InterpolationPoint

Returns interpolation points for lagrange polynomials on hexahedron.

The interpolation points are always returned in "VEFC" format.

• Vertex
• Edge
• Facet
• Cell

Interface 1

܀ Interface

INTERFACE InterpolationPoint_Hexahedron
  MODULE FUNCTION InterpolationPoint_Hexahedron1(order, ipType, &
    & layout, xij) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: order
    INTEGER(I4B), INTENT(IN) :: ipType
    CHARACTER(*), INTENT(IN) :: layout
    REAL(DFP), OPTIONAL, INTENT(IN) :: xij(:, :)
    REAL(DFP), ALLOCATABLE :: ans(:, :)
  END FUNCTION InterpolationPoint_Hexahedron1
END INTERFACE InterpolationPoint_Hexahedron

️܀ Example 1

program main
  use easifembase
  implicit none
  integer( i4b ) :: i1, i2, order
  real( dfp ), allocatable :: x(:,:)
  type(string) :: astr
  order=1
  x = InterpolationPoint_Hexahedron( order=order, ipType=Equidistance, layout="VEFC" )
  astr = "| no | $x_1$ | $x_2$ | $x_3$ |" // char_lf
  astr = astr //  mdencode( arange(1.0_DFP, real(size(x, 2), dfp) ) .colconcat. TRANSPOSE(x))
  call display( astr%chars(), "xij (order="//tostring(order)//")=" // char_lf // char_lf )
end program main

See results

xij (order=1)=

no	$x_1$	$x_2$	$x_3$
1	-1	-1	-1
2	1	-1	-1
3	1	1	-1
4	-1	1	-1
5	-1	-1	1
6	1	-1	1
7	1	1	1
8	-1	1	1

Example 2

program main
  use easifembase
  implicit none
  integer( i4b ) :: i1, i2, order
  real( dfp ), allocatable :: x(:,:)
  type(string) :: astr
  order=2
  x = InterpolationPoint_Hexahedron( order=order, ipType=Equidistance, layout="VEFC" )
  astr = "| no | $x_1$ | $x_2$ | $x_3$ |" // char_lf
  astr = astr //  mdencode( arange(1.0_DFP, real(size(x, 2), dfp) ) .colconcat. TRANSPOSE(x))
  call display( astr%chars(), "xij (order="//tostring(order)//")=" // char_lf // char_lf )
end program main

See results

xij (order=2)=

no	$x_1$	$x_2$	$x_3$
1	-1	-1	-1
2	1	-1	-1
3	1	1	-1
4	-1	1	-1
5	-1	-1	1
6	1	-1	1
7	1	1	1
8	-1	1	1
9	0	-1	-1
10	-1	0	-1
11	-1	-1	0
12	1	0	-1
13	1	-1	0
14	0	1	-1
15	1	1	0
16	-1	1	0
17	0	-1	1
18	-1	0	1
19	1	0	1
20	0	1	1
21	0	0	-1
22	0	0	1
23	-1	0	0
24	1	0	0
25	0	1	0
26	0	-1	0
27	0	0	0

Example 3

PROGRAM main
USE easifembase
IMPLICIT NONE
INTEGER(i4b) :: i1, i2, order
REAL(dfp), ALLOCATABLE :: x(:, :)
TYPE(string) :: astr
order = 3
  x = InterpolationPoint_Hexahedron( order=order, ipType=Equidistance, layout="VEFC" )
astr = "| no | $x_1$ | $x_2$ | $x_3$ |"//char_lf
  astr = astr //  mdencode( arange(1.0_DFP, real(size(x, 2), dfp) ) .colconcat. TRANSPOSE(x))
  call display( astr%chars(), "xij (order="//tostring(order)//")=" // char_lf // char_lf )
END PROGRAM main

See results

xij (order=3)=

no	$x_1$	$x_2$	$x_3$
1	-1	-1	-1
2	1	-1	-1
3	1	1	-1
4	-1	1	-1
5	-1	-1	1
6	1	-1	1
7	1	1	1
8	-1	1	1
9	-0.33333	-1	-1
10	0.33333	-1	-1
11	-1	-0.33333	-1
12	-1	0.33333	-1
13	-1	-1	-0.33333
14	-1	-1	0.33333
15	1	-0.33333	-1
16	1	0.33333	-1
17	1	-1	-0.33333
18	1	-1	0.33333
19	0.33333	1	-1
20	-0.33333	1	-1
21	1	1	-0.33333
22	1	1	0.33333
23	-1	1	-0.33333
24	-1	1	0.33333
25	-0.33333	-1	1
26	0.33333	-1	1
27	-1	-0.33333	1
28	-1	0.33333	1
29	1	-0.33333	1
30	1	0.33333	1
31	0.33333	1	1
32	-0.33333	1	1
33	-0.33333	-0.33333	-1
34	-0.33333	0.33333	-1
35	0.33333	0.33333	-1
36	0.33333	-0.33333	-1
37	-0.33333	-0.33333	1
38	0.33333	-0.33333	1
39	0.33333	0.33333	1
40	-0.33333	0.33333	1
41	-1	-0.33333	0.33333
42	-1	-0.33333	-0.33333
43	-1	0.33333	-0.33333
44	-1	0.33333	0.33333
45	1	-0.33333	0.33333
46	1	0.33333	0.33333
47	1	0.33333	-0.33333
48	1	-0.33333	-0.33333
49	0.33333	1	-0.33333
50	-0.33333	1	-0.33333
51	-0.33333	1	0.33333
52	0.33333	1	0.33333
53	-0.33333	-1	-0.33333
54	0.33333	-1	-0.33333
55	0.33333	-1	0.33333
56	-0.33333	-1	0.33333
57	-0.33333	-0.33333	-0.33333
58	0.33333	-0.33333	-0.33333
59	0.33333	0.33333	-0.33333
60	-0.33333	0.33333	-0.33333
61	-0.33333	-0.33333	0.33333
62	0.33333	-0.33333	0.33333
63	0.33333	0.33333	0.33333
64	-0.33333	0.33333	0.33333

↢

Interface 2

INTERFACE InterpolationPoint_Hexahedron
  MODULE FUNCTION InterpolationPoint_Hexahedron2(p, q, r, ipType1, ipType2, &
    & ipType3, xij) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: p
    INTEGER(I4B), INTENT(IN) :: q
    INTEGER(I4B), INTENT(IN) :: r
    INTEGER(I4B), INTENT(IN) :: ipType1
    INTEGER(I4B), INTENT(IN) :: ipType2
    INTEGER(I4B), INTENT(IN) :: ipType3
    REAL(DFP), OPTIONAL, INTENT(IN) :: xij(:, :)
    REAL(DFP), ALLOCATABLE :: ans(:, :)
  END FUNCTION InterpolationPoint_Hexahedron2
END INTERFACE InterpolationPoint_Hexahedron