Hi all, Okay, so I've been trying to implement the matrixfree class for a weak form of a parabolic equation in divergence form ( du/dt + div (coeff grad u ) = g ), where I want to use a viscous flux for the spatial derivative term. So, in particular, I need to find a way of implementing face terms for the fluxes (after multiplying by the shape functions and integrating by parts), etc., using the matrixfree class. I'm not quite clear how to go about doing this right now, in either 2 or 3 spatial dimensions (both ideally).
More clearly, by explicit (below), I mean, we would like to use an explicit time-integrator that does not (inherently) require, for example, a linear solve at all (for example, Wolfgang, like the DG adcirc code at ICES, in the sense of a local DG formulation). Though being able to solve this form as well as being able to resort to the sort of Chebyshev solver multigrid formulation in step-37, would be very nice if both could be implemented in one go (for comparison, etc.). But mostly, we need to get our hands on the local data for Local Lax-Freidrichs type fluxes, etc. Could anyone possibly give a few pointers? Best, Evan On Wed, Jan 20, 2010 at 1:49 PM, Wolfgang Bangerth <[email protected]>wrote: > > Evan, > > > I'm been working on trying to formulate a local DG scheme in deal.ii for > a > > reaction-diffusion system. The general formulations in the examples for > > the time dependent cases though -- for example in step-33 -- are sort of > CG > > based implicit solvers, while I want to build a local DG based explicit > > solver. Moving from the continuous to discontinuous elements seems > fairly > > straight forward, but what has been causing me some severe problems is > > constructing a system explicitly (and locally) using the usual > > system_matrix formulation, or otherwise. My feeling is this should be > > fairly easy, but a few words of initial advice might go a long way at > this > > point. > > I'm not entirely sure what exactly you are trying, but when you say > "explicit" > I assume you want to work matrix-free, right? In that case, you may want to > consider step-37, which you can get by checking out the current development > version of deal.II and which is also here: > http://www.dealii.org/developer/doxygen/deal.II/step_37.html > It shows how to solve linear systems without assembling a global matrix. > > If that isn't what you were looking for, can you explain a bit more what > exactly the problem is? > > Best > W. > > ------------------------------------------------------------------------- > Wolfgang Bangerth email: [email protected] > www: > http://www.math.tamu.edu/~bangerth/<http://www.math.tamu.edu/%7Ebangerth/> > >
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