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. > 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.
signature.asc
Description: PGP signature
