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.
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