Handling time-derivative source terms in heterogeneous media

[Yi-De Liou]

Dear Developer,

I’ve noticed that in the spectral framework, time derivatives are typically restricted to terms with spatially uniform coefficients and are generally placed on the left-hand side of the equations. I’m wondering if you could share your experience or suggestions for handling source terms that include time derivatives—particularly when these terms may have spatial dependence or nonlinear behavior. Examples include heterogeneous polarization currents in Maxwell’s equations or electrochemical reactions involving charge accumulation.

Any insights or recommended approaches would be greatly appreciated.

Best regards,

Yi-De Liou

[Daniel Lecoanet]

Hi Yi-De,

You can do this by defining auxiliary variables for the time derivatives of the usual variables, and putting nonlinear terms involving them on the RHS of the equations. If you have further questions it might be useful to provide a simple example of what you’re trying to do.

Daniel

On May 16, 2025, at 05:58, Yi-De Liou <leave...@gmail.com> wrote:

Dear Developer,

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