QuadraturePoint_Line

This routine returns the quadrature points on the line.

Calling example:

ans = QuadraturePoint_Line1( &
  & order, &
  & quadType, &
  & layout, &
  & xij, &
  & alpha, &
  & beta, &
  & lambda) 

ans

The last row of ans contains the weights. The first few rows contain the quadrature points. If xij is absent then ans has two rows. If xij is present then ans has SIZE(xij, 1)+1 rows.

• order is order of integrand
• xij contains nodal coordinates of line in xij format.
• SIZE(xij,1) = nsd, and SIZE(xij,2)=2
• If xij is absent then [-1,1] is used
• quadType is interpolation point type, it can take following values
  • GaussLegendre
  • GaussLegendreLobatto
  • GaussLegendreRadauLeft
  • GaussLegendreRadauRight
  • GaussChebyshev
  • GaussChebyshevLobatto
  • GaussChebyshevRadauLeft
  • GaussChebyshevRadauRight
  • GaussJacobi
  • GaussJacobiLobatto
  • GaussJacobiRadauLeft
  • GaussJacobiRadauRight
  • GaussUltraspherical
  • GaussUltrasphericalLobatto
  • GaussUltrasphericalRadauLeft
  • GaussUltrasphericalRadauRight
• layout specifies the arrangement of points. Following options are possible:
  • layout=VEFC vertex, edge, face, cell, in this case first two points are boundary points, remaining (from 3 to n) are internal points in increasing order.
  • layout=INCREASING points are arranged in increasing order

Interface

܀ Interface

INTERFACE QuadraturePoint_Line
  MODULE FUNCTION QuadraturePoint_Line1( &
    & order, &
    & quadType, &
    & layout, &
    & xij, &
    & alpha, &
    & beta, &
    & lambda) RESULT(ans)
    !!
    INTEGER(I4B), INTENT(IN) :: order
    !! Order of interpolation
    INTEGER(I4B), INTENT(IN) :: quadType
    !! Quadrature point type
    !! Equidistance,
    !! GaussLegendre,
    !! GaussLegendreLobatto,
    !! GaussChebyshev,
    !! GaussChebyshevLobatto,
    !! GaussJacobi,
    !! GaussJacobiLobatto
    CHARACTER(*), INTENT(IN) :: layout
    !! "VEFC"
    !! "INCREASING"
    REAL(DFP), OPTIONAL, INTENT(IN) :: xij(:, :)
    !! domain of interpolation
    REAL(DFP), OPTIONAL, INTENT(IN) :: alpha
    !! Jacobi parameter
    REAL(DFP), OPTIONAL, INTENT(IN) :: beta
    !! Jacobi parameter
    REAL(DFP), OPTIONAL, INTENT(IN) :: lambda
    !! Ultraspherical parameter
    REAL(DFP), ALLOCATABLE :: ans(:, :)
    !! quadrature points
    !! If xij is present then the number of rows in ans
    !! is same as size(xij,1) + 1.
    !! If xij is not present then the number of rows in
    !! ans is 2
    !! The last row of ans contains the weights
    !! The first few rows contains the quadrature points
  END FUNCTION QuadraturePoint_Line1
END INTERFACE QuadraturePoint_Line

️܀ See example

program main
  use easifemBase
  implicit none
  integer(i4b) :: order
  real(dfp) :: x
  real(dfp), allocatable :: xij(:,:), coeff(:,:), ans(:, :)
  character( len = * ), parameter :: layout="INCREASING" 
  integer(i4b) :: quadType

  order = 4_I4B

  quadType = GaussLegendre
  ans = QuadraturePoint_Line(order=order, quadType=quadType, layout=layout)
  call display(mdencode(ans), "GaussLegendre: " //char_lf//char_lf ) 

  quadType = GaussLegendreLobatto 
  ans = QuadraturePoint_Line(order=order, quadType=quadType, layout=layout, xij=xij)
  call display(mdencode(ans), "GaussLegendreLobatto: " //char_lf//char_lf)

  quadType = GaussChebyshev
  ans = QuadraturePoint_Line(order=order, quadType=quadType, layout=layout, xij=xij)
  call display(mdencode(ans), "GaussChebyshev: "//char_lf//char_lf)

  quadType = GaussChebyshevLobatto
  ans = QuadraturePoint_Line(order=order, quadType=quadType, layout=layout, xij=xij)
  call display(mdencode(ans), "GaussChebyshevLobatto: "//char_lf//char_lf)

end program main

See results

GaussLegendre:

-0.7746	3.71231E-16	0.7746
0.55556	0.88889	0.55556

GaussLegendreLobatto:

-1	-0.44721	0.44721	1
0.16667	0.83333	0.83333	0.16667

GaussChebyshev:

-0.86603	1.03412E-13	0.86603
1.0472	1.0472	1.0472

GaussChebyshevLobatto:

-1	-0.5	0.5	1
0.5236	1.0472	1.0472	0.5236

↢

Interface 2

܀ Interface

INTERFACE QuadraturePoint_Line
  MODULE FUNCTION QuadraturePoint_Line2( &
    & order, &
    & quadType, &
    & xij, &
    & layout, &
    & alpha, &
    & beta, &
    & lambda) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: order
    !! order of interpolation
    INTEGER(I4B), INTENT(IN) :: quadType
    !! Quadrature point type
    !! Equidistance
    !! GaussLegendre
    !! GaussLegendreLobatto
    !! GaussChebyshev,
    !! GaussChebyshevLobatto
    !! GaussJacobi
    !! GaussJacobiLobatto
    REAL(DFP), INTENT(IN) :: xij(2)
    !! end points
    CHARACTER(*), INTENT(IN) :: layout
    !! "VEFC"
    !! "INCREASING"
    REAL(DFP), OPTIONAL, INTENT(IN) :: alpha
    !! Jacobi parameter
    REAL(DFP), OPTIONAL, INTENT(IN) :: beta
    !! Jacobi parameter
    REAL(DFP), OPTIONAL, INTENT(IN) :: lambda
    !! Ultraspherical parameter
    REAL(DFP), ALLOCATABLE :: ans(:,:)
  END FUNCTION QuadraturePoint_Line2
END INTERFACE QuadraturePoint_Line

️܀ See example

See above example.

↢