misdcQ_initialize Subroutine

  subroutine misdcQ_initialize(this, lev)
    class(pf_misdcQ_t), intent(inout) :: this
    class(pf_level_t), intent(inout) :: lev

    real(pfdp) :: dsdc(lev%nnodes-1)
    integer    :: m, n, nnodes

    this%npieces = 3

    nnodes = lev%nnodes
    allocate(this%QdiffE(nnodes-1,nnodes)) ! S-FE
    allocate(this%QdiffI(nnodes-1,nnodes)) ! S-BE 
    allocate(this%QtilE(nnodes-1,nnodes)) ! S-FE
    allocate(this%QtilI(nnodes-1,nnodes)) ! S-BE
    allocate(this%dtsdc(nnodes-1))
    this%QtilE = 0.0_pfdp
    this%QtilI = 0.0_pfdp
    
        !>  Array of substep sizes
    this%dtsdc = lev%nodes(2:nnodes) - lev%nodes(1:nnodes-1)
    ! Implicit matrix
    if (this%use_LUq) then 
       ! Get the LU
       this%QtilI = lev%sdcmats%qmatLU

    else 
       this%QtilI = lev%sdcmats%qmatBE
    end if
    ! Explicit matrix    
    this%QtilE=lev%sdcmats%qmatFE

    this%QdiffE = lev%sdcmats%qmat-this%QtilE
    this%QdiffI = lev%sdcmats%qmat-this%QtilI

    !>  Make space for rhs
    call lev%ulevel%factory%create_single(this%rhs, lev%index,   lev%shape)

    !>  Make space for extra integration piece
    call lev%ulevel%factory%create_array(this%I3,lev%nnodes-1,lev%index,lev%shape)

  end subroutine misdcQ_initialize