RecursiveNode2D

Returns the barycentric coordinates of recursive nodes on the triangle.

Interface

INTERFACE
  MODULE FUNCTION RecursiveNode2D(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) = 3 corresponding to b0, b1, b2
      !! size(ans,2) total number of points
    CHARACTER(*), OPTIONAL, INTENT(IN) :: domain
      !! unit
      !! Biunit
      !! Equilateral
  END FUNCTION RecursiveNode2D
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 2.
• BIUNIT, biunit segment $[-1,1]$, in this case SIZE(ans, 1) is 2.
• BARYCENTRIC, in this case SIZE(ans,1) is 3. This is also the default value.

Examples

️܀ Example 1

• In this example ipType=Equidistance

PROGRAM main
use easifemBase
real( DFP ), allocatable :: b( :, : )
integer(i4b) :: iptype = Equidistance

  b = RecursiveNode2D(order=0, ipType=ipType)
  call Display(MdEncode(b), "b="//char_lf)

b=

0.33333
0.33333
0.33333

b = RecursiveNode2D(order=1, ipType=ipType)
call Display(MdEncode(b), "b="//char_lf)

b=

0	0	1
0	1	0
1	0	0

b = RecursiveNode2D(order=2, ipType=ipType)
call Display(MdEncode(b), "b="//char_lf)

b=

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

b = RecursiveNode2D(order=3, ipType=ipType)
call Display(MdEncode(transpose(b)), "b=")

b=

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

END PROGRAM main

Example 2

This example is similar to example 2, but in this case we test domain option.

PROGRAM main
use easifemBase
real( DFP ), allocatable :: b( :, : )
  b = RecursiveNode2D(order=3, ipType=Equidistance, domain="Unit")
  call Display(MdEncode(transpose(b)), "b=")

b=

x1	x2
0	0
0	0.33333
0	0.66667
0	1
0.33333	0
0.33333	0.33333
0.33333	0.66667
0.66667	0
0.66667	0.33333
1	0

b = RecursiveNode2D(order=3, ipType=Equidistance, domain="biunit")
call Display(MdEncode(transpose(b)), "b=")

b=

x1	x2
-1	-1
-1	-0.33333
-1	0.33333
-1	1
-0.33333	-1
-0.33333	-0.33333
-0.33333	0.33333
0.33333	-1
0.33333	-0.33333
1	-1

b = RecursiveNode2D(order=3, ipType=Equidistance, domain="barycentric")
call Display(MdEncode(transpose(b)), "b=")

b=

b0	b1	b2
0	0	1
0	0.33333	0.66667
0	0.66667	0.33333
0	1	0
0.33333	0	0.66667
0.33333	0.33333	0.33333
0.33333	0.66667	0
0.66667	0	0.33333
0.66667	0.33333	0
1	0	0

b = RecursiveNode2D(order=3, ipType=Equidistance, domain="Equilateral")
call Display(MdEncode(transpose(b)), "b=")

b=

x1	x2
-1	-0.57735
-0.66667	9.61481E-17
-0.33333	0.57735
1.11022E-16	1.1547
-0.33333	-0.57735
0	0
0.33333	0.57735
0.33333	-0.57735
0.66667	0
1	-0.57735

END PROGRAM main

• In this example ipType=GaussLegendreLobatto

PROGRAM main
use easifemBase
real( DFP ), allocatable :: b( :, : )
integer(i4b) :: iptype = GaussLegendreLobatto

b = RecursiveNode2D(order=0, ipType=ipType)
call Display(MdEncode(b), "b="//char_lf)

b=

0.33333
0.33333
0.33333

b = RecursiveNode2D(order=1, ipType=ipType)
call Display(MdEncode(b), "b="//char_lf)

b=

0	0	1
0	1	0
1	0	0

b = RecursiveNode2D(order=2, ipType=ipType)
call Display(MdEncode(b), "b="//char_lf)

b=

8.32667E-17	0	8.32667E-17	0.5	0.5	1
8.32667E-17	0.5	1	0	0.5	8.32667E-17
1	0.5	8.32667E-17	0.5	0	8.32667E-17

b = RecursiveNode2D(order=3, ipType=ipType)
call Display(MdEncode(transpose(b)), "b=")

b=

-8.32667E-17	-8.32667E-17	1
4.01682E-17	0.27639	0.72361
4.01682E-17	0.72361	0.27639
-8.32667E-17	1	-8.32667E-17
0.27639	4.01682E-17	0.72361
0.33333	0.33333	0.33333
0.27639	0.72361	4.01682E-17
0.72361	4.01682E-17	0.27639
0.72361	0.27639	4.01682E-17
1	-8.32667E-17	-8.32667E-17

END PROGRAM main

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