RecursiveNode1D

Returns the barycentric coordinates of recursive nodes on the line.

Interface

INTERFACE
  MODULE FUNCTION RecursiveNode1D(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
    CHARACTER(*), OPTIONAL, INTENT(IN) :: domain
      !! unit (0,1)
      !! biunit (-1, 1)
      !! equilateral
    REAL(DFP), ALLOCATABLE :: ans(:, :)
      !! barycentric coordinates, in xiJ format
      !! size(ans,1) = 2 corresponding to b0 and b1
      !! size(ans,2) total number of points
  END FUNCTION RecursiveNode1D
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 1.
• BIUNIT, biunit segment $[-1,1]$, in this case SIZE(ans, 1) is 1.
• BARYCENTRIC, in this case SIZE(ans,1) is 2.

️܀ Example 1

PROGRAM main
  use easifemBase
  real( DFP ), allocatable :: b( :, : )
  b = RecursiveNode1D(order=0, ipType=Equidistance)
  call Display(MdEncode(b), "b="//char_lf)
  b = RecursiveNode1D(order=1, ipType=Equidistance)
  call Display(MdEncode(b), "b="//char_lf)
  b = RecursiveNode1D(order=2, ipType=Equidistance)
  call Display(MdEncode(b), "b="//char_lf)
  b = RecursiveNode1D(order=3, ipType=Equidistance)
  call Display(MdEncode(b), "b="//char_lf)
END PROGRAM main

Order 0

b =

0.5
0.5

Order 1

b =

0	1
1	0

Order 2

b =

0	0.5	1
1	0.5	0

Order 3

b =

0	0.33333	0.66667	1
1	0.66667	0.33333	0

Example 2

This example is similar to example 1, but in this case we test domain option.

PROGRAM main
  use easifemBase
  real( DFP ), allocatable :: b( :, : )
  b = RecursiveNode1D(order=3, ipType=Equidistance, &
    & domain="Unit")
  call Display(b, "b Unit=")
  b = RecursiveNode1D(order=3, ipType=Equidistance, &
    & domain="Biunit")
  call Display(b, "b BiUnit=")
  b = RecursiveNode1D(order=3, ipType=Equidistance, &
    & domain="Barycentric")
  call Display(b, "b Barycentric=")
  b = RecursiveNode1D(order=3, ipType=Equidistance, &
    & domain="Equilateral")
  call Display(b, "b Equilateral=")
END PROGRAM main

See results

              b Unit=
----------------------------------
0.00000  0.33333  0.66667  1.00000

              b BiUnit=
--------------------------------------
-1.00000  -0.33333   0.33333   1.00000

          b Barycentric=
----------------------------------
0.00000  0.33333  0.66667  1.00000
1.00000  0.66667  0.33333  0.00000

            b Equilateral=
--------------------------------------
-1.00000  -0.33333   0.33333   1.00000

Example 3

• In this example ipType=GaussLegendreLobatto

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

  b = RecursiveNode1D(order=0, ipType=ipType)
  call Display(MdEncode(b), "b="//char_lf)

b=

0.5
0.5

  b = RecursiveNode1D(order=1, ipType=ipType)
  call Display(MdEncode(b), "b="//char_lf)

b=

0	1
1	0

  b = RecursiveNode1D(order=2, ipType=ipType)
  call Display(MdEncode(b), "b="//char_lf)

b=

1.11022E-16	0.5	1
1	0.5	1.11022E-16

  b = RecursiveNode1D(order=4, ipType=ipType)
  call Display(MdEncode(b), "b="//char_lf)

b=

-1.11022E-16	0.17267	0.5	0.82733	1
1	0.82733	0.5	0.17267	-1.11022E-16

END PROGRAM main

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