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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