<< Click to Display Table of Contents >> Navigation:  Sample Problems > Usage > Arrays+Matrices > matrix_boundary

{ MATRIX_BOUNDARY.PDE

 

 This example demonstrates the use of a data MATRIX in boundary definition.

 Coordinates are constructed by functional matrix definition,

 rotated by multiplication by a rotation matrix

 and joined in a spline fit to form the system boundary.

}

title 'MATRIX_BOUNDARY test'

Variables

   u

definitions

   a = 1

   rad = 1

  ! build a 2 x 21 matrix of x and y coordinates

   mb =matrix for i(1,2)  

              for ang(-pi/2 by pi/20 to pi/2)  

              : if(i=1) then rad*cos(ang) else rad*sin(ang)

  ! build a 2 x 2 rotation matrix

   rota=45

   rot = matrix[2,2] ((cos(rota degrees), -sin(rota degrees)),

                       (sin(rota degrees), cos(rota degrees)))

  ! rotate the coordinate list

   mbr = rot**mb

   s = 1

equations

   u:  div(a*grad(u)) + s  = 0;           { the heatflow equation }

boundaries

  region 1

    ! start curve at first point of rotated coordinates

    start(mbr[1,1], mbr[2,1])

        value(u)=0

        ! spline fit the 21-point table

        spline list (mbr)

        natural(u)=0

        line to close

plots

  contour(u) painted

  surface(u)

end