cg.f90

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module cg
  use neko_config, only : neko_blk_size
  use num_types, only : rp, xp
  use krylov, only : ksp_t, ksp_monitor_t, ksp_max_iter
  use precon, only : pc_t
  use ax_product, only : ax_t
  use field, only : field_t
  use coefs, only : coef_t
  use gather_scatter, only : gs_t, gs_op_add
  use scalar_bc_projector, only : scalar_bc_projector_t
  use vector_bc_projector, only : vector_bc_projector_t, &
       vector_bc_projector_components
  use math, only : glsc3, abscmp
  use comm, only : mpi_extra_precision, mpi_real_precision, neko_comm
  use mpi_f08, only : mpi_allreduce, mpi_in_place, mpi_sum
  implicit none
  private
 
  integer, parameter :: cg_p_space = 7
 
  type, public, extends(ksp_t) :: cg_t
     real(kind=rp), allocatable :: w(:)
     real(kind=rp), allocatable :: r(:)
     real(kind=rp), allocatable :: p(:,:)
     real(kind=rp), allocatable :: z(:)
     real(kind=rp), allocatable :: alpha(:)
   contains
     procedure, pass(this) :: init => cg_init
     procedure, pass(this) :: free => cg_free
     procedure, pass(this) :: solve => cg_solve
     procedure, pass(this) :: solve_coupled => cg_solve_coupled
  end type cg_t
 
contains
 
  subroutine cg_init(this, n, max_iter, M, rel_tol, abs_tol, monitor)
    class(cg_t), intent(inout), target :: this
    integer, intent(in) :: max_iter
    class(pc_t), optional, intent(in), target :: M
    integer, intent(in) :: n
    real(kind=rp), optional, intent(in) :: rel_tol
    real(kind=rp), optional, intent(in) :: abs_tol
    logical, optional, intent(in) :: monitor
 
    call this%free()
 
    allocate(this%w(n))
    allocate(this%r(n))
    allocate(this%p(n, cg_p_space))
    allocate(this%z(n))
    allocate(this%alpha(cg_p_space))
 
    if (present(m)) then
       this%M => m
    end if
    if (present(rel_tol) .and. present(abs_tol) .and. present(monitor)) then
       call this%ksp_init(max_iter, rel_tol, abs_tol, monitor = monitor)
    else if (present(rel_tol) .and. present(abs_tol)) then
       call this%ksp_init(max_iter, rel_tol, abs_tol)
    else if (present(monitor) .and. present(abs_tol)) then
       call this%ksp_init(max_iter, abs_tol = abs_tol, monitor = monitor)
    else if (present(rel_tol) .and. present(monitor)) then
       call this%ksp_init(max_iter, rel_tol, monitor = monitor)
    else if (present(rel_tol)) then
       call this%ksp_init(max_iter, rel_tol = rel_tol)
    else if (present(abs_tol)) then
       call this%ksp_init(max_iter, abs_tol = abs_tol)
    else if (present(monitor)) then
       call this%ksp_init(max_iter, monitor = monitor)
    else
       call this%ksp_init(max_iter)
    end if
 
  end subroutine cg_init
 
  subroutine cg_free(this)
    class(cg_t), intent(inout) :: this
 
    call this%ksp_free()
 
    if (allocated(this%w)) then
       deallocate(this%w)
    end if
 
    if (allocated(this%r)) then
       deallocate(this%r)
    end if
 
    if (allocated(this%p)) then
       deallocate(this%p)
    end if
 
    if (allocated(this%z)) then
       deallocate(this%z)
    end if
 
    if (allocated(this%alpha)) then
       deallocate(this%alpha)
    end if
 
    nullify(this%M)
 
  end subroutine cg_free
 
  function cg_solve(this, Ax, x, f, n, coef, bc_projector, gs_h, niter) &
       result(ksp_results)
    class(cg_t), intent(inout) :: this
    class(ax_t), intent(in) :: ax
    type(field_t), intent(inout) :: x
    integer, intent(in) :: n
    real(kind=rp), dimension(n), intent(in) :: f
    type(coef_t), intent(inout) :: coef
    class(scalar_bc_projector_t), intent(inout) :: bc_projector
    type(gs_t), intent(inout) :: gs_h
    type(ksp_monitor_t) :: ksp_results
    integer, optional, intent(in) :: niter
    integer :: iter, max_iter, i, j, k, p_cur, p_prev, ierr
    real(kind=rp) :: rnorm, rtr, rtz2, rtz1, x_plus(neko_blk_size)
    real(kind=rp) :: beta, pap, norm_fac, tmp
 
    if (present(niter)) then
       max_iter = niter
    else
       max_iter = this%max_iter
    end if
    norm_fac = 1.0_rp / sqrt(coef%volume)
 
    associate(w => this%w, r => this%r, p => this%p, &
         z => this%z, alpha => this%alpha)
 
      rtz1 = 1.0_rp
      rtr = 0.0_rp
      !$omp parallel do reduction(+:rtr)
      do i = 1, n
         x%x(i,1,1,1) = 0.0_rp
         p(i, cg_p_space) = 0.0_rp
         r(i) = f(i)
         rtr = rtr + (r(i) * coef%mult(i,1,1,1) * r(i))
      end do
      !$omp end parallel do
 
      call mpi_allreduce(mpi_in_place, rtr, 1, &
           mpi_real_precision, mpi_sum, neko_comm, ierr)
 
      rnorm = sqrt(rtr) * norm_fac
      ksp_results%res_start = rnorm
      ksp_results%res_final = rnorm
      ksp_results%iter = 0
      if (abscmp(rnorm, 0.0_rp)) then
         ksp_results%converged = .true.
         return
      end if
 
      p_prev = cg_p_space
      p_cur = 1
      call this%monitor_start('CG')
      do iter = 1, max_iter
         call this%M%solve(z, r, n)
         rtz2 = rtz1
         rtz1 = glsc3(r, coef%mult, z, n)
 
         beta = rtz1 / rtz2
         if (iter .eq. 1) beta = 0.0_rp
         !$omp parallel do
         do i = 1, n
            p(i, p_cur) = z(i) + beta * p(i, p_prev)
         end do
         !$omp end parallel do
 
         call ax%compute(w, p(1, p_cur), coef, x%msh, x%Xh)
         call gs_h%op(w, n, gs_op_add)
         call bc_projector%apply(w, n)
 
         pap = glsc3(w, coef%mult, p(1, p_cur), n)
 
         alpha(p_cur) = rtz1 / pap
         call second_cg_part(rtr, r, coef%mult, w, alpha(p_cur), n)
         rnorm = sqrt(rtr) * norm_fac
         call this%monitor_iter(iter, rnorm)
 
         if ((p_cur .eq. cg_p_space) .or. &
              (rnorm .lt. this%abs_tol) .or. iter .eq. max_iter) then
            !$omp parallel do private(j, k, x_plus, tmp)
            do i = 0, n-1, neko_blk_size
               if (i + neko_blk_size .le. n) then
                  !$omp simd
                  do k = 1, neko_blk_size
                     x_plus(k) = 0.0_rp
                  end do
                  do j = 1, p_cur
                     !$omp simd
                     do k = 1, neko_blk_size
                        x_plus(k) = x_plus(k) + alpha(j) * p(i+k,j)
                     end do
                  end do
                  !$omp simd
                  do k = 1, neko_blk_size
                     x%x(i+k,1,1,1) = x%x(i+k,1,1,1) + x_plus(k)
                  end do
               else
                  do k = 1, n - i
                     tmp = 0.0_rp
                     do j = 1, p_cur
                        tmp = tmp + alpha(j) * p(i+k,j)
                     end do
                     x%x(i+k,1,1,1) = x%x(i+k,1,1,1) + tmp
                  end do
               end if
            end do
            !$omp end parallel do
            p_prev = p_cur
            p_cur = 1
            if (rnorm .lt. this%abs_tol) exit
         else
            p_prev = p_cur
            p_cur = p_cur + 1
         end if
      end do
    end associate
    call this%monitor_stop()
    ksp_results%res_final = rnorm
    ksp_results%iter = iter
    ksp_results%converged = this%is_converged(iter, rnorm)
  end function cg_solve
 
  subroutine second_cg_part(rtr, r, mult, w, alpha, n)
    integer, intent(in) :: n
    real(kind=rp), intent(inout) :: r(n), rtr
    real(kind=xp) :: tmp
    real(kind=rp), intent(in) ::mult(n), w(n), alpha
    integer :: i, ierr
 
    tmp = 0.0_xp
    !$omp parallel do reduction(+:tmp)
    do i = 1, n
       r(i) = r(i) - alpha*w(i)
       tmp = tmp + r(i) * r(i) * mult(i)
    end do
    !$omp end parallel do
    call mpi_allreduce(mpi_in_place, tmp, 1, &
         mpi_extra_precision, mpi_sum, neko_comm, ierr)
    rtr = tmp
 
  end subroutine second_cg_part
 
  function cg_solve_coupled(this, Ax, x, y, z, fx, fy, fz, &
       n, coef, bc_projector, gs_h, niter) result(ksp_results)
    class(cg_t), intent(inout) :: this
    class(ax_t), intent(in) :: ax
    type(field_t), intent(inout) :: x
    type(field_t), intent(inout) :: y
    type(field_t), intent(inout) :: z
    integer, intent(in) :: n
    real(kind=rp), dimension(n), intent(in) :: fx
    real(kind=rp), dimension(n), intent(in) :: fy
    real(kind=rp), dimension(n), intent(in) :: fz
    type(coef_t), intent(inout) :: coef
    class(vector_bc_projector_t), intent(inout) :: bc_projector
    type(gs_t), intent(inout) :: gs_h
    type(ksp_monitor_t), dimension(3) :: ksp_results
    integer, optional, intent(in) :: niter
    type(scalar_bc_projector_t), pointer :: bc_x, bc_y, bc_z
 
    call vector_bc_projector_components(bc_projector, bc_x, bc_y, bc_z)
    ksp_results(1) = this%solve(ax, x, fx, n, coef, bc_x, gs_h, niter)
    ksp_results(2) = this%solve(ax, y, fy, n, coef, bc_y, gs_h, niter)
    ksp_results(3) = this%solve(ax, z, fz, n, coef, bc_z, gs_h, niter)
 
  end function cg_solve_coupled
 
end module cg