On Tue, Mar 1, 2016 at 1:15 PM, Jed Brown <[email protected]> wrote: > Mohammad Mirzadeh <[email protected]> writes: > > > I am not familiar with the terminology used here. What does the refluxing > > mean? > > The Chombo/BoxLib family of methods evaluate fluxes between coarse grid > cells overlaying refined grids, then later visit the fine grids and > reevaluate those fluxes. The correction needs to be propagated back to > the adjoining coarse grid cell to maintain conservation. It's an > implementation detail that they call refluxing. >
Thanks for clarification. > > > Right. I think if the discretization is conservative, i.e. discretizing > div > > of grad, and is compact, i.e. only involves neighboring cells sharing a > > common face, then it is possible to construct symmetric discretization. > An > > example, that I have used before in other contexts, is described here: > > http://physbam.stanford.edu/~fedkiw/papers/stanford2004-02.pdf > > It's unfortunate that this paper repeats some unfounded multigrid > slander and then basically claims to have uniform convergence using > incomplete Cholesky with CG. In reality, incomplete Cholesky is > asymptotically no better than Jacobi. > > > An interesting observation is although the fluxes are only first order > > accurate, the final solution to the linear system exhibits super > > convergence, i.e. second-order accurate, even in L_inf. > > Perhaps for aligned coefficients; definitely not for unaligned > coefficients. > Could you elaborate what you mean by aligned/unaligned coefficients? Do you mean anisotropic diffusion coefficient?
