sheet_precondition Function

  function sheet_precondition(this, previous_states, melt_rate, &
                              basal_drag_parameter, water_density, &
                              delta_state) result(preconditioned)
    !* Author: Chris MacMackin
    !  Date: January 2016
    !
    ! Provides a preconditioner for the nonlinear solver trying to
    ! bring the residual to zero. The Jacobian is approximated as a
    ! block matrix, where each block is a tridiagonal matrix using a
    ! finite difference method for differentiation.
    !
    class(ice_sheet), intent(inout)     :: this
    class(glacier), dimension(:), intent(in) :: previous_states
      !! The states of the glacier in the previous time steps. The
      !! first element of the array should be the most recent. The
      !! default implementation will only make use of the most
      !! recent state, but the fact that this is an array allows
      !! overriding methods to use older states for higher-order
      !! integration methods.
    class(scalar_field), intent(in)          :: melt_rate
      !! Thickness of the ice above the glacier
    class(scalar_field), intent(in)     :: basal_drag_parameter
      !! A paramter, e.g. coefficient of friction, needed to calculate
      !! the drag on basal surface of the glacier.
    real(r8), intent(in)                :: water_density
      !! The density of the water below the glacier
    real(r8), dimension(:), intent(in)  :: delta_state
      !! The change to the state vector which is being preconditioned.
    real(r8), dimension(:), allocatable :: preconditioned
      !! The result of applying the preconditioner to `delta_state`.
  end function sheet_precondition