A correction: it is B=A+sigma*I when you *add* 1e-6 to the diagonal entries. but if you "multiply each diagonal of the system matrix with (1.0 + 1.0e-6)" you are doing a different thing.
> El 27 feb 2022, a las 9:21, Jose E. Roman <[email protected]> escribió: > > In both cases, it is like you are solving a nonsingular system with a matrix > B. With MatNullSpace, B=A-e*e' where e=ones(n,1) normalized, and with your > approach it is B=A+sigma*I with sigma=1e-6. The first approach shifts the > zero eigenvalue, while in the second approach all eigenvalues are shifted. > > Jose > > >> El 27 feb 2022, a las 8:36, Bojan Niceno <[email protected]> >> escribió: >> >> Dear all, >> >> I have coupled PETSc with my computational fluid dynamics (CFD) solver for >> incompressible flows where the most computationally intensive part is a >> solution of the linear system for pressure - which is singular. >> >> A simple call to PETSc solvers resulted in divergence, as expected, but >> things work when I set the null space for the pressure matrix as >> demonstrated in src/ksp/ksp/tutorials/ex29.c: >> MatNullSpace nullspace; >> ierr = >> MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);CHKERRQ(ierr); >> ierr = MatSetNullSpace(J,nullspace);CHKERRQ(ierr); >> ierr = MatNullSpaceDestroy(&nullspace);CHKERRQ(ierr); >> >> However, the effect of setting the null space as described above, has almost >> the same effect (convergence history is almost the same) as if when I >> multiply each diagonal of the system matrix with (1.0 + 1.0e-6), i.e., >> desingularize the matrix by making it slightly diagonally dominant. >> >> I prefer the former solution as the latter one seems a bit like an ad-hoc >> patch and I am not sure how general it is, but I wonder, from a mathematical >> point of view, is it the same thing? Any thoughts on that? >> >> >> Cheers, >> >> Bojan Niceno >
