Hexahedron
This tutorial covers how to generate quadrature points on Hexahedron.
For creating Isotropic quadrature see example 1 and example 2.
For creating Anisotropic quadrature see example 3
Isotropic Gauss Legendre points on biunit Hexahedron
PROGRAM main
USE easifemBase
IMPLICIT NONE
TYPE(QuadraturePoint_) :: obj
TYPE(ReferenceHexahedron_) :: refelem
INTEGER(I4B) :: order
refelem = ReferenceHexahedron(nsd=3_I4B)
order = 2_I4B
CALL initiate(obj=obj, &
& refelem=refelem, &
& order=order, &
& quadratureType=GaussLegendre)
CALL display(mdencode(obj), "ans: ")
END PROGRAM main
| x1 | -0.57735 | -0.57735 | -0.57735 | -0.57735 | 0.57735 | 0.57735 | 0.57735 | 0.57735 |
| x2 | -0.57735 | -0.57735 | 0.57735 | 0.57735 | -0.57735 | -0.57735 | 0.57735 | 0.57735 |
| x3 | -0.57735 | 0.57735 | -0.57735 | 0.57735 | -0.57735 | 0.57735 | -0.57735 | 0.57735 |
| w | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Isotropic Gauss-Legendre points on unit Hexahedron
Just pass coordinates of a unit Hexahedron to initiate method of ReferenceHexahedron.
PROGRAM main
USE easifemBase
IMPLICIT NONE
TYPE(QuadraturePoint_) :: obj
TYPE(ReferenceHexahedron_) :: refelem
INTEGER(I4B) :: order
refelem = ReferenceHexahedron(nsd=3_I4B, xij=RefCoord_Hexahedron("UNIT"))
order = 2_I4B
CALL initiate(obj=obj, &
& refelem=refelem, &
& order=order, &
& quadratureType=GaussLegendre)
CALL display(mdencode(obj) , "")
END PROGRAM main
| x1 | 0.21132 | 0.21132 | 0.21132 | 0.21132 | 0.78868 | 0.78868 | 0.78868 | 0.78868 |
| x2 | 0.21132 | 0.21132 | 0.78868 | 0.78868 | 0.21132 | 0.21132 | 0.78868 | 0.78868 |
| x3 | 0.21132 | 0.78868 | 0.21132 | 0.78868 | 0.21132 | 0.78868 | 0.21132 | 0.78868 |
| w | 0.125 | 0.125 | 0.125 | 0.125 | 0.125 | 0.125 | 0.125 | 0.125 |
Anisotropic Gauss-Legendre points on biunit Hexahedron
PROGRAM main
USE easifemBase
IMPLICIT NONE
TYPE(QuadraturePoint_) :: obj
TYPE(ReferenceHexahedron_) :: refelem
INTEGER(I4B) :: order
refelem = ReferenceHexahedron(nsd=3_I4B)
CALL initiate(obj=obj, &
& refelem=refelem, &
& p=4, &
& q=3, &
& r=2, &
& quadratureType1=GaussLegendre, &
& quadratureType2=GaussLegendre, &
& quadratureType3=GaussLegendre &
& )
CALL display(mdencode(obj) , "")
END PROGRAM main
note
You can specify different order of accuracy (p,q,r) and different types of quadrature points (by using quadratureType1, quadratureType2, quadratureType3) in x, y, and z directions.
| x1 | -0.7746 | -0.7746 | -0.7746 | -0.7746 | 3.64292E-16 | 3.46945E-16 | 3.46945E-16 | 3.88578E-16 | 0.7746 | 0.7746 | 0.7746 | 0.7746 |
| x2 | -0.57735 | -0.57735 | 0.57735 | 0.57735 | -0.57735 | -0.57735 | 0.57735 | 0.57735 | -0.57735 | -0.57735 | 0.57735 | 0.57735 |
| x3 | -0.57735 | 0.57735 | -0.57735 | 0.57735 | -0.57735 | 0.57735 | -0.57735 | 0.57735 | -0.57735 | 0.57735 | -0.57735 | 0.57735 |
| w | 0.55556 | 0.55556 | 0.55556 | 0.55556 | 0.88889 | 0.88889 | 0.88889 | 0.88889 | 0.55556 | 0.55556 | 0.55556 | 0.55556 |