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spclibs/multigrid/src/test_mgp.f90
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test_mgp.f90
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!>
!> @file test_mgp.f90
!>
!> @brief
!>
!> @copyright
!> Copyright (©) 2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
!> SPC (Swiss Plasma Center)
!>
!> SPClibs is free software: you can redistribute it and/or modify it under
!> the terms of the GNU Lesser General Public License as published by the Free
!> Software Foundation, either version 3 of the License, or (at your option)
!> any later version.
!>
!> SPClibs is distributed in the hope that it will be useful, but WITHOUT ANY
!> WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
!> FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
!>
!> You should have received a copy of the GNU Lesser General Public License
!> along with this program. If not, see <https://www.gnu.org/licenses/>.
!>
!> @author
!> (in alphabetical order)
!> @author Trach-Minh Tran <trach-minh.tran@epfl.ch>
!>
PROGRAM main
!
! Test multigrid V-cycle for periodic problems
!
USE multigrid
IMPLICIT NONE
!
INTEGER :: nx=8, nidbas=1, ngauss=2, nits=40
INTEGER :: levels=2, nu1=1, nu2=1, mu=1, nu0=1
CHARACTER(len=4) :: relax='jac '
LOGICAL :: nlfixed = .FALSE.
DOUBLE PRECISION :: sigma=1.0d0, kmode=10.0, pi=4.0d0*ATAN(1.0d0)
DOUBLE PRECISION :: omega=2.0d0/3.0d0
INTEGER :: l, nrank, dim, its
DOUBLE PRECISION :: errdisc_dir
DOUBLE PRECISION, ALLOCATABLE :: u_direct(:), u_exact(:), u_calc(:)
DOUBLE PRECISION, ALLOCATABLE :: sol_direct(:), sol_calc(:), sol_grid(:)
DOUBLE PRECISION, ALLOCATABLE :: err(:), resid(:), errdisc(:)
DOUBLE PRECISION, ALLOCATABLE :: errdisc_fmg(:)
!
TYPE(grid1d), ALLOCATABLE :: gridx(:)
TYPE(mg_info) :: info
!
NAMELIST /newrun/ nx, nidbas, ngauss, sigma, kmode, &
& relax, nits, nlfixed, levels, nu1, nu2, mu, nu0
!--------------------------------------------------------------------------------
! 1. Prologue
! Inputs
!
READ(*,newrun)
WRITE(*,newrun)
!
levels = MIN(levels, get_lmax(nx))
!
info%nu1 = nu1
info%nu2 = nu2
info%mu = mu
info%nu0 = nu0
info%levels = levels
info%relax = relax
info%omega = omega
!
! Create grids
!
ALLOCATE(gridx(levels))
CALL create_grid(nx, nidbas, ngauss, 0, gridx, period=.TRUE.)
WRITE(*,'(a/(20i6))') 'Number of intervals in grids', (gridx(l)%n, l=1,levels)
!
! Create FE matrice and set BC u(0)=u(1)=0
!
DO l=1,levels
CALL femat(gridx(l)%spl, gridx(l)%matap, coefeq)
END DO
!
! Construct RHS only on the finest grid
!
nrank = gridx(1)%rank ! Rank of the system (number of unknowns)
dim = nrank+nidbas ! Dimension of Splines space
CALL disrhs(gridx(1)%spl, gridx(1)%f, rhs)
!--------------------------------------------------------------------------------
! 2. Direct solution
!
WRITE(*,'(//a)') 'Direct solution for the finest grid problem'
ALLOCATE(u_direct(0:nx))
ALLOCATE(sol_direct(nrank))
ALLOCATE(sol_grid(dim)) ! Required by GRIDVAL
!
CALL direct_solve(gridx(1), sol_direct)
sol_grid(1:nrank) = sol_direct(1:nrank)
sol_grid(nrank+1:dim) = sol_direct(1:nidbas)
CALL gridval(gridx(1)%spl, gridx(1)%x, u_direct, 0, sol_grid)
!
errdisc_dir = disc_err(gridx(1)%spl, sol_grid, sol)
WRITE(*,'(a,1pe12.3)') 'Discretization error', errdisc_dir
!--------------------------------------------------------------------------------
! 3. Solution from MG V-cycles
!
WRITE(*,'(//a)') 'Multigrid MG V-cycles'
ALLOCATE(sol_calc(nrank))
ALLOCATE(err(0:nits))
ALLOCATE(errdisc(0:nits))
ALLOCATE(resid(0:nits))
!
! Initial guess
!
sol_calc(:) = 0.0d0
sol_grid(:) = 0.0d0
IF(nlfixed) THEN
sol_calc(:) = sol_direct(:)
sol_grid(1:nrank) = sol_calc(1:nrank)
sol_grid(nrank+1:dim) = sol_calc(1:nidbas)
END IF
gridx(1)%v(:) = sol_calc(:)
err(0) = normf(gridx(1)%matmp, sol_calc-sol_direct)
errdisc(0) = disc_err(gridx(1)%spl, sol_grid, sol)
resid(0) = residue(gridx(1)%matap, gridx(1)%f, sol_calc)
!
! Iterations
!
DO its=1,nits
!
CALL mg(gridx, info, 1)
sol_calc(:) = gridx(1)%v(:)
sol_grid(1:nrank) = sol_calc(1:nrank)
sol_grid(nrank+1:dim) = sol_calc(1:nidbas)
!
err(its) = normf(gridx(1)%matmp, sol_calc-sol_direct)
errdisc(its) = disc_err(gridx(1)%spl, sol_grid, sol) ! will call GRIDVAL
resid(its) = residue(gridx(1)%matap, gridx(1)%f, sol_calc)
END DO
!
WRITE(*,'(a4,3(a12,a8))') 'its', 'error', 'ratio', 'residue', 'ratio', &
& 'disc. err', 'ratio'
WRITE(*,'(i4,3(1pe12.3,8x))') 0, err(0), resid(0), errdisc(0)
WRITE(*,'((i4,3(1pe12.3,0pf8.2)))') (its, err(its), err(its)/err(its-1), &
& resid(its), resid(its)/resid(its-1), &
& errdisc(its), errdisc(its)/errdisc(its-1), its=1,nits)
!--------------------------------------------------------------------------------
! 4. Solution from FMG
!
WRITE(*,'(//a)') 'Full Multigrid'
ALLOCATE(errdisc_fmg(nits))
DO its=1,nits
info%nu0 = its
!
CALL fmg(gridx, info, 1)
sol_calc(:) = gridx(1)%v(:)
sol_grid(1:nrank) = sol_calc(1:nrank)
sol_grid(nrank+1:dim) = sol_calc(1:nidbas)
!
errdisc_fmg(its) = disc_err(gridx(1)%spl, sol_grid, sol) ! will call GRIDVAL
resid(its) = residue(gridx(1)%matap, gridx(1)%f, sol_calc)
END DO
WRITE(*,'(a4,2(a12,a8))') 'nu0', 'residue', 'ratio','disc. err', 'ratio'
WRITE(*,'((i4,2(1pe12.3,0pf8.3)))') (its, resid(its), resid(its)/resid(its-1), &
& errdisc_fmg(its),errdisc_fmg(its)/errdisc_dir, its=1,nits)
!
! Grid values at final iteration
!
ALLOCATE(u_exact(0:nx))
ALLOCATE(u_calc(0:nx))
u_exact = sol(gridx(1)%x)
CALL gridval(gridx(1)%spl, gridx(1)%x, u_calc, 0, sol_grid)
!--------------------------------------------------------------------------------
! 9. Epilogue
!
! Creata HDF5 file
!
CALL h5file
!--------------------------------------------------------------------------------
CONTAINS
FUNCTION rhs(x)
DOUBLE PRECISION, INTENT(in) :: x
DOUBLE PRECISION :: rhs
rhs = SIN(pi*kmode*x)
END FUNCTION rhs
FUNCTION sol(x)
DOUBLE PRECISION, INTENT(in) :: x(:)
DOUBLE PRECISION :: sol(SIZE(x))
sol(:) = 1.0d0/((pi*kmode)**2+sigma)*SIN(pi*kmode*x(:))
END FUNCTION sol
SUBROUTINE coefeq(x, idt, idw, c)
DOUBLE PRECISION, INTENT(in) :: x
INTEGER, INTENT(out) :: idt(:), idw(:)
DOUBLE PRECISION, INTENT(out) :: c(:)
c(1) = 1.0d0
idt(1) = 1
idw(1) = 1
c(2) = sigma
idt(2) = 0
idw(2) = 0
END SUBROUTINE coefeq
SUBROUTINE h5file
USE futils
CHARACTER(len=128) :: file='test_mgp.h5'
INTEGER :: fid
INTEGER :: l
CHARACTER(len=64) :: dsname
CALL creatf(file, fid, real_prec='d')
CALL attach(fid, '/', 'NX', nx)
CALL attach(fid, '/', 'NIDBAS', nidbas)
CALL attach(fid, '/', 'SIGMA', sigma)
CALL attach(fid, '/', 'KMODE', kmode)
CALL attach(fid, '/', 'RELAX', relax)
CALL attach(fid, '/', 'NITS', nits)
CALL attach(fid, '/', 'NLFIXED', nlfixed)
CALL attach(fid, '/', 'LEVELS', levels)
CALL attach(fid, '/', 'NU1', nu1)
CALL attach(fid, '/', 'NU2', nu2)
CALL attach(fid, '/', 'NU0', nu0)
CALL attach(fid, '/', 'MU', mu)
CALL creatg(fid, '/mglevels')
DO l=1,levels
WRITE(dsname,'("/mglevels/level.",i2.2)') l
CALL creatg(fid, TRIM(dsname))
CALL putarr(fid, TRIM(dsname)//'/mata', gridx(l)%matap%val)
IF(l.GT.1) THEN
CALL putarr(fid, TRIM(dsname)//'/matp', gridx(l)%transf%val)
CALL attach(fid, TRIM(dsname)//'/matp', 'M', gridx(l)%transf%mrows)
CALL attach(fid, TRIM(dsname)//'/matp', 'N', gridx(l)%transf%ncols)
END IF
CALL putarr(fid, TRIM(dsname)//'/f', gridx(l)%f)
CALL putarr(fid, TRIM(dsname)//'/v', gridx(l)%v)
END DO
CALL creatg(fid, '/Iterations')
CALL putarr(fid, '/Iterations/errors', err)
CALL putarr(fid, '/Iterations/residues', resid)
CALL putarr(fid, '/Iterations/disc_errors', errdisc)
CALL putarr(fid, '/Iterations/disc_errors_fmg', errdisc_fmg)
CALL putarr(fid, '/Iterations/xgrid', gridx(1)%x)
CALL putarr(fid, '/Iterations/u_direct', u_direct)
CALL putarr(fid, '/Iterations/u_exact', u_exact)
CALL putarr(fid, '/Iterations/u_calc', u_calc)
CALL closef(fid)
END SUBROUTINE h5file
END PROGRAM main
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