Detailed Description

Definition of 1D, 2D, and 3D quadrature rules.

Symmetric quadrature rules defined by Zhang et al.

"Zhang, L., Cui, T., & Liu, H. (January 01, 2009) A set of symmetric quadrature rules on triangles and tetrahedra. Journal of Computational Mathematics, 27, 1, 89-96."

Authors: Chris Hansen

Date: August 2011

Functions/Subroutines
type(oft_quad_type) function	quad_1d_p1 ()
	Set 1D quadrature rule for 1st order.

type(oft_quad_type) function	quad_1d_p3 ()
	Set 1D quadrature rule for 3rd order.

type(oft_quad_type) function	quad_1d_p5 ()
	Set 1D quadrature rule for 5th order.

type(oft_quad_type) function	quad_1d_p7 ()
	Set 1D quadrature rule for 7th order.

type(oft_quad_type) function	quad_2d_p1 ()
	Set 2D quadrature rule for 1st order.

type(oft_quad_type) function	quad_2d_p10 ()
	Set 2D quadrature rule for 10th order.

type(oft_quad_type) function	quad_2d_p11 ()
	Set 2D quadrature rule for 11th order.

type(oft_quad_type) function	quad_2d_p12 ()
	Set 2D quadrature rule for 12th order.

type(oft_quad_type) function	quad_2d_p14 ()
	Set 2D quadrature rule for 14th order.

type(oft_quad_type) function	quad_2d_p16 ()
	Set 2D quadrature rule for 16th order.

type(oft_quad_type) function	quad_2d_p18 ()
	Set 2D quadrature rule for 18th order.

type(oft_quad_type) function	quad_2d_p2 ()
	Set 2D quadrature rule for 2nd order.

type(oft_quad_type) function	quad_2d_p3 ()
	Set 2D quadrature rule for 3rd order.

type(oft_quad_type) function	quad_2d_p4 ()
	Set 2D quadrature rule for 4th order.

type(oft_quad_type) function	quad_2d_p5 ()
	Set 2D quadrature rule for 5th order.

type(oft_quad_type) function	quad_2d_p6 ()
	Set 2D quadrature rule for 6th order.

type(oft_quad_type) function	quad_2d_p7 ()
	Set 2D quadrature rule for 7th order.

type(oft_quad_type) function	quad_2d_p8 ()
	Set 2D quadrature rule for 8th order.

type(oft_quad_type) function	quad_2d_p9 ()
	Set 2D quadrature rule for 9th order.

type(oft_quad_type) function	quad_3d_p1 ()
	Set 3D quadrature rule for 1st order.

type(oft_quad_type) function	quad_3d_p10 ()
	Set 3D quadrature rule for 10th order.

type(oft_quad_type) function	quad_3d_p11 ()
	Set 3D quadrature rule for 11th order.

type(oft_quad_type) function	quad_3d_p2 ()
	Set 3D quadrature rule for 2nd order.

type(oft_quad_type) function	quad_3d_p3 ()
	Set 3D quadrature rule for 3rd order.

type(oft_quad_type) function	quad_3d_p4 ()
	Set 3D quadrature rule for 4th order.

type(oft_quad_type) function	quad_3d_p5 ()
	Set 3D quadrature rule for 5th order.

type(oft_quad_type) function	quad_3d_p6 ()
	Set 3D quadrature rule for 6th order.

type(oft_quad_type) function	quad_3d_p7 ()
	Set 3D quadrature rule for 7th order.

type(oft_quad_type) function	quad_3d_p8 ()
	Set 3D quadrature rule for 8th order.

type(oft_quad_type) function	quad_3d_p9 ()
	Set 3D quadrature rule for 9th order.

subroutine	quad_add_p21 (wt, i, quad)
	Add points to 2D quadrature rule of the form (1/3,1/3,1/3)

subroutine	quad_add_p22 (wt, a, i, quad)
	Add points to 2D quadrature rule of the form (a,a,1-2*a)

subroutine	quad_add_p23 (wt, a, b, i, quad)
	Add points to 2D quadrature rule of the form (a,b,1-a-b)

real(r8) function, dimension(2)	quad_p11 ()
	Set 1D points to (1/2,1/2)

real(r8) function, dimension(2, 2)	quad_p12 (a)
	Permute 1D points of the form (a,1-a)

real(r8) function, dimension(4, 1)	quad_p31 ()
	Set 3D points to (1/4,1/4,1/4,1/4)

real(r8) function, dimension(4, 4)	quad_p32 (a)
	Permute 3D points of the form (a,a,a,1-3*a)

real(r8) function, dimension(4, 6)	quad_p33 (a)
	Permute 3D points of the form (a,a,1/2-a,1/2-a)

real(r8) function, dimension(4, 12)	quad_p34 (a, b)
	Permute 3D points of the form (a,a,b,1-2*a-b)

real(r8) function, dimension(4, 24)	quad_p35 (a, b, c)
	Permute 3D points of the form (a,b,c,1-a-b-c)

subroutine, public	set_quad_1d (quad, order)
	Get 1D quadrature rule for specified order (max = 7)

subroutine, public	set_quad_2d (quad, order)
	Get 2D quadrature rule for specified order (max = 11)

subroutine, public	set_quad_3d (quad, order)
	Get 3D quadrature rule for specified order (max = 11)

Function/Subroutine Documentation

◆ quad_1d_p1()

type(oft_quad_type) function quad_1d_p1

private

Set 1D quadrature rule for 1st order.

Returns: Quadrature rule

◆ quad_1d_p3()

type(oft_quad_type) function quad_1d_p3

private

Set 1D quadrature rule for 3rd order.

Returns: Quadrature rule

◆ quad_1d_p5()

type(oft_quad_type) function quad_1d_p5

private

Set 1D quadrature rule for 5th order.

Returns: Quadrature rule

◆ quad_1d_p7()

type(oft_quad_type) function quad_1d_p7

private

Set 1D quadrature rule for 7th order.

Returns: Quadrature rule

◆ quad_2d_p1()

type(oft_quad_type) function quad_2d_p1

private

Set 2D quadrature rule for 1st order.

Returns: Quadrature rule

◆ quad_2d_p10()

type(oft_quad_type) function quad_2d_p10

private

Set 2D quadrature rule for 10th order.

Returns: Quadrature rule

◆ quad_2d_p11()

type(oft_quad_type) function quad_2d_p11

private

Set 2D quadrature rule for 11th order.

Returns: Quadrature rule

◆ quad_2d_p12()

type(oft_quad_type) function quad_2d_p12

private

Set 2D quadrature rule for 12th order.

Returns: Quadrature rule

◆ quad_2d_p14()

type(oft_quad_type) function quad_2d_p14

private

Set 2D quadrature rule for 14th order.

Returns: Quadrature rule

◆ quad_2d_p16()

type(oft_quad_type) function quad_2d_p16

private

Set 2D quadrature rule for 16th order.

Returns: Quadrature rule

◆ quad_2d_p18()

type(oft_quad_type) function quad_2d_p18

private

Set 2D quadrature rule for 18th order.

Returns: Quadrature rule

◆ quad_2d_p2()

type(oft_quad_type) function quad_2d_p2

private

Set 2D quadrature rule for 2nd order.

Returns: Quadrature rule

◆ quad_2d_p3()

type(oft_quad_type) function quad_2d_p3

private

Set 2D quadrature rule for 3rd order.

Returns: Quadrature rule

◆ quad_2d_p4()

type(oft_quad_type) function quad_2d_p4

private

Set 2D quadrature rule for 4th order.

Returns: Quadrature rule

◆ quad_2d_p5()

type(oft_quad_type) function quad_2d_p5

private

Set 2D quadrature rule for 5th order.

Returns: Quadrature rule

◆ quad_2d_p6()

type(oft_quad_type) function quad_2d_p6

private

Set 2D quadrature rule for 6th order.

Returns: Quadrature rule

◆ quad_2d_p7()

type(oft_quad_type) function quad_2d_p7

private

Set 2D quadrature rule for 7th order.

Returns: Quadrature rule

◆ quad_2d_p8()

type(oft_quad_type) function quad_2d_p8

private

Set 2D quadrature rule for 8th order.

Returns: Quadrature rule

◆ quad_2d_p9()

type(oft_quad_type) function quad_2d_p9

private

Set 2D quadrature rule for 9th order.

Returns: Quadrature rule

◆ quad_3d_p1()

type(oft_quad_type) function quad_3d_p1

private

Set 3D quadrature rule for 1st order.

Returns: Quadrature rule

◆ quad_3d_p10()

type(oft_quad_type) function quad_3d_p10

private

Set 3D quadrature rule for 10th order.

Returns: Quadrature rule

◆ quad_3d_p11()

type(oft_quad_type) function quad_3d_p11

private

Set 3D quadrature rule for 11th order.

Returns: Quadrature rule

◆ quad_3d_p2()

type(oft_quad_type) function quad_3d_p2

private

Set 3D quadrature rule for 2nd order.

Returns: Quadrature rule

◆ quad_3d_p3()

type(oft_quad_type) function quad_3d_p3

private

Set 3D quadrature rule for 3rd order.

Returns: Quadrature rule

◆ quad_3d_p4()

type(oft_quad_type) function quad_3d_p4

private

Set 3D quadrature rule for 4th order.

Returns: Quadrature rule

◆ quad_3d_p5()

type(oft_quad_type) function quad_3d_p5

private

Set 3D quadrature rule for 5th order.

Returns: Quadrature rule

◆ quad_3d_p6()

type(oft_quad_type) function quad_3d_p6

private

Set 3D quadrature rule for 6th order.

Returns: Quadrature rule

◆ quad_3d_p7()

type(oft_quad_type) function quad_3d_p7

private

Set 3D quadrature rule for 7th order.

Returns: Quadrature rule

◆ quad_3d_p8()

type(oft_quad_type) function quad_3d_p8

private

Set 3D quadrature rule for 8th order.

Returns: Quadrature rule

◆ quad_3d_p9()

type(oft_quad_type) function quad_3d_p9

private

Set 3D quadrature rule for 9th order.

Returns: Quadrature rule

◆ quad_add_p21()

subroutine quad_add_p21	(	real(8), intent(in)	wt,
		integer(4), intent(inout)	i,
		type(oft_quad_type), intent(inout)	quad
	)

private

Add points to 2D quadrature rule of the form (1/3,1/3,1/3)

Parameters

[in]	wt	Weight value for points
[in,out]	i	Starting index to add points
[in,out]	quad	Quadrature rule

◆ quad_add_p22()

subroutine quad_add_p22	(	real(8), intent(in)	wt,
		real(8), intent(in)	a,
		integer(4), intent(inout)	i,
		type(oft_quad_type), intent(inout)	quad
	)

private

Add points to 2D quadrature rule of the form (a,a,1-2*a)

Parameters

[in]	wt	Weight value for points
[in]	a	Parameter 1
[in,out]	i	Starting index to add points
[in,out]	quad	Quadrature rule

◆ quad_add_p23()

subroutine quad_add_p23	(	real(8), intent(in)	wt,
		real(8), intent(in)	a,
		real(8), intent(in)	b,
		integer(4), intent(inout)	i,
		type(oft_quad_type), intent(inout)	quad
	)

private

Add points to 2D quadrature rule of the form (a,b,1-a-b)

Parameters

[in]	wt	Weight value for points
[in]	a	Parameter 1
[in]	b	Parameter 2
[in,out]	i	Starting index to add points
[in,out]	quad	Quadrature rule

◆ quad_p11()

real(r8) function, dimension(2) quad_p11

private

Set 1D points to (1/2,1/2)

Returns: Evaluation points

◆ quad_p12()

real(r8) function, dimension(2,2) quad_p12 ( real(r8), intent(in) a )

private

Permute 1D points of the form (a,1-a)

Parameters

[in] a Parameter 1

Returns: Evaluation points from permutation [2,2]

◆ quad_p31()

real(r8) function, dimension(4,1) quad_p31

private

Set 3D points to (1/4,1/4,1/4,1/4)

Returns: Evaluation points

◆ quad_p32()

real(r8) function, dimension(4,4) quad_p32 ( real(r8), intent(in) a )

private

Permute 3D points of the form (a,a,a,1-3*a)

Parameters

[in] a Parameter 1

Returns: Evaluation points from permutation

◆ quad_p33()

real(r8) function, dimension(4,6) quad_p33 ( real(r8), intent(in) a )

private

Permute 3D points of the form (a,a,1/2-a,1/2-a)

param[in] a Parameter 1

Returns: Evaluation points from permutation

Parameters

[in] a Parameter 1

Returns: Evaluation points from permutation

◆ quad_p34()

real(r8) function, dimension(4,12) quad_p34	(	real(r8), intent(in)	a,
		real(r8), intent(in)	b
	)

private

Permute 3D points of the form (a,a,b,1-2*a-b)

Parameters

[in]	a	Parameter 1
[in]	b	Parameter 2

Returns: Evaluation points from permutation

◆ quad_p35()

real(r8) function, dimension(4,24) quad_p35	(	real(r8), intent(in)	a,
		real(r8), intent(in)	b,
		real(r8), intent(in)	c
	)

private

Permute 3D points of the form (a,b,c,1-a-b-c)

Parameters

[in]	a	Parameter 1
[in]	b	Parameter 2
[in]	c	Parameter 3

Returns: Evaluation points from permutation

◆ set_quad_1d()

subroutine, public set_quad_1d	(	type(oft_quad_type), intent(inout)	quad,
		integer(i4), intent(in)	order
	)

Get 1D quadrature rule for specified order (max = 7)

Parameters

[in,out]	quad	Quadrature rule
[in]	order	Desired quadrature order

◆ set_quad_2d()

subroutine, public set_quad_2d	(	type(oft_quad_type), intent(inout)	quad,
		integer(i4), intent(in)	order
	)

Get 2D quadrature rule for specified order (max = 11)

Parameters

[in,out]	quad	Quadrature rule
[in]	order	Desired quadrature order

◆ set_quad_3d()

subroutine, public set_quad_3d	(	type(oft_quad_type), intent(inout)	quad,
		integer(i4), intent(in)	order
	)

Get 3D quadrature rule for specified order (max = 11)

Parameters

[in,out]	quad	Quadrature rule
[in]	order	Desired quadrature order

Detailed Description

Functions/Subroutines

Function/Subroutine Documentation

◆ quad_1d_p1()

◆ quad_1d_p3()

◆ quad_1d_p5()

◆ quad_1d_p7()

◆ quad_2d_p1()

◆ quad_2d_p10()

◆ quad_2d_p11()

◆ quad_2d_p12()

◆ quad_2d_p14()

◆ quad_2d_p16()

◆ quad_2d_p18()

◆ quad_2d_p2()

◆ quad_2d_p3()

◆ quad_2d_p4()

◆ quad_2d_p5()

◆ quad_2d_p6()

◆ quad_2d_p7()

◆ quad_2d_p8()

◆ quad_2d_p9()

◆ quad_3d_p1()

◆ quad_3d_p10()

◆ quad_3d_p11()

◆ quad_3d_p2()

◆ quad_3d_p3()

◆ quad_3d_p4()

◆ quad_3d_p5()

◆ quad_3d_p6()

◆ quad_3d_p7()

◆ quad_3d_p8()

◆ quad_3d_p9()

◆ quad_add_p21()

◆ quad_add_p22()

◆ quad_add_p23()

◆ quad_p11()

◆ quad_p12()

◆ quad_p31()

◆ quad_p32()

◆ quad_p33()

◆ quad_p34()

◆ quad_p35()

◆ set_quad_1d()

◆ set_quad_2d()

◆ set_quad_3d()