I'm solving a coupled set of equations, so each "block" corresponds to a set of unknowns for a particular spatial cell. The matrix is structured such that all of the unknowns for a given spatial cell have adjacent global matrix indices (i.e., they're next to each other in the global solution vector). Effectively, I want to do red-black Gauss Seidel, but with blocks. Alternatively, it's the same as applying block Jacobi for all the red cells and then applying block Jacobi for all the black cells.
The color of the block is determined from the geometry of the problem which is stored in various structures in the code I'm working on, independent of petsc. (Physically, I generally have a nice 3d cartesian spatial grid and the coloring is just a checkerboard in that case.) The reason I want to do this is for research purposes. I've implemented my own interpolation matrices for PCMG, and, in my simpler 1d codes and convergence analyses, I've found that doing a red-black smoothing significantly improved convergence for my particular problem (though I'm aware that this generally leads to poor cache efficiency). On Aug 29, 2017 7:33 PM, "Barry Smith" <[email protected]> wrote: Ben, Please explain more what you mean by "a red-black block Jacobi smoother". What is your matrix structure? What are the blocks? How do you decide which ones are which color? Why do you wish to use some a smoother. Barry > On Aug 29, 2017, at 6:19 PM, Ben Yee <[email protected]> wrote: > > Hi, > > For the smoother in PCMG, I want to use a red-black block Jacobi smoother. Is this available with the existing PETSc options? If so, how do I designate which blocks are red and which are black? > > If it is not possible, what would be the best way to implement this? Would I use KSPRICHARDSON+PCSHELL? > > Thanks! > > -- > Ben Yee > > NERS PhD Candidate, University of Michigan > B.S. Mech. & Nuclear Eng., U.C. Berkeley
