BarycentricEdgeBasis

Returns the edge basis functions on reference Triangle.

Interface

܀ Interface

INTERFACE
  MODULE PURE FUNCTION BarycentricEdgeBasis_Triangle(pe1, pe2, pe3, lambda) &
    & RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: pe1
    !! order on  edge (e1)
    INTEGER(I4B), INTENT(IN) :: pe2
    !! order on edge (e2)
    INTEGER(I4B), INTENT(IN) :: pe3
    !! order on edge (e3)
    REAL(DFP), INTENT(IN) :: lambda(:, :)
    !! point of evaluation in terms of barycentric coordinates
    !! Number of rows in lambda is equal to three.
    REAL(DFP) :: ans(SIZE(lambda, 2), pe1 + pe2 + pe3 - 3)
  END FUNCTION BarycentricEdgeBasis_Triangle
END INTERFACE

️܀ See example

program main
  use easifembase
  use easifemClasses
  implicit none
  real(dfp), allocatable :: xij(:,:), avec(:), lambda(:, :)
  integer(i4b) :: ii, jj, cnt, n

  n = 51
  call reallocate(avec, n)
  call reallocate(xij, 2, int((n+1)*(n+2)/2))
  avec= linspace(0.0_DFP, 1.0_DFP, n)
  cnt=0
  do ii = 1, n
    do jj = 1, n-ii+1
      cnt=cnt+1
      xij(1,cnt) = avec(ii)
      xij(2,cnt) = avec(jj)
    end do
  end do

  lambda = BarycentricCoordTriangle(xij, "UNIT")

  BLOCK
    real(dfp), allocatable :: ans(:,:)
    integer(i4b) :: ii, order, pe1, pe2, pe3
    type( VTKPlot_ ) :: aplot
    character(len=*), parameter :: fname="./results/"
    !!
    order=4
    pe1=order; pe2 = order; pe3 = order
    !!
    ans = BarycentricEdgeBasis_Triangle(&
      & pe1=pe1, pe2=pe2, pe3=pe3 , &
      & lambda=lambda )
    !!
    do ii  = 1, size(ans,2)
      call aplot%scatter3D(x=xij(1,:), y=xij(2, :), z=ans(:,ii), &
        & filename=fname//"PVertexBary( order=" // tostring(order) // &
          & ", pe1="//tostring(pe1) // &
          & ", pe2="//tostring(pe2) // &
          & ", pe3="//tostring(pe3) // &
          & " )" // tostring(ii) // &
          & " )" // tostring(ii) // &
          & ".vtp", &
        & label="P")
    end do
    !!
  END BLOCK
end program main

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