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Nonlinear term in the Coefficient Form PDE solver

Posted Jul 25, 2017, 11:31 a.m. EDT 1 Reply

gezibash
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I would like to solve the following equation

div ( u grad(u) ) = 0

The problem is I am trying to set the 'c' coefficient to be

c = u

But it doesn't work. The result will not converge. Can this be done in the PDE solver?
1 Reply Last Post Jul 25, 2017, 3:33 p.m. EDT
Jeff Hiller COMSOL Employee

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Posted: 7 years ago Jul 25, 2017, 3:33 p.m. EDT
Updated: 7 years ago Jul 26, 2017, 8:56 a.m. EDT
There's no conceptual problem with setting up coefficients that depend on the solution itself. But obviously nonlinear problems require more caution than linear ones. With nonlinear equations, you have to be especially careful not to set up a problem that does not have any solution, or has several, for instance (The same concerns exist also with linear equations, of course, but such situations are much easier to detect and remedy). For nonlinear equations, it's also particularly important to set up suitable initial values for the variables that are being solved for. In your case, the default initial value (zero) is particularly poorly suited, since it results in a singular stiffness matrix.
If these pointers do not help, consider posting your model file.
Best,
Jeff
There's no conceptual problem with setting up coefficients that depend on the solution itself. But obviously nonlinear problems require more caution than linear ones. With nonlinear equations, you have to be especially careful not to set up a problem that does not have any solution, or has several, for instance (The same concerns exist also with linear equations, of course, but such situations are much easier to detect and remedy). For nonlinear equations, it's also particularly important to set up suitable initial values for the variables that are being solved for. In your case, the default initial value (zero) is particularly poorly suited, since it results in a singular stiffness matrix. If these pointers do not help, consider posting your model file. Best, Jeff

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