> On Jan 13, 2016, at 9:57 PM, Justin Chang <[email protected]> wrote: > > Hi all, > > 1) I am guessing MATMPIBAIJ could theoretically have better performance than > simply using MATMPIAIJ. Why is that? Is it similar to the reasoning that > block (dense) matrix-vector multiply is "faster" than simple matrix-vector?
See for example table 1 in http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.38.7668&rep=rep1&type=pdf > > 2) I am looking through the manual and online documentation and it seems the > term "block" used everywhere. In the section on "block matrices" (3.1.3 of > the manual), it refers to field splitting, where you could either have a > monolithic matrix or a nested matrix. Does that concept have anything to do > with MATMPIBAIJ? Unfortunately the numerical analysis literature uses the term block in multiple ways. For small blocks, sometimes called "point-block" with BAIJ and for very large blocks (where the blocks are sparse themselves). I used fieldsplit for big sparse blocks to try to avoid confusion in PETSc. > > It makes sense to me that one could create a BAIJ where if you have 5 dofs of > the same type of physics (e.g., five different primary species of a > geochemical reaction) per grid point, you could create a block size of 5. And > if you have different physics (e.g., velocity and pressure) you would ideally > want to separate them out (i.e., nested matrices) for better preconditioning. Sometimes you put them together with BAIJ and sometimes you keep them separate with nested matrices. > > Thanks, > Justin
