Vandermonde1D Function

  1. submodule_DG_implementation.f90
  2. DG_implementation
  3. Vandermonde1D

function Vandermonde1D(n, x)

Initialize the 1D Vandermonde matrix, for the Legendre-Gauss-Lobatto quadrature points.

Arguments

Type IntentOptional AttributesName
integer(kind=ip), intent(in) :: n

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

The points at which to evaluate the Vandermonde matrix.

Return Value real(kind=wp), dimension(size(x),n+1)

The return value is the Vandermonde matrix,


Calls

proc~~vandermonde1d~~CallsGraph proc~vandermonde1d Vandermonde1D proc~jacobip JacobiP proc~vandermonde1d->proc~jacobip

Called by

proc~~vandermonde1d~~CalledByGraph proc~vandermonde1d Vandermonde1D proc~init_ref_element init_ref_element proc~init_ref_element->proc~vandermonde1d 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

Vandermonde1D

Source Code

    function Vandermonde1D ( n, x )
    !! Initialize the 1D Vandermonde matrix, \(\mathcal{V}_{ij}=P_j(x_i)\) 
    !! for the Legendre-Gauss-Lobatto quadrature points.
      integer(ip), intent(in) :: n
      !! The order of the Jacobi polynomials.
      real(wp), dimension(:), intent(in) :: x
      !! The points \(x\in[-1:1]\) at which to evaluate the Vandermonde matrix. 
      real(wp), dimension(size(x),n+1) :: Vandermonde1D
      !! The return value is the Vandermonde matrix, \(\mathcal{V}_{ij}\)

      integer :: j

      do j=1,n+1
        Vandermonde1D(:,j) = JacobiP(x, 0.0_wp, 0.0_wp, j-1)
      end do
      return
    end function VanderMonde1D