Nonlinear Coefficients and Equations

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Nonlinear Coefficients and Equations

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One common complication that arises is that either the terms of the equation or the material properties are complicated functions of the system variables.  FlexPDE understands this, and has made full provision for handling such systems.

Suppose, for example, that the conductivity in the 'blob' of our example problem were in fact a strong function of the temperature.  Say, for example, that K=exp(-5*phi).  The solution couldn't be simpler.  Just define it the way you want it and click "run":

REGION 2        'blob'        { the embedded blob }

k = exp(-5*phi)


The appearance of a nonlinear dependence will automatically activate the nonlinear solver, and all the dependency details will be handled by FlexPDE.

The modified result appears immediately:




Nonlinear terms in the equation are just as easy.  If our system has a nonlinear sinusoidal source, for example, we may type:


Div(k*grad(phi)) + 0.01*phi*sin(phi) = 0


Click "run", and the solution appears: