RecursiveNode3D

Returns the barycentric coordinates of recursive nodes on a tetrahedron.

Interface

INTERFACE
  MODULE FUNCTION RecursiveNode3D(order, ipType, &
    & domain) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: order
      !! order >= 0
    INTEGER(I4B), INTENT(IN) :: ipType
      !! interpolation point type
      !! Equidistance
      !! LobattoGaussJacobi
      !! LobattoGaussChebyshev
      !! LobattoGaussGegenbauer
      !! GaussJacobi
      !! GaussChebyshev
      !! GaussGegenbauer
    REAL(DFP), ALLOCATABLE :: ans(:, :)
      !! barycentric coordinates, in xiJ format
      !! size(ans,1) = 4 corresponding to b0, b1, b2, b3
      !! size(ans,2) total number of points
    CHARACTER(*), OPTIONAL, INTENT(IN) :: domain
      !! unit
      !! Biunit
      !! Equilateral
  END FUNCTION RecursiveNode3D
END INTERFACE

order

Order of element.

ipType

Interpolation point type. Following values are allowed.

• Equidistance
• GaussJacobi
• GaussJacobiLobatto
• GaussChebyshev
• GaussChebyshevLobatto
• GaussLegendre
• GaussLegendreLobatto
• GaussUltraspherical
• GaussUltrasphericalLobatto

domain

It specifies the domain of the element. It is an optional argument. It can take following values:

• UNIT, unit segment $[0,1]$, in this case SIZE(ans,1) is 3.
• BIUNIT, biunit segment $[-1,1]$, in this case SIZE(ans, 1) is 3.
• BARYCENTRIC, in this case SIZE(ans,1) is 4. This is also the default value.

Examples

️܀ Example

PROGRAM main
use easifemBase
real( DFP ), allocatable :: b( :, : )

  b = RecursiveNode3D(order=0, ipType=Equidistance)
  call Display(b, "b=")

  b = RecursiveNode3D(order=1, ipType=Equidistance)
  call Display(MdEncode(b), "b=")

b=

0	0	0	1
0	0	1	0
0	1	0	0
1	0	0	0

  b = RecursiveNode3D(order=2, ipType=Equidistance)
  call Display(MdEncode(b), "b=")

b=

0	0	0	0	0	0	0.5	0.5	0.5	1
0	0	0	0.5	0.5	1	0	0	0.5	0
0	0.5	1	0	0.5	0	0	0.5	0	0
1	0.5	0	0.5	0	0	0.5	0	0	0

  b = RecursiveNode3D(order=3, ipType=Equidistance)
  call Display(MdEncode(transpose(b)), "b=")

b=

0	0	0	1
0	0	0.33333	0.66667
0	0	0.66667	0.33333
0	0	1	0
0	0.33333	0	0.66667
0	0.33333	0.33333	0.33333
0	0.33333	0.66667	0
0	0.66667	0	0.33333
0	0.66667	0.33333	0
0	1	0	0
0.33333	0	0	0.66667
0.33333	0	0.33333	0.33333
0.33333	0	0.66667	0
0.33333	0.33333	0	0.33333
0.33333	0.33333	0.33333	0
0.33333	0.66667	0	0
0.66667	0	0	0.33333
0.66667	0	0.33333	0
0.66667	0.33333	0	0
1	0	0	0

END PROGRAM main

Example 2

This example is similar to example 3 but in this case we test domain.

PROGRAM main
use easifemBase
real( DFP ), allocatable :: b( :, : )

  b = RecursiveNode3D(order=2, ipType=Equidistance, &
    & domain="unit")
  call Display(MdEncode(transpose(b)), "b=")

b=

x1	x2	x3
0	0	0
0	0	0.5
0	0	1
0	0.5	0
0	0.5	0.5
0	1	0
0.5	0	0
0.5	0	0.5
0.5	0.5	0
1	0	0

  b = RecursiveNode3D(order=2, ipType=Equidistance, &
    & domain="biunit")
  call Display(MdEncode(transpose(b)), "b=")

b=

x1	x2	x3
-1	-1	-1
-1	-1	0
-1	-1	1
-1	0	-1
-1	0	0
-1	1	-1
0	-1	-1
0	-1	0
0	0	-1
1	-1	-1

  b = RecursiveNode3D(order=2, ipType=Equidistance, &
    & domain="barycentric")
  call Display(MdEncode(transpose(b)), "b=")

b=

b0	b1	b2	b3
0	0	0	1
0	0	0.5	0.5
0	0	1	0
0	0.5	0	0.5
0	0.5	0.5	0
0	1	0	0
0.5	0	0	0.5
0.5	0	0.5	0
0.5	0.5	0	0
1	0	0	0

!!! note "Equilateral"

  b = RecursiveNode3D(order=2, ipType=Equidistance, &
    & domain="Equilateral")
  call Display(MdEncode(transpose(b)), "b=")

b=

x1	x2	x3
-1	-0.57735	-0.40825
-0.5	-0.28868	0.40825
0	0	1.2247
-0.5	0.28868	-0.40825
-5.55112E-17	0.57735	0.40825
0	1.1547	-0.40825
5.55112E-17	-0.57735	-0.40825
0.5	-0.28868	0.40825
0.5	0.28868	-0.40825
1	-0.57735	-0.40825

END PROGRAM main

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