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# array_variables

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# array_variables   { ARRAY_VARIABLES.PDE

This example demonstrates the use of ARRAY VARIABLES.

A set of heat equations is solved as a demonstration.

}

title 'ARRAY Variable test'

variables

U=array                 { an array of field variables }

global variables

g(threshold=0.1) = array { and an array of global variables }

definitions

u0 = 1-x^2-y^2

s = array(1,2,3,4,5) { each equation has a different source }

{ use initial equations to diffuse the otherwise discontinuous initial value caused by value BC }

initial equations

repeat i=1 to 5

U[i]:   del2(u[i])  = 0

endrepeat

equations

repeat i=1 to 5

U[i]:   del2(u[i]) +s[i] = dt(u[i])

g[i]:   dt(g[i]) = i-g[i]

endrepeat

boundaries

Region 1

start(-1,-1)

repeat i=1 to 5

value(u[i])=u0

endrepeat

line to (1,-1) to (1,1) to (-1,1) to close

time 0 to 10

plots

for cycle=10

contour(u_1)                 ! variables may be indexed with underscores

repeat i=1 to 5

contour(u[i])   as "U_"+\$i   ! variables may be indexed with brackets

endrepeat

history(g)

history(u) at  (0,0) (1/4,1/4)(1/2,1/2)(3/4,3/4)

vtk(u,g)

table(u,g)

transfer(u,g)

end