ipar(*)
integer thispe
integer mxsubg, mysubg, nlocalg
parameter (mxsubg = 5, mysubg = 5)
parameter (nlocalg = mxsubg*mysubg)
double precision dx, dy, coeffx, coeffy, coeffxy, rpar(*)
double precision uext((mxsubg+2)*(mysubg+2))
c
c local variables
c
integer reserr
double precision tres
double precision u(*), up(*), res(*)
c
common /pcom/ dx, dy, coeffx, coeffy, coeffxy, uext,
& nlocal, neq, mx, my, mxsub, mysub, npey, npex,
& ixsub, jysub, thispe
c
call fidacommfn(nlocal, tres, u, up, ipar, rpar, reserr)
c
call fidaglocfn(nlocal, tres, u, up, res, ipar, rpar, reserr)
c
return
end
c
c ==========
c
subroutine fidacommfn(nloc, tres, u, up, ipar, rpar, reserr)
c
include "mpif.h"
c
c global variables
c
integer*4 nlocal, neq, npex, npey, mxsub, mysub, mx, my
integer*4 ixsub, jysub, ipar(*)
integer thispe
integer mxsubg, mysubg, nlocalg
parameter (mxsubg = 5, mysubg = 5)
parameter (nlocalg = mxsubg*mysubg)
double precision dx, dy, coeffx, coeffy, coeffxy, rpar(*)
double precision uext((mxsubg+2)*(mysubg+2))
c
c local variables
c
integer*4 nloc
integer reserr
double precision tres, u(*), up(*)
c
integer request(mpi_status_size)
double precision buffer(2*mysub)
c
common /pcom/ dx, dy, coeffx, coeffy, coeffxy, uext,
& nlocal, neq, mx, my, mxsub, mysub, npey, npex,
& ixsub, jysub, thispe
c
call brecvpost(request, mxsub, mysub, buffer)
c
call bsend(mxsub, mysub, u)
c
call brecvwait(request, mxsub, buffer)
c
return
end
c
c ==========
c
subroutine fidaglocfn(nloc, tres, u, up, res, ipar, rpar, reserr)
c
c global variables
c
integer*4 nlocal, neq, npex, npey, mxsub, mysub, mx, my
integer*4 ixsub, jysub, ipar(*)
integer thispe
integer mxsubg, mysubg, nlocalg
parameter (mxsubg = 5, mysubg = 5)
parameter (nlocalg = mxsubg*mysubg)
double precision dx, dy, coeffx, coeffy, coeffxy, rpar(*)
double precision uext((mxsubg+2)*(mysubg+2))
c
c local variables
c
integer*4 nloc
integer reserr
double precision tres, u(*), up(*), res(*)
c
integer*4 i, lx, ly, offsetu, offsetue, locu, locue
integer*4 ixbegin, ixend, jybegin, jyend, mxsub2
double precision termx, termy, termctr
c
common /pcom/ dx, dy, coeffx, coeffy, coeffxy, uext,
& nlocal, neq, mx, my, mxsub, mysub, npey, npex,
& ixsub, jysub, thispe
c
mxsub2 = mxsub+2
c
do 19 i = 1, nlocal
res(i) = u(i)
19 continue
c
offsetu = 0
offsetue = mxsub2+1
do 20 ly = 0, mysub-1
do 21 lx = 0, mxsub-1
uext(offsetue+lx+1) = u(offsetu+lx+1)
21 continue
offsetu = offsetu+mxsub
offsetue = offsetue+mxsub2
20 continue
c
ixbegin = 0
ixend = mxsub-1
jybegin = 0
jyend = mysub-1
if (ixsub .eq. 0) then
ixbegin = ixbegin+1
endif
if (ixsub .eq. npex-1) then
ixend = ixend-1
endif
if (jysub .eq. 0) then
jybegin = jybegin+1
endif
if (jysub .eq. npey-1) then
jyend = jyend-1
endif
c
do 22 ly = jybegin, jyend
do 23 lx = ixbegin, ixend
locu = lx+ly*mxsub
locue = (lx+1)+(ly+1)*mxsub2
termx = coeffx*(uext(locue)+uext(locue+2))
termy = coeffy*(uext(locue-mxsub2+1)+uext(locue+mxsub2+1))
termctr = coeffxy*uext(locue+1)
res(locu+1) = up(locu+1)-(termx+termy-termctr)
23 continue
22 continue
c
return
end
c
c ==========
c
subroutine bsend(dsizex, dsizey, uarray)
c
include "mpif.h"
c
c global variables
c
integer*4 nlocal, neq, npex, npey, mxsub, mysub, mx, my
integer*4 ixsub, jysub
integer thispe
integer mxsubg, mysubg, nlocalg
parameter (mxsubg = 5, mysubg = 5)
parameter (nlocalg = mxsubg*mysubg)
double precision dx, dy, coeffx, coeffy, coeffxy
double precision uext((mxsubg+2)*(mysubg+2))
c
c local variables
c
integer*4 dsizex, dsizey
double precision uarray(*)
c
integer ier, offsetu
double precision bufleft(mysub), bufright(mysub)
c
common /pcom/ dx, dy, coeffx, coeffy, coeffxy, uext,
& nlocal, neq, mx, my, mxsub, mysub, npey, npex,
& ixsub, jysub, thispe
c
if (jysub .ne. 0) then
call mpi_send(uarray(1), dsizex, mpi_double_precision,
& thispe-npex, 0, mpi_comm_world, ier)
endif
c
if (jysub .ne. npey-1) then
offsetu = (mysub-1)*dsizex
call mpi_send(uarray(offsetu+1), dsizex, mpi_double_precision,
& thispe+npex, 0, mpi_comm_world, ier)
endif
c
if (ixsub .ne. 0) then
do 24 ly = 0, mysub-1
offsetu = ly*dsizex
bufleft(ly+1) = uarray(offsetu+1)
24 continue
call mpi_send(bufleft(1), dsizey, mpi_double_precision,
& thispe-1, 0, mpi_comm_world, ier)
endif
c
if (ixsub .ne. npex-1) then
do 25 ly = 0, mysub-1
offsetu = ly*mxsub+(mxsub-1)
bufright(ly+1) = uarray(offsetu+1)
25 continue
call mpi_send(bufright(1), dsizey, mpi_double_precision,
& thispe+1, 0, mpi_comm_world, ier)
endif
c
return
end
c
c ==========
c
subroutine brecvpost(request, dsizex, dsizey, buffer)
c
include "mpif.h"
c
c global variables
c
integer*4 nlocal, neq, npex, npey, mxsub, mysub, mx, my
integer*4 ixsub, jysub
integer thispe
integer mxsubg, mysubg, nlocalg
parameter (mxsubg = 5, mysubg = 5)
parameter (nlocalg = mxsubg*mysubg)
double precision dx, dy, coeffx, coeffy, coeffxy
double precision uext((mxsubg+2)*(mysubg+2))
c
c local variables
c
integer*4 dsizex, dsizey
integer request(*)
double precision buffer(*)
c
integer ier
integer*4 offsetue
c
common /pcom/ dx, dy, coeffx, coeffy, coeffxy, uext,
& nlocal, neq, mx, my, mxsub, mysub, npey, npex,
& ixsub, jysub, thispe
c
if (jysub .ne. 0) then
call mpi_irecv(uext(2), dsizex, mpi_double_precision,
& thispe-npex, 0, mpi_comm_world, request(1),
& ier)
endif
c
if (jysub .ne. npey-1) then
offsetue = (1+(mysub+1)*(mxsub+2))
call mpi_irecv(uext(offsetue+1), dsizex, mpi_double_precision,
& thispe+npex, 0, mpi_comm_world, request(2),
& ier)
endif
c
if (ixsub .ne. 0) then
call mpi_irecv(buffer(1), dsizey, mpi_double_precision,
& thispe-1, 0, mpi_comm_world, request(3),
& ier)
endif
c
if (ixsub .ne. npex-1) then
call mpi_irecv(buffer(1+mysub), dsizey, mpi_double_precision,
& thispe+1, 0, mpi_comm_world, request(4),
& ier)
endif
c
return
end
c
c ==========
c
subroutine brecvwait(request, dsizex, buffer)
c
include "mpif.h"
c
c global variables
c
integer*4 nlocal, neq, npex, npey, mxsub, mysub, mx, my
integer*4 ixsub, jysub
integer thispe
integer mxsubg, mysubg, nlocalg
parameter (mxsubg = 5, mysubg = 5)
parameter (nlocalg = mxsubg*mysubg)
double precision dx, dy, coeffx, coeffy, coeffxy
double precision uext((mxsubg+2)*(mysubg+2))
c
c local variables
c
integer request(*)
integer*4 dsizex
double precision buffer(*)
c
integer*4 ly, dsizex2, offsetue
integer ier, status(mpi_status_size)
c
common /pcom/ dx, dy, coeffx, coeffy, coeffxy, uext,
& nlocal, neq, mx, my, mxsub, mysub, npey, npex,
& ixsub, jysub, thispe
c
dsizex2 = dsizex+2
c
if (jysub .ne. 0) then
call mpi_wait(request(1), status, ier)
endif
c
if (jysub .ne. npey-1) then
call mpi_wait(request(2), status, ier)
endif
c
if (ixsub .ne. 0) then
call mpi_wait(request(3), status, ier)
do 26 ly = 0, mysub-1
offsetue = (ly+1)*dsizex2
uext(offsetue+1) = buffer(ly+1)
26 continue
endif
c
if (ixsub .ne. npex-1) then
call mpi_wait(request(4), status, ier)
do 27 ly = 0, mysub-1
offsetue = (ly+2)*dsizex2-1
uext(offsetue+1) = buffer(ly+mysub+1)
27 continue
endif
c
return
end
c
c ==========
c
subroutine prntoutput(tret, u, iout, rout)
c
c global variables
c
integer*4 nlocal, neq, npex, npey, mxsub, mysub, mx, my
integer*4 ixsub, jysub
integer thispe
integer mxsubg, mysubg, nlocalg
parameter (mxsubg = 5, mysubg = 5)
parameter (nlocalg = mxsubg*mysubg)
double precision dx, dy, coeffx, coeffy, coeffxy
double precision uext((mxsubg+2)*(mysubg+2))
c
c local variables
c
integer*4 iout(*), lenrwbbd, leniwbbd, ngebbd
double precision tret, umax, u(*), rout(*)
c
common /pcom/ dx, dy, coeffx, coeffy, coeffxy, uext,
& nlocal, neq, mx, my, mxsub, mysub, npey, npex,
& ixsub, jysub, thispe
c
call maxnorm(u, umax)
c
if (thispe .eq. 0) then
call fidabbdopt(lenrwbbd, leniwbbd, ngebbd)
write(*,28) tret, umax, iout(9), iout(3), iout(7),
& iout(20), iout(4), iout(16), ngebbd, rout(2),
& iout(18), iout(19)
28 format(' ', e10.4, ' ', e13.5, ' ', i1, ' ', i2,
& ' ', i3, ' ', i3, ' ', i2,'+',i2, ' ',
& i3, ' ', e9.2, ' ', i2, ' ', i3)
endif
c
return
end
c
c ==========
c
subroutine maxnorm(u, unorm)
c
include "mpif.h"
c
c global variables
c
integer*4 nlocal, neq, npex, npey, mxsub, mysub, mx, my
integer*4 ixsub, jysub
integer thispe
integer mxsubg, mysubg, nlocalg
parameter (mxsubg = 5, mysubg = 5)
parameter (nlocalg = mxsubg*mysubg)
double precision dx, dy, coeffx, coeffy, coeffxy
double precision uext((mxsubg+2)*(mysubg+2))
c
c local variables
c
integer*4 i
integer ier
double precision temp, unorm, u(*)
c
common /pcom/ dx, dy, coeffx, coeffy, coeffxy, uext,
& nlocal, neq, mx, my, mxsub, mysub, npey, npex,
& ixsub, jysub, thispe
c
temp = 0.0d0
c
do 29 i = 1, nlocal
temp = max(abs(u(i)), temp)
29 continue
c
call mpi_allreduce(temp, unorm, 1, mpi_double_precision,
& mpi_max, mpi_comm_world, ier)
c
c unorm = temp
c
return
end
c
c ==========
c
subroutine prntintro(rtol, atol)
c
c global variables
c
integer*4 nlocal, neq, npex, npey, mxsub, mysub, mx, my
integer*4 ixsub, jysub
integer thispe
integer mxsubg, mysubg, nlocalg
parameter (mxsubg = 5, mysubg = 5)
parameter (nlocalg = mxsubg*mysubg)
double precision dx, dy, coeffx, coeffy, coeffxy
double precision uext((mxsubg+2)*(mysubg+2))
c
c local variables
c
double precision rtol, atol
c
common /pcom/ dx, dy, coeffx, coeffy, coeffxy, uext,
& nlocal, neq, mx, my, mxsub, mysub, npey, npex,
& ixsub, jysub, thispe
c
write(*,30) mx, my, neq, mxsub, mysub, npex, npey, rtol, atol
30 format(/'fidaHeat2D_kry_bbd_p: Heat equation, parallel example',
& ' for FIDA', /, 16x,'Discretized heat equation',
& ' on 2D unit square.', /, 16x,'Zero boundary',
& ' conditions, polynomial conditions.', /,
& 16x,'Mesh dimensions: ', i2, ' x ', i2,
& ' Total system size: ', i3, //,
& 'Subgrid dimensions: ', i2, ' x ', i2,
& ' Processor array: ', i2, ' x ', i2, /,
& 'Tolerance parameters: rtol = ', e8.2, ' atol = ',
& e8.2, /, 'Constraints set to force all solution',
& ' components >= 0.', /, 'SUPPRESSALG = TRUE to remove',
& ' boundary components from the error test.', /,
& 'Linear solver: SPGMR. Preconditioner: BBDPRE - ',
& 'Banded-block-diagonal.')
c
return
end
c
c ==========
c
subroutine prntcase(num, mudq, mukeep)
c
c local variables
c
integer*4 mudq, mukeep
integer num
c
write(*,31) num, mudq, mukeep
31 format(//, 'Case ', i2, /, ' Difference quotient half-',
& 'bandwidths =', i2, /, ' Retained matrix half-bandwidths =',
& i2, //, 'Output Summary',/,' umax = max-norm of solution',
& /,' nre = nre + nreLS (total number of RES evals.)',
& //, ' time umax k nst nni nli nre',
& ' nge h npe nps', /,
& '-------------------------------------------------------',
& '-------------------')
c
return
end
c
c ==========
c
subroutine prntfinalstats(iout)
c
c local variables
c
integer*4 iout(*)
c
write(*,32) iout(5), iout(6), iout(21)
32 format(/, 'Error test failures =', i3, /,
& 'Nonlinear convergence failures =', i3, /,
& 'Linear convergence failures =', i3)
c
return
end
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