{ SUM.PDE }
{
This problem demonstrates the use of the SUM function.
It poses a heatflow problem with a heat source made up of four
gaussians. The source is composed by a SUM over gaussians
referenced to arrays of center coordinates.
}
title 'Sum test'
Variables
u
definitions
k = 1
u0 = 1-x**2-y**2 { boundary forced to parabolic values }
xc = array(-0.5,0.5,0.5,-0.5) { arrays of source spot coordinates }
yc = array(-0.5,-0.5,0.5,0.5)
s = sum( i, 1, 4, exp(-10*[(x-xc[i])^2+(y-yc[i])^2]) ) { summed Gaussian source }
equations
div(K*grad(u)) +s = 0
boundaries
Region 1
start(-1,-1)
value(u)=u0 line to (1,-1) to (1,1) to (-1,1) to close
monitors
grid(x,y)
contour(u)
contour(s)
plots
grid(x,y)
contour(u)
contour(s)
end