oft_tet_quadrature Module Reference

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 11th order.
type(oft_quad_type) function	quad_2d_p14 ()
	Set 2D quadrature rule for 11th order.
type(oft_quad_type) function	quad_2d_p16 ()
	Set 2D quadrature rule for 11th order.
type(oft_quad_type) function	quad_2d_p18 ()
	Set 2D quadrature rule for 11th 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)
	Set 2D points to (1/3,1/3,1/3).
subroutine	quad_add_p22 (wt, a, i, quad)
	Permute 2D points of the form (a,a,1-2*a).
subroutine	quad_add_p23 (wt, a, b, i, quad)
	Permute 2D points 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(3)	quad_p21 ()
	Set 2D points to (1/3,1/3,1/3).
real(r8) function, dimension(3, 3)	quad_p22 (a)
	Permute 2D points of the form (a,a,1-2*a).
real(r8) function, dimension(3, 6)	quad_p23 (a, b)
	Permute 2D points of the form (a,b,1-a-b).
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.
subroutine, public	set_quad_2d (quad, order)
	Get 2D quadrature rule for specified order.
subroutine, public	set_quad_3d (quad, order)
	Get 3D quadrature rule for specified order.

Function/Subroutine Documentation

quad_1d_p1()

type(oft_quad_type) function quad_1d_p1

private

Set 1D quadrature rule for 1st order.

Returns

quad Quadrature rule

quad_1d_p3()

type(oft_quad_type) function quad_1d_p3

private

Set 1D quadrature rule for 3rd order.

Returns

quad Quadrature rule

quad_1d_p5()

type(oft_quad_type) function quad_1d_p5

private

Set 1D quadrature rule for 5th order.

Returns

quad Quadrature rule

quad_1d_p7()

type(oft_quad_type) function quad_1d_p7

private

Set 1D quadrature rule for 7th order.

Returns

quad Quadrature rule

quad_2d_p1()

type(oft_quad_type) function quad_2d_p1

private

Set 2D quadrature rule for 1st order.

Returns

quad Quadrature rule

quad_2d_p10()

type(oft_quad_type) function quad_2d_p10

private

Set 2D quadrature rule for 10th order.

Returns

quad Quadrature rule

quad_2d_p11()

type(oft_quad_type) function quad_2d_p11

private

Set 2D quadrature rule for 11th order.

Returns

quad Quadrature rule

quad_2d_p12()

type(oft_quad_type) function quad_2d_p12

private

Set 2D quadrature rule for 11th order.

Returns

quad Quadrature rule

quad_2d_p14()

type(oft_quad_type) function quad_2d_p14

private

Set 2D quadrature rule for 11th order.

Returns

quad Quadrature rule

quad_2d_p16()

type(oft_quad_type) function quad_2d_p16

private

Set 2D quadrature rule for 11th order.

Returns

quad Quadrature rule

quad_2d_p18()

type(oft_quad_type) function quad_2d_p18

private

Set 2D quadrature rule for 11th order.

Returns

quad Quadrature rule

quad_2d_p2()

type(oft_quad_type) function quad_2d_p2

private

Set 2D quadrature rule for 2nd order.

Returns

quad Quadrature rule

quad_2d_p3()

type(oft_quad_type) function quad_2d_p3

private

Set 2D quadrature rule for 3rd order.

Returns

quad Quadrature rule

quad_2d_p4()

type(oft_quad_type) function quad_2d_p4

private

Set 2D quadrature rule for 4th order.

Returns

quad Quadrature rule

quad_2d_p5()

type(oft_quad_type) function quad_2d_p5

private

Set 2D quadrature rule for 5th order.

Returns

quad Quadrature rule

quad_2d_p6()

type(oft_quad_type) function quad_2d_p6

private

Set 2D quadrature rule for 6th order.

Returns

quad Quadrature rule

quad_2d_p7()

type(oft_quad_type) function quad_2d_p7

private

Set 2D quadrature rule for 7th order.

Returns

quad Quadrature rule

quad_2d_p8()

type(oft_quad_type) function quad_2d_p8

private

Set 2D quadrature rule for 8th order.

Returns

quad Quadrature rule

quad_2d_p9()

type(oft_quad_type) function quad_2d_p9

private

Set 2D quadrature rule for 9th order.

Returns

quad Quadrature rule

quad_3d_p1()

type(oft_quad_type) function quad_3d_p1

private

Set 3D quadrature rule for 1st order.

Returns

quad Quadrature rule

quad_3d_p10()

type(oft_quad_type) function quad_3d_p10

private

Set 3D quadrature rule for 10th order.

Returns

quad Quadrature rule

quad_3d_p11()

type(oft_quad_type) function quad_3d_p11

private

Set 3D quadrature rule for 11th order.

Returns

quad Quadrature rule

quad_3d_p2()

type(oft_quad_type) function quad_3d_p2

private

Set 3D quadrature rule for 2nd order.

Returns

quad Quadrature rule

quad_3d_p3()

type(oft_quad_type) function quad_3d_p3

private

Set 3D quadrature rule for 3rd order.

Returns

quad Quadrature rule

quad_3d_p4()

type(oft_quad_type) function quad_3d_p4

private

Set 3D quadrature rule for 4th order.

Returns

quad Quadrature rule

quad_3d_p5()

type(oft_quad_type) function quad_3d_p5

private

Set 3D quadrature rule for 5th order.

Returns

quad Quadrature rule

quad_3d_p6()

type(oft_quad_type) function quad_3d_p6

private

Set 3D quadrature rule for 6th order.

Returns

quad Quadrature rule

quad_3d_p7()

type(oft_quad_type) function quad_3d_p7

private

Set 3D quadrature rule for 7th order.

Returns

quad Quadrature rule

quad_3d_p8()

type(oft_quad_type) function quad_3d_p8

private

Set 3D quadrature rule for 8th order.

Returns

quad Quadrature rule

quad_3d_p9()

type(oft_quad_type) function quad_3d_p9

private

Set 3D quadrature rule for 9th order.

Returns

quad 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

Set 2D points to (1/3,1/3,1/3).

Returns

Evaluation points

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

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

param[in] a Parameter 1

Returns

Evaluation points from permutation

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

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

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

Returns

Evaluation points from permutation

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).

param[in] a Parameter 1

Returns

Evaluation points from permutation

quad_p21()

real(r8) function, dimension(3) quad_p21

private

Set 2D points to (1/3,1/3,1/3).

Returns

Evaluation points

quad_p22()

real(r8) function, dimension(3,3) quad_p22 ( real(r8), intent(in)  a )

private

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

param[in] a Parameter 1

Returns

Evaluation points from permutation

quad_p23()

real(r8) function, dimension(3,6) quad_p23 ( real(r8), intent(in)  a, real(r8), intent(in)  b  )

private

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

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

Returns

Evaluation points from permutation

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).

param[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

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).

param[in] a Parameter 1 param[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).

param[in] a Parameter 1 param[in] b Parameter 2 param[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, intent(in)	order
	)

Get 1D quadrature rule for specified order.

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

Parameters

[in,out]	quad	Quadrature rule
[in]	order	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.

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

Parameters

[in,out]	quad	Quadrature rule
[in]	order	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.

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

Parameters

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