Initiate

This subroutine constructs the quadrature points.

Interface 1

܀ Interface

INTERFACE Initiate
  MODULE SUBROUTINE quad_initiate3(obj, refElem, order, quadratureType,  &
    & alpha, beta, lambda)
    TYPE(QuadraturePoint_), INTENT(INOUT) :: obj
    !! Total number of xidimension
    CLASS(ReferenceElement_), INTENT(IN) :: refElem
    !! Reference element
    INTEGER(I4B), INTENT(IN) :: order
    !! order of integrand
    CHARACTER(*), INTENT(IN) :: quadratureType
    !! Type of quadrature points
    !! "GaussLegendre"
    !! "GaussLegendreLobatto"
    !! "GaussLegendreRadau", "GaussLegendreRadauLeft"
    !! "GaussLegendreRadauRight"
    !! "GaussChebyshev"
    !! "GaussChebyshevLobatto"
    !! "GaussChebyshevRadau", "GaussChebyshevRadauLeft"
    !! "GaussChebyshevRadauRight"
    REAL(DFP), OPTIONAL, INTENT(IN) :: alpha
    !! Jacobi parameter
    REAL(DFP), OPTIONAL, INTENT(IN) :: beta
    !! Jacobi parameter
    REAL(DFP), OPTIONAL, INTENT(IN) :: lambda
    !! Ultraspherical parameter
  END SUBROUTINE quad_initiate3
END INTERFACE Initiate

quadratureType

Type of quadrature points:

• "GaussLegendre"
• "GaussLegendreLobatto"
• "GaussLegendreRadau", "GaussLegendreRadauLeft"
• "GaussLegendreRadauRight"
• "GaussChebyshev"
• "GaussChebyshevLobatto"
• "GaussChebyshevRadau", "GaussChebyshevRadauLeft"
• "GaussChebyshevRadauRight"
• "GaussJacobi"
• "GaussJacobiLobatto"
• "GaussJacobiRadau", "GaussJacobiRadauLeft"
• "GaussJacobiRadauRight"
• "GaussUltraspherical"
• "GaussUltrasphericalLobatto"
• "GaussUltrasphericalRadau", "GaussUltraspericalRadauLeft"
• "GaussUltrasphericalRadauRight"

In the case of Jacobi alpha and beta should be given, and in the case of Ultraspherical lambda should be given.

️܀ See example

PROGRAM main
USE easifemBase
IMPLICIT NONE

TYPE(QuadraturePoint_) :: obj
TYPE(ReferenceLine_) :: refelem
INTEGER(I4B) :: order
refelem = ReferenceLine(nsd=1_I4B)
order = 4_I4B
CALL initiate(obj=obj, &
  & refelem=refelem, &
  & order=order,  &
  & quadratureType="GaussLegendre")
CALL display(mdencode(obj), "")
END PROGRAM main

↢

Interface 2

INTERFACE Initiate
  MODULE SUBROUTINE quad_initiate4(obj, refElem, nips, quadratureType, &
    & alpha, beta, lambda)
    TYPE(QuadraturePoint_), INTENT(INOUT) :: obj
    !! Total number of xidimension
    CLASS(ReferenceElement_), INTENT(IN) :: refElem
    !! Reference element
    INTEGER(I4B), INTENT(IN) :: nips(1)
    !! order of integrand
    CHARACTER(*), INTENT(IN) :: quadratureType
    REAL(DFP), OPTIONAL, INTENT(IN) :: alpha
    !! Jacobi parameter
    REAL(DFP), OPTIONAL, INTENT(IN) :: beta
    !! Jacobi parameter
    REAL(DFP), OPTIONAL, INTENT(IN) :: lambda
    !! Ultraspherical parameter
  END SUBROUTINE quad_initiate4
END INTERFACE Initiate

info

This method allows us to initiate the quadrature points by specifying the number of integration points, and quadrature type.

Interface 3

܀ Interface

INTERFACE Initiate
  MODULE SUBROUTINE quad_initiate5( &
    & obj, &
    & refElem, &
    & order, &
    & quadratureType,  &
    & alpha, beta, lambda)
    TYPE(QuadraturePoint_), INTENT(INOUT) :: obj
    !! Total number of xidimension
    CLASS(ReferenceElement_), INTENT(IN) :: refElem
    !! Reference-element
    INTEGER(I4B), INTENT(IN) :: order
    !! order of integrand
    INTEGER(I4B), INTENT(IN) :: quadratureType
    !! Type of quadrature points
    !! GaussLegendre
    !! GaussLegendreLobatto
    !! GaussLegendreRadau
    !! GaussLegendreRadauLeft
    !! GaussLegendreRadauRight
    !! GaussChebyshev
    !! GaussChebyshevLobatto
    !! GaussChebyshevRadau
    !! GaussChebyshevRadauLeft
    !! GaussChebyshevRadauRight
    REAL(DFP), OPTIONAL, INTENT(IN) :: alpha
    !! Jacobi parameter
    REAL(DFP), OPTIONAL, INTENT(IN) :: beta
    !! Jacobi parameter
    REAL(DFP), OPTIONAL, INTENT(IN) :: lambda
    !! Ultraspherical parameter
  END SUBROUTINE quad_initiate5
END INTERFACE Initiate

quadratureType

Type of quadrature points:

• GaussLegendre
• GaussLegendreLobatto
• GaussLegendreRadau, GaussLegendreRadauLeft
• GaussLegendreRadauRight
• GaussChebyshev
• GaussChebyshevLobatto
• GaussChebyshevRadau, GaussChebyshevRadauLeft
• GaussChebyshevRadauRight
• GaussJacobi
• GaussJacobiLobatto
• GaussJacobiRadau, GaussJacobiRadauLeft
• GaussJacobiRadauRight
• GaussUltraspherical
• GaussUltrasphericalLobatto
• GaussUltrasphericalRadau, GaussUltraspericalRadauLeft
• GaussUltrasphericalRadauRight

In the case of Jacobi alpha and beta should be given, and in the case of Ultraspherical lambda should be given.

️܀ See example

PROGRAM main
USE easifemBase
IMPLICIT NONE
TYPE(QuadraturePoint_) :: obj
TYPE(ReferenceLine_) :: refelem
INTEGER(I4B) :: order

refelem = ReferenceLine(nsd=1_I4B)
order = 4_I4B
CALL initiate(obj=obj, &
  & refelem=refelem, &
  & order=order,  &
  & quadratureType=GaussLegendre)
CALL display(mdencode(obj), "")
END PROGRAM main

↢

Interface 4

INTERFACE Initiate
  MODULE SUBROUTINE quad_initiate6( &
    & obj, &
    & refElem, &
    & nips, &
    & quadratureType, &
    & alpha, &
    & beta, &
    & lambda)
    TYPE(QuadraturePoint_), INTENT(INOUT) :: obj
    !! Total number of xidimension
    CLASS(ReferenceElement_), INTENT(IN) :: refElem
    !! Reference element
    INTEGER(I4B), INTENT(IN) :: nips(1)
    !! order of integrand
    INTEGER(I4B), INTENT(IN) :: quadratureType
    !! Type of quadrature points
    !! GaussLegendre
    !! GaussLegendreLobatto
    !! GaussLegendreRadau
    !! GaussLegendreRadauLeft
    !! GaussLegendreRadauRight
    !! GaussChebyshev
    !! GaussChebyshevLobatto
    !! GaussChebyshevRadau
    !! GaussChebyshevRadauLeft
    !! GaussChebyshevRadauRight
    REAL(DFP), OPTIONAL, INTENT(IN) :: alpha
    !! Jacobi parameter
    REAL(DFP), OPTIONAL, INTENT(IN) :: beta
    !! Jacobi parameter
    REAL(DFP), OPTIONAL, INTENT(IN) :: lambda
    !! Ultraspherical parameter
  END SUBROUTINE quad_initiate6
END INTERFACE Initiate

Interface 5

INTERFACE Initiate
  MODULE SUBROUTINE quad_initiate7( &
    & obj, &
    & refElem, &
    & p, q, r, &
    & quadratureType1, &
    & quadratureType2, &
    & quadratureType3, &
    & alpha1, beta1, lambda1,  &
    & alpha2, beta2, lambda2,  &
    & alpha3, beta3, lambda3)
    TYPE(QuadraturePoint_), INTENT(INOUT) :: obj
    !! Total number of xidimension
    CLASS(ReferenceElement_), INTENT(IN) :: refElem
    !! Reference-element
    INTEGER(I4B), INTENT(IN) :: p
    !! order of integrand in x
    INTEGER(I4B), INTENT(IN) :: q
    !! order of integrand in y
    INTEGER(I4B), INTENT(IN) :: r
    !! order of integrand in z direction
    INTEGER(I4B), INTENT(IN) :: quadratureType1
    !! Type of quadrature points
    !! GaussLegendre
    !! GaussLegendreLobatto
    !! GaussLegendreRadau
    !! GaussLegendreRadauLeft
    !! GaussLegendreRadauRight
    !! GaussChebyshev
    !! GaussChebyshevLobatto
    !! GaussChebyshevRadau
    !! GaussChebyshevRadauLeft
    !! GaussChebyshevRadauRight
    INTEGER(I4B), INTENT(IN) :: quadratureType2
    !! Type of quadrature points
    INTEGER(I4B), INTENT(IN) :: quadratureType3
    !! Type of quadrature points
    REAL(DFP), OPTIONAL, INTENT(IN) :: alpha1, beta1, lambda1
    !! Jacobi parameter and Ultraspherical parameters
    REAL(DFP), OPTIONAL, INTENT(IN) :: alpha2, beta2, lambda2
    !! Jacobi parameter and Ultraspherical parameters
    REAL(DFP), OPTIONAL, INTENT(IN) :: alpha3, beta3, lambda3
    !! Jacobi parameter and Ultraspherical parameters
  END SUBROUTINE quad_initiate7
END INTERFACE Initiate

Interface 6

INTERFACE Initiate
  MODULE SUBROUTINE quad_initiate8( &
    & obj, &
    & refElem, &
    & nipsx, &
    & nipsy, &
    & nipsz, &
    & quadratureType1, &
    & quadratureType2, &
    & quadratureType3, &
    & alpha1, beta1, lambda1, &
    & alpha2, beta2, lambda2, &
    & alpha3, beta3, lambda3)
    TYPE(QuadraturePoint_), INTENT(INOUT) :: obj
    !! Total number of xidimension
    CLASS(ReferenceElement_), INTENT(IN) :: refElem
    !! Reference element
    INTEGER(I4B), INTENT(IN) :: nipsx(1)
    !! number of integration points in x direction
    INTEGER(I4B), INTENT(IN) :: nipsy(1)
    !! number of integration points in y direction
    INTEGER(I4B), INTENT(IN) :: nipsz(1)
    !! number of integration points in z direction
    INTEGER(I4B), INTENT(IN) :: quadratureType1
    !! Type of quadrature points
    !! GaussLegendre
    !! GaussLegendreLobatto
    !! GaussLegendreRadau
    !! GaussLegendreRadauLeft
    !! GaussLegendreRadauRight
    !! GaussChebyshev
    !! GaussChebyshevLobatto
    !! GaussChebyshevRadau
    !! GaussChebyshevRadauLeft
    !! GaussChebyshevRadauRight
    INTEGER(I4B), INTENT(IN) :: quadratureType2
    !! Type of quadrature points
    INTEGER(I4B), INTENT(IN) :: quadratureType3
    !! Type of quadrature points
    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
  END SUBROUTINE quad_initiate8
END INTERFACE Initiate

Interface 7

MODULE PURE SUBROUTINE Initiate( obj, Points )
  CLASS( QuadraturePoint_ ), INTENT( INOUT ) :: obj
  REAL( DFP ), INTENT( IN ) :: Points( :, : )
    !! Points contains the quadrature points and weights
    !! Points( :, ipoint ) contains quadrature points and weights of ipoint
    !! quadrature point. The last row contains the weight. The rest of the
    !! rows contains the coordinates of quadrature.
END SUBROUTINE Initiate

This subroutine converts the quadrature points into QuadraturePoint_ data type.

caution

This routine is for developers only, normal user should not worry about this interface.

Points

• Points contains the quadrature points and weights
• for example, Points( :, ipoint ) contains quadrature points and weights of ipoint quadrature point.
• The last row always contains the weight.
• The rest of the rows contains the coordinates of quadrature.

Interface 8

developers only

MODULE PURE SUBROUTINE Initiate( obj, tXi, tPoints )
  CLASS( QuadraturePoint_ ), INTENT( INOUT ) :: obj
  INTEGER( I4B ), INTENT( IN ) :: tXi
  !! Total number of xidimension
  !! For line tXi=1
  !! For 2D element tXi=2
  !! For 3D element tXi=3
  INTEGER( I4B ), INTENT( IN ) :: tPoints
  !! Total number quadrature points
END SUBROUTINE Initiate

The following interface allocates the memory for storing the quadrature points.

caution

This routine is for developers only, normal user should not worry about this interface.

QuadraturePoint (Constructor function)

MODULE PURE FUNCTION QuadraturePoint( Points ) RESULT( obj )
  TYPE( QuadraturePoint_ ) :: obj
  REAL( DFP ), INTENT( IN ) :: Points( :, : )
END FUNCTION QuadraturePoint

This function converts Points to an instance of QuadraturePoint.

QuadraturePoint_Pointer

MODULE PURE FUNCTION QuadraturePoint_Pointer( Points ) RESULT( obj )
  CLASS( QuadraturePoint_ ), POINTER :: obj
  REAL( DFP ), INTENT( IN ) :: Points( :, : )
END FUNCTION QuadraturePoint_Pointer