QuadraturePoint

This routine returns the quadrature points on Quadrangle.

Calling example:

program main
ans = QuadraturePoint_Quadrangle(order, quadType, &
    & xij, alpha, beta, lambda)
end program main

Interface

܀ Interface

INTERFACE QuadraturePoint_Quadrangle
  MODULE FUNCTION QuadraturePoint_Quadrangle1(order, quadType, &
    & xij, alpha, beta, lambda) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: order
    !! order of integrand in x and y direction
    INTEGER(I4B), INTENT(IN) :: quadType
    !! Quadrature point type
    REAL(DFP), OPTIONAL, INTENT(IN) :: xij(:, :)
    !! four vertices of quadrangle in xij format
    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(:, :)
    !! interpolation points in xij format
  END FUNCTION QuadraturePoint_Quadrangle1
END INTERFACE QuadraturePoint_Quadrangle

xij

• xij contains nodal coordinates of quadrangle in xij format.
• The number of rows in xij can be 2 or 3 (for 2D or 3D)
• The number of columns in xij is 4
• If xij is absent then biunit quadrangle is assumed.

quadType

• 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

alpha, beta, lambda

• alpha and beta are parameters for Jacobi quadrature points
• lambda is the parameter for Ultraspherical quadrature points

️܀ GaussLegendre

program main
  use easifembase
  implicit none
  integer( i4b ) :: i1, i2, order, quadType
  real( dfp ), allocatable :: x(:,:), xij(:, :)

  order=2
  xij = RefQuadrangleCoord("BIUNIT")
  quadType=GaussLegendre

  x =QuadraturePoint_Quadrangle(  &
    & order=order, &
    & quadType=quadType)

  call display( Mdencode(x), "xij (order="//tostring(order)//")=" )

end program main

See results

xij (order=2)=

$\xi$	-0.57735	-0.57735	0.57735	0.57735
$\eta$	-0.57735	0.57735	-0.57735	0.57735
w	1	1	1	1

GaussLegendreLobatto

program main
  use easifembase
  implicit none
  integer( i4b ) :: i1, i2, order, quadType
  real( dfp ), allocatable :: x(:,:), xij(:, :)

  order=2
  xij = RefQuadrangleCoord("BIUNIT")
  quadType=GaussLegendreLobatto

  x =QuadraturePoint_Quadrangle(  &
    & order=order, &
    & quadType=quadType)

  call display( Mdencode(x), "xij (order="//tostring(order)//")=" // char_lf // char_lf )

end program main

See results

xij (order=2)=

-1	-1	-1	-2.66578E-17	-2.66578E-17	-2.66578E-17	1	1	1
-1	-2.66578E-17	1	-1	-2.66578E-17	1	-1	-2.66578E-17	1
0.11111	0.44444	0.11111	0.44444	1.7778	0.44444	0.11111	0.44444	0.11111

etails>

GaussLegendreRadauLeft

program main
  use easifembase
  implicit none
  integer( i4b ) :: i1, i2, order, quadType
  real( dfp ), allocatable :: x(:,:), xij(:, :)

  order=2
  xij = RefQuadrangleCoord("BIUNIT")
  quadType=GaussLegendreRadauLeft

  x =QuadraturePoint_Quadrangle(  &
    & order=order, &
    & quadType=quadType)

  call display( Mdencode(x), "xij (order="//tostring(order)//")=" // char_lf // char_lf )

end program main

See results

xij (order=2)=

-1	-1	-1	-2.66578E-17	-2.66578E-17	-2.66578E-17	1	1	1
-1	-2.66578E-17	1	-1	-2.66578E-17	1	-1	-2.66578E-17	1
0.11111	0.44444	0.11111	0.44444	1.7778	0.44444	0.11111	0.44444	0.11111

etails>

↢

Interface 2

Interface

INTERFACE QuadraturePoint_Quadrangle
  MODULE FUNCTION QuadraturePoint_Quadrangle2(  &
    & p, q, quadType1, quadType2, xij, alpha1, beta1, &
    & lambda1, alpha2, beta2, lambda2) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: p
    !! order of integrand in x direction
    INTEGER(I4B), INTENT(IN) :: q
    !! order of  integrand in y direction
    INTEGER(I4B), INTENT(IN) :: quadType1
    !! quadrature point type in x direction
    INTEGER(I4B), INTENT(IN) :: quadType2
    !! quadrature point type in y direction
    REAL(DFP), OPTIONAL, INTENT(IN) :: xij(:, :)
    !! four vertices of quadrangle in xij format
    REAL(DFP), OPTIONAL, INTENT(IN) :: alpha1
    !! Jacobi parameter
    REAL(DFP), OPTIONAL, INTENT(IN) :: beta1
    !! Jacobi parameter
    REAL(DFP), OPTIONAL, INTENT(IN) :: lambda1
    !! Ultraspherical parameter
    REAL(DFP), OPTIONAL, INTENT(IN) :: alpha2
    !! Jacobi parameter
    REAL(DFP), OPTIONAL, INTENT(IN) :: beta2
    !! Jacobi parameter
    REAL(DFP), OPTIONAL, INTENT(IN) :: lambda2
    !! Ultraspherical parameter
    REAL(DFP), ALLOCATABLE :: ans(:, :)
    !! interpolation points in xij format
  END FUNCTION QuadraturePoint_Quadrangle2
END INTERFACE QuadraturePoint_Quadrangle

Interface 3

INTERFACE QuadraturePoint_Quadrangle
  MODULE FUNCTION QuadraturePoint_Quadrangle3(nips, quadType, &
    & xij, alpha, beta, lambda) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: nips(1)
    !! number of integration points in x and y direction
    INTEGER(I4B), INTENT(IN) :: quadType
    !! quadrature point type
    REAL(DFP), OPTIONAL, INTENT(IN) :: xij(:, :)
    !! four vertices of quadrangle in xij format
    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(:, :)
    !! interpolation points in xij format
  END FUNCTION QuadraturePoint_Quadrangle3
END INTERFACE QuadraturePoint_Quadrangle

Interface 4

INTERFACE QuadraturePoint_Quadrangle
  MODULE FUNCTION QuadraturePoint_Quadrangle4(  &
    & nipsx, nipsy, quadType1, quadType2, xij, alpha1, beta1, &
    & lambda1, alpha2, beta2, lambda2) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: nipsx(1)
    !! order of integrand in x direction
    INTEGER(I4B), INTENT(IN) :: nipsy(1)
    !! order of  integrand in y direction
    INTEGER(I4B), INTENT(IN) :: quadType1
    !! quadrature point type in x direction
    INTEGER(I4B), INTENT(IN) :: quadType2
    !! quadrature point type in y direction
    REAL(DFP), OPTIONAL, INTENT(IN) :: xij(:, :)
    !! four vertices of quadrangle in xij format
    REAL(DFP), OPTIONAL, INTENT(IN) :: alpha1
    !! Jacobi parameter
    REAL(DFP), OPTIONAL, INTENT(IN) :: beta1
    !! Jacobi parameter
    REAL(DFP), OPTIONAL, INTENT(IN) :: lambda1
    !! Ultraspherical parameter
    REAL(DFP), OPTIONAL, INTENT(IN) :: alpha2
    !! Jacobi parameter
    REAL(DFP), OPTIONAL, INTENT(IN) :: beta2
    !! Jacobi parameter
    REAL(DFP), OPTIONAL, INTENT(IN) :: lambda2
    !! Ultraspherical parameter
    REAL(DFP), ALLOCATABLE :: ans(:, :)
    !! interpolation points in xij format
  END FUNCTION QuadraturePoint_Quadrangle4
END INTERFACE QuadraturePoint_Quadrangle