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{ IFTHEN.PDE
This example demonstrates the use of "IF...THEN" conditionals in arithmetic statements.
We solve a heat equation in which the conductivity is defined by a conditional
(IF..THEN) expression.
Caveat:
IF..THEN can be dangerous if used improperly.
Equation coefficients that are discontinuous functions of the system
variables can cause convergence failure or tiny timesteps and slow
execution. See SWAGETEST.PDE.
}
title 'Nonlinear heatflow, conditional conductivity'
Variables
u
definitions
a = IF (u<0.5) and (x<100)
THEN IF u < 0.2
THEN 1.4
ELSE 1+2*abs(u)
ELSE 2
Initial values
u = 1 - (x-1)^2 - (y-1)^2
equations
U: div(a*grad(u)) + 4 = 0;
boundaries
Region 1
start(0,0)
value(u)=0
line to (2,0) to (2,2) to (0,2) to close
monitors
contour(u)
plots
surface(u)
contour(u)
contour(a) as "Conditional Conductivity"
elevation(a,u) from (0,1) to (2,1) as "Conductivity and Solution"
end