quadgrid1 Function

public pure function quadgrid1(fnc, grid, average) result(res)

Cell-integral or cell-average of over grid, using Simpson's 1/3 rule.

  f(x) ^
       |                * * * *
       |          * * *++++++++++ *
       |        *                  *
       |     ++*++++++               *
       |     *                    ++++*+++++
       |                                 * *
      -|----|----.----|-----.----|----.-----|---->
              x_{i-i}      x_i      x_{i+1}

Arguments

Type IntentOptional Attributes Name
procedure(fx) :: fnc

function to integrate/average over grid cells
type(grid1), intent(in) :: grid

grid1 object
logical, intent(in), optional :: average

flag to compute cell-average instead of cell-integral

Return Value real(kind=rk), (grid%ncells)


Calls

proc~~quadgrid1~~CallsGraph proc~quadgrid1 quadgrid1 center center proc~quadgrid1->center edges edges proc~quadgrid1->edges optval optval proc~quadgrid1->optval

Source Code

   pure function quadgrid1(fnc, grid, average) result(res)
   !! Cell-integral or cell-average of \( f(x) \) over grid, using Simpson's 1/3 rule.
   !! ```
   !!   f(x) ^
   !!        |                * * * *
   !!        |          * * *++++++++++ *
   !!        |        *                  *
   !!        |     ++*++++++               *
   !!        |     *                    ++++*+++++
   !!        |                                 * *
   !!       -|----|----.----|-----.----|----.-----|---->
   !!               x_{i-i}      x_i      x_{i+1}
   !! ```
      procedure(fx) :: fnc
         !! function \( f(x) \) to integrate/average over grid cells
      type(grid1), intent(in) :: grid
         !! `grid1` object
      logical, intent(in), optional :: average
         !! flag to compute cell-average instead of cell-integral
      real(rk) :: res(grid%ncells)

      real(rk) :: fedges(0:grid%ncells), fcenter(grid%ncells)
      integer :: i

      associate (nc => grid%ncells)

         ! Evaluate f(x) at grid edges
         do concurrent(i=0:nc)
            fedges(i) = fnc(grid%edges(i))
         end do

         ! Evaluate f(x) at grid centers
         do concurrent(i=1:nc)
            fcenter(i) = fnc(grid%center(i))
         end do

         ! Cell-average using Simpson's 1/3 rule
         res = (4*fcenter + fedges(0:nc - 1) + fedges(1:nc))/6

         ! Convert cell-average to cell-integral
         if (.not. (optval(average, .false.))) then
            res = res*grid%width
         end if

      end associate

   end function quadgrid1