I posted a reply focusing on the parts of this thread which are in the original question (and thus on the SO site). Feel free to edit/suggest edits.
Ray On Mon, Apr 4, 2016 at 7:19 PM, Raymond Smith <[email protected]> wrote: > Thanks, Jon. > > I'll post something to StackOverflow in the next few days. > > Also, that makes sense about the steady state ignoring the initial > condition and finding the zero solution. I'd forgotten seeing that in the > example. > > Ray > > On Mon, Apr 4, 2016 at 10:06 AM, Guyer, Jonathan E. Dr. (Fed) < > [email protected]> wrote: > >> Ray - >> >> Thanks for your very complete and very correct answers to Dario. >> >> If you wouldn't mind transcribing your answer to Dario's question on >> StackOverflow, I'd be happy to up-vote it. >> >> >> In answer to *your* questions: >> >> > On Apr 3, 2016, at 11:09 AM, Raymond Smith <[email protected]> wrote: >> > >> > Actually, I'm not sure how FiPy treats the steady-state initial guess >> for Laplace's equation with no flux boundary conditions like yours here. >> The governing equation + BC's without an initial condition admits any >> uniform profile as a solution. >> >> >> > I'm still unsure about the treatment of the initial phi values in this >> sense as mentioned above. >> > However, the direct-to-steady approach merits a few words of caution. >> First, there isn't really a good numerical way of directly computing steady >> state solutions for general systems. Often, your best bet is actually to >> solve the transient equation by time stepping from some initial condition >> until you reach steady state, as that's actually probably the most robust >> algorithm for solving for steady state profiles. >> >> The situation is as you expect. We talk about this toward the end of >> >> >> http://www.ctcms.nist.gov/fipy/examples/diffusion/generated/examples.diffusion.mesh1D.html >> >> (search for "Fully implicit solutions are not without their pitfalls"). >> Basically, a steady-state diffusive problem will "lose" its initial >> condition and should instead be solved by relaxation. The timestep can be >> made very large; there just needs to be a TransientTerm. >> >> >> Note, also, that it's not necessary to constrain the gradient to zero to >> get no-flux. FiPy is a cell-centered finite volume code, so no-flux is the >> natural boundary condition if nothing else is specified. >> >> - Jon >> _______________________________________________ >> fipy mailing list >> [email protected] >> http://www.ctcms.nist.gov/fipy >> [ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy ] >> > >
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