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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