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# matrix_boundary

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# 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

! 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)

! 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