imex_sweep Subroutine

  subroutine imex_sweep(this, pf, lev, t0, dt)
    use pf_mod_timer

    class(pf_imex_t),  intent(inout) :: this
    type(pf_pfasst_t), intent(inout) :: pf
    real(pfdp),        intent(in   ) :: dt, t0
    class(pf_level_t), intent(inout) :: lev

    integer     :: m, n
    real(pfdp)  :: t
    real(pfdp)  :: dtsdc(1:lev%nnodes-1)
    class(pf_encap_t), allocatable :: rhs
    call start_timer(pf, TLEVEL+lev%index-1)

    ! compute integrals and add fas correction
    do m = 1, lev%nnodes-1
       call lev%S(m)%setval(0.0_pfdp)
       do n = 1, lev%nnodes
          call lev%S(m)%axpy(dt*this%SdiffE(m,n), lev%F(n,1))
          call lev%S(m)%axpy(dt*this%SdiffI(m,n), lev%F(n,2))
       end do
       if (allocated(lev%tau)) then
          call lev%S(m)%axpy(1.0_pfdp, lev%tau(m))
       end if
    end do

    ! do the time-stepping
    call lev%Q(1)%copy(lev%q0)

    call this%f_eval(lev%Q(1), t0, lev%index, lev%F(1,1),1)    
    call this%f_eval(lev%Q(1), t0, lev%index, lev%F(1,2),2)

    call lev%ulevel%factory%create_single(rhs, lev%index,  lev%shape)

    t = t0
    dtsdc = dt * (lev%nodes(2:lev%nnodes) - lev%nodes(1:lev%nnodes-1))
    do m = 1, lev%nnodes-1
       t = t + dtsdc(m)

       call rhs%copy(lev%Q(m))
       call rhs%axpy(dtsdc(m), lev%F(m,1))
       call rhs%axpy(1.0_pfdp, lev%S(m))

       call this%f_comp(lev%Q(m+1), t, dtsdc(m), rhs, lev%index, lev%F(m+1,2),2)
       call this%f_eval(lev%Q(m+1), t, lev%index, lev%F(m+1,1),1)
    end do

    call lev%qend%copy(lev%Q(lev%nnodes))

    ! done
    call lev%ulevel%factory%destroy_single(rhs, lev%index,  lev%shape)
   
    call end_timer(pf, TLEVEL+lev%index-1)
  end subroutine imex_sweep