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Lagrange2D example 1

This example shows the usage of [[Lagrange2D_]] class.

Modules and classes​

  • [[Lagrange2D_]]

Usage​

PROGRAM main
use easifemBase
use easifemClasses
implicit none
type(Lagrange2D_) :: f1
type(Lagrange2D_), allocatable :: f(:)
real(dfp), allocatable :: x( :, : )
integer(i4b) :: ii, order, n

!!! note "order=1"

  order=1
  x = EquidistancePoint(order=order, elemType=Triangle)
  f1=Lagrange2D( order=order, i=1, x=x, name1="x", name2="y", elemType=Triangle )
  call f1%display( 'f(x)=' )
  f1=Lagrange2D( order=order, i=2, x=x, name1="x", name2="y", elemType=Triangle )
  call f1%display( 'f(x)=' )
  f1=Lagrange2D( order=order, i=3, x=x, name1="x", name2="y", elemType=Triangle )
  call f1%display( 'f(x)=' )

!!! example "result"

f(x)=+1−1y1−1x1f(x)=+1x1f(x)=+1y1f(x)=+1-1 y^1-1x^1 \\ f(x)=+1x^1 \\ f(x)=+1 y^1

!!! note "order=2"

  order = 2_I4B
  x = EquidistancePoint(order=order, elemType=Triangle)
  n = LagrangeDOF( order=order, elemType=Triangle )
  allocate( f(n) )
  do ii = 1, n
    f(ii) = Lagrange2D(i=ii, x=x, order=order, &
      & name1="x", name2="y", elemType=Triangle)
    call f(ii)%display("l_{"//tostring(ii)//"}=")
  end do
  deallocate(f)

!!! example "result"

l1=+1−3y1+2y2+4x1y1−3x1+2x2l2=−1x1+2x2l3=−1y1+2y2l4=−4x1y1+4x1−4x2l5=+4x1y1l6=+4y1−4y2−4x1y1l_{1}=+1-3 y^1+2 y^2+4x^1 y^1-3x^1+2x^2 \\ l_{2}=-1x^1+2x^2 \\ l_{3}=-1 y^1+2 y^2 \\ l_{4}=-4x^1 y^1+4x^1-4x^2 \\ l_{5}=+4x^1 y^1 \\ l_{6}=+4 y^1-4 y^2-4x^1 y^1

!!! note "order=3"

  order = 3_I4B
  x = EquidistancePoint(order=order, elemType=Triangle)
  n = LagrangeDOF( order=order, elemType=Triangle )
  allocate( f(n) )
  do ii = 1, n
    f(ii) = Lagrange2D(i=ii, x=x, order=order, &
      & name1="x", name2="y", elemType=Triangle)
    call f(ii)%display("l_{"//tostring(ii)//"}=")
  end do
  deallocate(f)

!!! example "result"

l1=+1+9y2−5.5y1−4.5y3−13.5x1y2+18x1y1−5.5x1+9x2−13.5x2y1−4.5x3l2=+1x1−4.5x2+4.5x3l3=−4.5y2+1y1+4.5y3l4=+13.5x1y2−22.5x1y1+9x1−22.5x2+27x2y1+13.5x3l5=+4.5x1y1−4.5x1+18x2−13.5x2y1−13.5x3l6=−4.5x1y1+13.5x2y1l7=+13.5x1y2−4.5x1y1l8=+18y2−4.5y1−13.5y3−13.5x1y2+4.5x1y1l9=−22.5y2+9y1+13.5y3+27x1y2−22.5x1y1+13.5x2y1l10=−27x1y2+27x1y1−27x2y1l_{1}=+1+9 y^2-5.5 y^1-4.5 y^3-13.5x^1 y^2+18x^1 y^1-5.5x^1+9x^2-13.5x^2 y^1-4.5x^3 \\ l_{2}=+1x^1-4.5x^2+4.5x^3 \\ l_{3}=-4.5 y^2+1 y^1+4.5 y^3 \\ l_{4}=+13.5x^1 y^2-22.5x^1 y^1+9x^1-22.5x^2+27x^2 y^1+13.5x^3 \\ l_{5}=+4.5x^1 y^1-4.5x^1+18x^2-13.5x^2 y^1-13.5x^3 \\ l_{6}=-4.5x^1 y^1+13.5x^2 y^1 \\ l_{7}=+13.5x^1 y^2-4.5x^1 y^1 \\ l_{8}=+18 y^2-4.5 y^1-13.5 y^3-13.5x^1 y^2+4.5x^1 y^1 \\ l_{9}=-22.5 y^2+9 y^1+13.5 y^3+27x^1 y^2-22.5x^1 y^1+13.5x^2 y^1 \\ l_{10}=-27x^1 y^2+27x^1 y^1-27x^2 y^1 
END PROGRAM main