Quadrangle

Gauss-Legendre on Biunit quadrangle

PROGRAM main
USE easifemBase
IMPLICIT NONE
TYPE(QuadraturePoint_) :: obj
TYPE(ReferenceQuadrangle_) :: refelem
INTEGER(I4B) :: order
refelem = ReferenceQuadrangle(nsd=2_I4B)
order = 4_I4B
CALL initiate(obj=obj, &
  & refelem=refelem, &
  & order=order,  &
  & quadratureType=GaussLegendre)
CALL display(mdencode(obj) , "")
END PROGRAM main

See results

x1	-0.7746	-0.7746	-0.7746	1.8735E-16	1.66533E-16	1.66533E-16	0.7746	0.7746	0.7746
x2	-0.7746	2.22045E-16	0.7746	-0.7746	1.66533E-16	0.7746	-0.7746	1.80411E-16	0.7746
w	0.30864	0.49383	0.30864	0.49383	0.79012	0.49383	0.30864	0.49383	0.30864

note

You can set quadratureType to following values:

GaussLegendre; GaussLegendreLobatto; GaussLegendreRadauLeft; GaussLegendreRadauRight; GaussJacobi; GaussJacobiLobatto; GaussJacobiRadauLeft; GaussJacobiRadauRight; GaussUltraspherical; GaussUltrasphericalLobatto; GaussUltrasphericalRadauLeft; GaussUltrasphericalRadauRight

Gauss-Legendre points on unit quadrangle

PROGRAM main
USE easifemBase
IMPLICIT NONE
TYPE(QuadraturePoint_) :: obj
TYPE(ReferenceQuadrangle_) :: refelem
INTEGER(I4B) :: order
refelem = ReferenceQuadrangle(nsd=2_I4B, xij=RefCoord_Quadrangle("UNIT"))
order = 4_I4B
CALL initiate(obj=obj, &
  & refelem=refelem, &
  & order=order,  &
  & quadratureType=GaussLegendre)
CALL display(mdencode(obj), "")
END PROGRAM main

See results

x1	0.1127	0.1127	0.1127	0.5	0.5	0.5	0.8873	0.8873	0.8873
x2	0.1127	0.5	0.8873	0.1127	0.5	0.8873	0.1127	0.5	0.8873
w	7.71605E-02	0.12346	7.71605E-02	0.12346	0.19753	0.12346	7.71605E-02	0.12346	7.71605E-02

Anisotropic order

PROGRAM main
USE easifemBase
IMPLICIT NONE
TYPE(QuadraturePoint_) :: obj
TYPE(ReferenceQuadrangle_) :: refelem
INTEGER(I4B) :: order
refelem = ReferenceQuadrangle(nsd=2_I4B)
order = 4_I4B
CALL initiate(obj=obj, &
  & refelem=refelem, &
  & p=4,  &
  & q=3,  &
  & r=1,  &
  & quadratureType1=GaussLegendre, &
  & quadratureType2=GaussLegendre, &
  & quadratureType3=GaussLegendre )
CALL display(mdencode(obj) , "")
END PROGRAM main

See results

x1	-0.7746	-0.7746	3.60822E-16	3.33067E-16	0.7746	0.7746
x2	-0.57735	0.57735	-0.57735	0.57735	-0.57735	0.57735
w	0.55556	0.55556	0.88889	0.88889	0.55556	0.55556