Hello Daniel and Jonathan, Thanks for the suggestions!
I have looked up Picard sweeps and Newton sweeps. I have implemented them before in MATLAB but not in FiPy, so I was wondering if you could provide some toy examples or some references to illustrate how both kinds of sweeps can be coded in FiPy (I don't recall seeing such examples in the documentation). Regarding Jonathan's comments, I assume the residual that the sweep method returns is the absolute, and not relative, residual? I have also just looked into adaptive time-stepping to see if I can choose the time step in a smart manner since Jonathan is probably right small time steps are not needed for all times. Thanks again! Best, Edwin On Mon, May 6, 2013 at 10:46 AM, Daniel Wheeler <[email protected]>wrote: > > > > On Fri, May 3, 2013 at 3:08 PM, Edwin Sze Lun Khoo <[email protected]>wrote: > >> Hello Jonathan and Daniel, >> >> Thanks for the useful suggestions. What do you mean by using Newton steps >> and correction variables? >> > > > I'm referring to the method used for the outer iterations (sweeps, or > non-linear iterations) as opposed to the method used to the inner linear > iterations, which the linear solver takes care of. There are basically two > methods that are generally used. The first and least complicated to > implement is Picard sweeps (also known as method of successive > substitutions or fixed point iteration). This is just when the previous > solution is used as the initial guess and the equations are used directly > to solve for the new variable. The second method is Newton sweeps, which > requires substituting the variable + correction and then solving for the > first order expansion with the zero order expansion as the residual using > the previous solution to calculate the residual. Maybe try searching for > Newton versus Picard to get a better explanation. > > I thought it might be worth trying Newton for this problem because it > seems like a more natural linearization of the convection term. > > I hope the above helps some. > > Cheers. > > -- > Daniel Wheeler > > _______________________________________________ > 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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