BarycentricVertexBasis

Returns the vertex basis functions on reference Triangle.

Interface

INTERFACE
  MODULE PURE FUNCTION BarycentricVertexBasis_Triangle(lambda) &
    & RESULT(ans)
    REAL(DFP), INTENT(IN) :: lambda(:, :)
    !! point of evaluation in terms of barycentrix coords
    REAL(DFP) :: ans(SIZE(lambda, 2), 3)
    !! ans(:,v1) basis function of vertex v1 at all points
  END FUNCTION BarycentricVertexBasis_Triangle
END INTERFACE

lambda

Barycentric coordinates. The vertex basis function will be evaluated here. The number of rows in lambda is 3 and the number of columns is the number of points. The three rows of lambda dentoe the $\lambda_{i=1,2,3}$ .

ans

The number of rows in ans is equal to the number of points of evaluation. The number of columns is 3. The three columns of ans denote the basis functions of vertex $v=1,2,3$ at all points.

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 = BarycentricVertexBasis_Triangle(&
      & lambda=lambda )
    !!
    do ii  = 1, size(ans,2)
      call aplot%scatter3D(x=xij(1,:), y=xij(2, :), z=ans(:,ii), &
        & filename=fname//"PVertexBary-" // tostring(ii) // &
        & tostring(ii) //".vtp", &
        & label="P")
    end do
    !!
  END BLOCK
end program main

Interface​

Interface