Looks great, thanks. > On Apr 5, 2016, at 4:22 PM, Raymond Smith <[email protected]> wrote: > > 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 ] > > > _______________________________________________ > fipy mailing list > [email protected] > http://www.ctcms.nist.gov/fipy > [ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy ]
_______________________________________________ fipy mailing list [email protected] http://www.ctcms.nist.gov/fipy [ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy ]
