<html><head><meta http-equiv="Content-Type" content="text/html charset=us-ascii"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class=""><br class=""><div><blockquote type="cite" class=""><div class="">On Mar 1, 2016, at 9:59 AM, Mark Adams <<a href="mailto:mfadams@lbl.gov" class="">mfadams@lbl.gov</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div dir="ltr" class=""><br class=""><div class="gmail_extra"><br class=""><div class="gmail_quote">On Mon, Feb 29, 2016 at 5:42 PM, Boyce Griffith <span dir="ltr" class=""><<a href="mailto:griffith@cims.nyu.edu" target="_blank" class="">griffith@cims.nyu.edu</a>></span> wrote:<br class=""><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><div class="h5"><br class=""><div class=""><blockquote type="cite" class=""><div class="">On Feb 29, 2016, at 5:36 PM, Mark Adams <<a href="mailto:mfadams@lbl.gov" target="_blank" class="">mfadams@lbl.gov</a>> wrote:</div><br class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><span class=""><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><div class=""><br class=""></div><div class="">GAMG is use for AMR problems like this a lot in BISICLES.</div></div></div></div></blockquote><div class=""><br class=""></div></span><div class="">Thanks for the reference. However, a quick look at their paper suggests they are using a finite volume discretization which should be symmetric and avoid all the shenanigans I'm going through! </div></div></div></div></blockquote><div class=""><br class=""></div><div class="">No, they are not symmetric. FV is even worse than vertex centered methods. The BCs and the C-F interfaces add non-symmetry.</div></div></div></div></div></blockquote></div><div class=""><br class=""></div></div></div><div class="">If you use a different discretization, it is possible to make the c-f interface discretization symmetric --- but symmetry appears to come at a cost of the reduction in the formal order of accuracy in the flux along the c-f interface. I can probably dig up some code that would make it easy to compare.</div></div></blockquote><div class=""><br class=""></div><div class="">I don't know. Chombo/Boxlib have a stencil for C-F and do F-C with refluxing, which I do not linearize. PETSc sums fluxes at faces directly, perhaps this IS symmetric? Toby might know.</div></div></div></div></div></blockquote><div><br class=""></div><div>If you are talking about solving Poisson on a composite grid, then refluxing and summing up fluxes are probably the same procedure.</div><div><br class=""></div><div>Users of these kinds of discretizations usually want to use the conservative divergence at coarse-fine interfaces, and so the main question is how to set up the viscous/diffusive flux stencil at coarse-fine interfaces (or, equivalently, the stencil for evaluating ghost cell values at coarse-fine interfaces). It is possible to make the overall discretization symmetric if you use a particular stencil for the flux computation. I think this paper (<a href="http://www.ams.org/journals/mcom/1991-56-194/S0025-5718-1991-1066831-5/S0025-5718-1991-1066831-5.pdf" class="">http://www.ams.org/journals/mcom/1991-56-194/S0025-5718-1991-1066831-5/S0025-5718-1991-1066831-5.pdf</a>) is one place to look. (This stuff is related to "mimetic finite difference" discretizations of Poisson.) This coarse-fine interface discretization winds up being symmetric (although possibly only w.r.t. a weighted inner product --- I can't remember the details), but the fluxes are only first-order accurate at coarse-fine interfaces.</div><div><br class=""></div><div>-- Boyce</div></div></body></html>