Hello, I am a new FiPy user, hoping it will be possible to replace a modest home-built, Matlab-based PDE solver codebase, both in research and graduate classes. It looks amazing, but I wanted to ask how severe are the restrictions on the form of PDEs that can be solved. The response in the FAQ to the question, "What if my term involves the dependent variable, but not where FiPy puts it?" seems to be, "Try to manipulate it into a combination of standard forms."
I'm particularly interested in using FiPy to study weakly-nonlinear equations associated with pattern formation in multiple dimensions. A classical problem there is the Kuramoto-Sivashinsky equation: h_t = - \nabla^2 h - \nabla^4 h - (1/2) | \nabla h |**2 where h is the dependent variable. I'm not seeing how to turn the last term into a difference of Convection/Diffusion terms, and the documentation seems to indicate that ImplicitSource terms are limited to being linear in the dependent variable. I've seen references to things like getGrad() and getDiv(), but little documentation, and vague references to things not working well if you try to add these explicitly to an equation. Can terms like this be fit into FiPy's framework efficiently (i.e., without drastic decrease in accuracy / increase in solution time)? If it's possible, I'd be happy to help write some documentation on how to code up various kinds of terms, as a part of my learning curve. If it's not possible, is there a deeper issue associated with the FVM? I grew up learning FDM, where it's possible to write a fairly basic solver for this problem. However, to the extent that I understand the basics of FVM, it's not clear to me how a volume integral of the last term could be converted into a surface integral. Thanks in advance for any help. -- Dr. Scott A. Norris Assistant Professor of Mathematics Southern Methodist University, Dallas, TX
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