QuadraturePoint

Returns quadrature points on hexahedron.

Interface 1

܀ Interface
️܀ Example 1
Example 2
Example 3
↢

INTERFACE QuadraturePoint_Hexahedron
  MODULE FUNCTION QuadraturePoint_Hexahedron1( &
    & order, &
    & quadType, &
    & xij, &
    & alpha, &
    & beta, &
    & lambda) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: order
    !! order of integrand in x, y, and z direction
    INTEGER(I4B), INTENT(IN) :: quadType
    !! quadrature point type
    !! GaussLegendre
    !! GaussLegendreLobatto
    !! GaussLegendreRadauLeft
    !! GaussLegendreRadauRight
    !! GaussChebyshev1
    !! GaussChebyshev1Lobatto
    !! GaussChebyshev1RadauLeft
    !! GaussChebyshev1RadauRight
    !! GaussUltraspherical
    !! GaussUltrasphericalLobatto
    !! GaussUltrasphericalRadauLeft
    !! GaussUltrasphericalRadauRight
    !! GaussJacobi
    !! GaussJacobiLobatto
    !! GaussJacobiRadauLeft
    !! GaussJacobiRadauRight
    REAL(DFP), OPTIONAL, INTENT(IN) :: xij(:, :)
    !! nodal coordiantes of hexahedron 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(:, :)
    !! quadrature points in xij format
  END FUNCTION QuadraturePoint_Hexahedron1
END INTERFACE QuadraturePoint_Hexahedron

order

order of accuracy in x, y, and z directions.

xij

xij contains nodal coordinates of hexahedron in xij format.
- The number of rows in xij is 3
- The number of columns in xij is 8
- If xij is absent then biunit hexahedron is assumed.

quadType

quadType is quadrature 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

program main
  use easifembase
  implicit none
  integer( i4b ) :: i1, i2, order
  real( dfp ), allocatable :: x(:,:)
  type(string) :: astr
  order=1
  x = QuadraturePoint_Hexahedron(  &
  & order=order, &
  & quadType=GaussLegendre )
  call display(x, "ans:")


  order=2
  x = QuadraturePoint_Hexahedron(  &
  & order=order, &
  & quadType=GaussLegendre )
  call display(x, "ans:")
end program main

program main
  use easifembase
  implicit none
  integer( i4b ) :: i1, i2, order
  real( dfp ), allocatable :: x(:,:)
  type(string) :: astr
  order=1
  x = QuadraturePoint_Hexahedron(  &
  & order=order, &
  & quadType=GaussLegendreLobatto )
  call display(x, "ans:")


  order=2
  x = QuadraturePoint_Hexahedron(  &
  & order=order, &
  & quadType=GaussLegendreLobatto )
  call display(x, "ans:")
end program main

program main
  use easifembase
  implicit none
  integer( i4b ) :: i1, i2, order
  real( dfp ), allocatable :: x(:,:)
  type(string) :: astr
  order=1
  x = QuadraturePoint_Hexahedron(  &
  & order=order, &
  & quadType=GaussChebyshev )
  call display(x, "ans:")


  order=2
  x = QuadraturePoint_Hexahedron(  &
  & order=order, &
  & quadType=GaussChebyshev )
  call display(x, "ans:")
end program main

Interface 2

INTERFACE QuadraturePoint_Hexahedron
  MODULE FUNCTION QuadraturePoint_Hexahedron2(  &
    & p, q, r, &
    & quadType1, quadType2, quadType3, &
    & xij, &
    & alpha1, beta1, lambda1, &
    & alpha2, beta2, lambda2, &
    & alpha3, beta3, lambda3 &
    & ) 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) :: r
    !! order of  integrand in z direction
    INTEGER(I4B), INTENT(IN) :: quadType1, quadType2, quadType3
    !! quadrature point type in x direction
    !! Equidistance
    !! GaussLegendre
    !! GaussLegendreLobatto
    !! GaussLegendreRadauLeft
    !! GaussLegendreRadauRight
    !! GaussChebyshev1
    !! GaussChebyshev1Lobatto
    !! GaussChebyshev1RadauLeft
    !! GaussChebyshev1RadauRight
    !! GaussUltraspherical
    !! GaussUltrasphericalLobatto
    !! GaussUltrasphericalRadauLeft
    !! GaussUltrasphericalRadauRight
    !! GaussJacobi
    !! GaussJacobiLobatto
    !! GaussJacobiRadauLeft
    !! GaussJacobiRadauRight
    REAL(DFP), OPTIONAL, INTENT(IN) :: xij(:, :)
    !! four vertices of quadrangle in xij format
    REAL(DFP), OPTIONAL, INTENT(IN) :: alpha1, beta1, lambda1
    !! Jacobi parameter and Ultraspherical parameter
    REAL(DFP), OPTIONAL, INTENT(IN) :: alpha2, beta2, lambda2
    !! Jacobi parameter and Ultraspherical parameter
    REAL(DFP), OPTIONAL, INTENT(IN) :: alpha3, beta3, lambda3
    !! Jacobi parameter and Ultraspherical parameter
    REAL(DFP), ALLOCATABLE :: ans(:, :)
    !! interpolation points in xij format
  END FUNCTION QuadraturePoint_Hexahedron2
END INTERFACE QuadraturePoint_Hexahedron

p,q,r

Order of accuracy in x, y, and z directions.

quadType1, quadType2, quadType3

Quadrature type in x, y, and z direction. It can take following values

GaussLegendre
GaussLegendreLobatto
GaussLegendreRadauLeft
GaussLegendreRadauRight
GaussChebyshev
GaussChebyshevLobatto
GaussChebyshevRadauLeft
GaussChebyshevRadauRight
GaussJacobi
GaussJacobiLobatto
GaussJacobiRadauLeft
GaussJacobiRadauRight
GaussUltraspherical
GaussUltrasphericalLobatto
GaussUltrasphericalRadauLeft
GaussUltrasphericalRadauRight

alpha, beta, and lambda

These are parameters of Jacobi and Ultraspherical quadrature points.

Interface 3

INTERFACE QuadraturePoint_Hexahedron
  MODULE FUNCTION QuadraturePoint_Hexahedron3(nips, quadType, &
    & xij, alpha, beta, lambda) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: nips(1)
    !! number of integration points in x, y, and z direction
    INTEGER(I4B), INTENT(IN) :: quadType
    !! interpolation point type
    !! GaussLegendre
    !! GaussLegendreLobatto
    !! GaussLegendreRadauLeft
    !! GaussLegendreRadauRight
    !! GaussChebyshev1
    !! GaussChebyshev1Lobatto
    !! GaussChebyshev1RadauLeft
    !! GaussChebyshev1RadauRight
    !! GaussUltraspherical
    !! GaussUltrasphericalLobatto
    !! GaussUltrasphericalRadauLeft
    !! GaussUltrasphericalRadauRight
    !! GaussJacobi
    !! GaussJacobiLobatto
    !! GaussJacobiRadauLeft
    !! GaussJacobiRadauRight
    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_Hexahedron3
END INTERFACE QuadraturePoint_Hexahedron

nips

Number of integration points in x, y, and z direction.

Interface 4

INTERFACE QuadraturePoint_Hexahedron
  MODULE FUNCTION QuadraturePoint_Hexahedron4(  &
    & nipsx, nipsy, nipsz, &
    & quadType1, quadType2, quadType3, &
    & xij, &
    & alpha1, beta1, lambda1, &
    & alpha2, beta2, lambda2, &
    & alpha3, beta3, lambda3 &
    & ) 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) :: nipsz(1)
    !! order of  integrand in z direction
    INTEGER(I4B), INTENT(IN) :: quadType1, quadType2, quadType3
    !! quadrature point type in x, y, and z direction
    !! Equidistance
    !! GaussLegendre
    !! GaussLegendreLobatto
    !! GaussLegendreRadauLeft
    !! GaussLegendreRadauRight
    !! GaussChebyshev1
    !! GaussChebyshev1Lobatto
    !! GaussChebyshev1RadauLeft
    !! GaussChebyshev1RadauRight
    !! GaussUltraspherical
    !! GaussUltrasphericalLobatto
    !! GaussUltrasphericalRadauLeft
    !! GaussUltrasphericalRadauRight
    !! GaussJacobi
    !! GaussJacobiLobatto
    !! GaussJacobiRadauLeft
    !! GaussJacobiRadauRight
    REAL(DFP), OPTIONAL, INTENT(IN) :: xij(:, :)
    !! four vertices of quadrangle in xij format
    REAL(DFP), OPTIONAL, INTENT(IN) :: alpha1, beta1, lambda1
    !! Jacobi and Ultraspherical parameter
    REAL(DFP), OPTIONAL, INTENT(IN) :: alpha2, beta2, lambda2
    !! Jacobi and Ultraspherical parameter
    REAL(DFP), OPTIONAL, INTENT(IN) :: alpha3, beta3, lambda3
    !! Jacobi and Ultraspherical parameter
    REAL(DFP), ALLOCATABLE :: ans(:, :)
    !! interpolation points in xij format
  END FUNCTION QuadraturePoint_Hexahedron4
END INTERFACE QuadraturePoint_Hexahedron

nipsx, nipsy, nipsz

Number of integration points in x, y, and z direction.

Interface 1​

Interface 2​

Interface 3​

Interface 4​

Interface 1

Interface 2

Interface 3

Interface 4