GaussWeigths Subroutine

  1. submodule_DG_implementation.f90
  2. DG_implementation
  3. GaussWeigths

subroutine GaussWeigths(alpha, beta, n, r, w)

Routine to calculate the integration weights for the Gauss-Lobatto Quadrature points.

Note. I currently don't remember where this equation comes from.

Arguments

Type IntentOptional AttributesName
real(kind=wp), intent(in) :: alpha

The value of .
real(kind=wp), intent(in) :: beta

The value of .
integer(kind=ip), intent(in) :: n

The order of the Jacobi polynomials.
real(kind=wp), intent(in), dimension(:):: r

The points for which the weights should be determined.
real(kind=wp), intent(out), dimension(:):: w

On return the integration weights.

Calls

proc~~gaussweigths~~CallsGraph proc~gaussweigths GaussWeigths proc~jacobip JacobiP proc~gaussweigths->proc~jacobip

Called by

proc~~gaussweigths~~CalledByGraph proc~gaussweigths GaussWeigths proc~init_ref_element init_ref_element proc~init_ref_element->proc~gaussweigths interface~init_ref_element init_ref_element interface~init_ref_element->proc~init_ref_element interface~ref_element ref_element interface~ref_element->interface~init_ref_element proc~scal_schw_init scal_schw_init proc~scal_schw_init->interface~ref_element program~test test program~test->interface~ref_element interface~scal_schw_init scal_schw_init interface~scal_schw_init->proc~scal_schw_init

Contents

Source Code

GaussWeigths

Source Code

    subroutine GaussWeigths( alpha, beta, n, r, w )
    !! Routine to calculate the integration weights for the Gauss-Lobatto
    !! Quadrature points.
    !!
    !! Note. I currently don't remember where this equation comes from.
      real(wp), dimension(:), intent(in) :: r
      !! The points for which the weights should be determined.
      real(wp), intent(in) :: alpha
      !! The value of \(\alpha\).
      real(wp), intent(in) :: beta
      !! The value of \(\beta\).
      integer(ip), intent(in) :: n
      !! The order of the Jacobi polynomials.
      real(wp), dimension(:), intent(out) :: w
      !! On return the integration weights.

      w = (2.0_wp*n+1.0_wp)/(n*(n+1.0_wp)) / JacobiP(r, alpha, beta, n)**2
    end subroutine GaussWeigths