>I did unstructured hexes. You still haven't said what you'll use for >relaxation. High-order discretizations tend to have poor h-ellipticity, so they either need heavy smoothers or a correction based on a discretization with better h-ellipticity. Quite frankly, I was not aware of the poor h-ellipticity of higher order elements and I was assuming I would use the regular GS/GMRES/etc for relaxation. I looked up h-ellipticity of higher order elements and now this adds to my worries :(. I may be asking for too much here.... but what do you mean by heavy smoothers? or correction based on a discretization?.
On Thu, Oct 17, 2013 at 10:36 PM, Jed Brown <[email protected]> wrote: > Shiva Rudraraju <[email protected]> writes: > > > By Spectral Elements I mean spectral quadrilateral/hexahedral elements > > based on tensor product lagrangian polynomials on Gauss Lobatto Legendre > > points. > > Okay "both Lagrange and Spectral elements" sounded like you wanted to > distinguish between two classes of methods. > > > >You could reorder your equations, but multicolor GS is not a very good > or > > representative algorithm on cache-based architectures, due to its poor > > cache reuse. I suggest just using standard GS smoothers (-pc_type sor > with > > default relaxation parameter of 1.0). > > I plan to implement multicolor GS precisely to demonstrate its poor > > performance as compared to other iterative and MG schemes, because in the > > Phase Field community multicolor GS is still quite popular and lingers > > around as a solver. The main point of this work is to clearly demonstrate > > the ill-suitedness of GS for these coupled transport problems. > > Block Jacobi/SOR is still popular and useful. > > > > > So just wondering if there are any related examples showing multicolor > > GS as a solver. Also, since you mentioned, are there any references > > which demonstrate the poor cache reuse of multicolor GS or is it too > > obvious?... just curious. > > I though multicolor GS mostly died when cache-based architectures beat > out vector machines. One well-optimized application that uses > multicolor GS is FUN3D, but it is doing nonlinear point-block > Gauss-Seidel with a second order residual and first-order correction, > and adds line smoothers for boundary layers. > > > Sorry I forgot to mention..... I am only interested in structured > quad/hex > > elements. I have my old implementations of higher order Lagrange elements > > and also used deal.ii's Spectral elements.... but for this work I will > more > > or less write one from scratch. So any pointers to efficient tensor grid > > FEM implementation will really help me. > > I did unstructured hexes. You still haven't said what you'll use for > relaxation. High-order discretizations tend to have poor h-ellipticity, > so they either need heavy smoothers or a correction based on a > discretization with better h-ellipticity. >
