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forever

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forever   {  FOREVER.PDE

This problem displays the behaviour of FlexPDE in time dependent problems.

We posit a field with paraboloidal shape and with amplitude sinusoidal

in time.  We then derive the source function necessary to achieve this

solution, and follow the integration for ten cycles, comparing the solution

to the known analytic solution.

}

title 'A forever test'

variables

Temp (threshold=0.1)

definitions

K = 1

eps = 0

shape = (1-x^2-y^2)

Texact = shape*sin(t)

initial values

Temp = Texact

equations

Temp : div(K*grad(Temp)) + source = dt(Temp)

boundaries

Region 1

start(-1,-1)

value(Temp)=Texact

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

time 0 to 20*pi by 0.01

monitors

for cycle=5

contour(Temp)         { show the Temperature during solution }

plots                         { write these plots to the .PGX file }

for t = pi/2 by pi to endtime

contour(Temp)

surface(Temp)

contour(Temp-Texact) as "Error"

vector(-dx(Temp),-dy(Temp)) as "Heat Flow"

histories

history(Temp) at (0,0) (0.5,0.5) integrate

history(Temp-Texact) at (0,0) (0.5,0.5)

end