Pardon me for my apparent lack of understanding over what may be simple concepts, but why is div[u]*div[v] singular in the context of LSFEM?
On Fri, Dec 11, 2015 at 12:15 PM, Jed Brown <j...@jedbrown.org> wrote: > Justin Chang <jychan...@gmail.com> writes: > > > Jed, > > > > 1) What exactly are the PETSc options for CGNE? > > -ksp_type cgne > > (Conjugate Gradients on the Normal Equations) > > > Also, would LSQR be worth trying? I am doing all of this through > > Firedrake, so I hope these things can be done directly through simply > > providing command line PETSc options :) > > You can try, but I think this line of thinking is getting off in the weeds. > > > 2) So i spoke with Matt the other day, and the primary issue I am having > > with LSFEM is finding a suitable preconditioner for the problematic > penalty > > term in Darcy's equation (i.e., the div-div term). So if I had this: > > > > (u, v) + (u, grad(q)) + (grad(p), v) + (grad(p), grad(q)) + (div(u), > > (div(v)) = (rho*b, v + grad(q)) > > > > If I remove the div-div term, I have a very nice SPD system which could > > simply be solved with CG/HYPRE. Do you know of any good preconditioning > > strategies for this type of problem? > > That term is singular, so if the penalty is strong, it will be a bear to > solve. > > Penalties suck. > > Sometimes you can add more variables to get better compatibility. See > FOSLL*, for example. > > My opinion is that least squares methods are riddled with lame > compromises and tradeoffs that you shouldn't have to make. If you want > something robust, use compatible spaces and (possibly) deal with the > fact that you are solving a saddle point problem. >
