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{  POINT_LOAD.PDE

 

  This example demonstrates the use of the POINT LOAD bc.

  It is a modification of the example POLAR_COORDINATES.PDE.

}

 

title 'Point Load'

 

Variables

    u

 

definitions

    k = 1

    u0 = 1-r^2

    s = 4

    dr(f) = (x/r)*dx(f) + (y/r)*dy(f)     { functional definition of polar derivatives... }

    dphi(f) = (-y)*dx(f) + x*dy(f)     {... in cartesian coordinates }

    pload = staged (0, 2)

 

equations { equation expressed in polar coordinates }

          { (Multiplied by r^2 to clear the r=0 singularity) }

    U: r*dr(r*dr(u)) + dphi(dphi(u)) + r*r*s = 0

 

boundaries

    Region 1

      start(0,0) point load(u)=pload

      natural(u) = 0 line to (1,0)

      value(u)=u0 arc(center=0,0) angle=90

      natural(u)=0 line to close

 

 monitors

    grid(x,y) as "Computation Mesh"

    contour(u) as "Solution"

    contour(u-u0) as "Error (u-u0)"

 

plots

    grid(x,y) as "Computation Mesh"

    contour(u) as "Solution"

    contour(u-u0) as "Error (u-u0)"

 
end