[petsc-users] Action of inverse of Cholesky factors in parallel

[Johannes Haubner]

Given a s.p.d. matrix A and a right-hand-side b, we want to compute (L^T)^{-1}b and L^{-1}b, where A= L L^T is the Cholesky decomposition of A. In serial, we are able to do this using pc_factor_mat_solver_type petsc and using "solveForward" and "solveBackward" (see https://github.com/JohannesHaubner/petsc-cholesky/blob/main/main.py). In parallel, we are not able to do this yet. According to p. 52 https://slepc.upv.es/documentation/slepc.pdf , PETSc's Cholesky factorization is not parallel. However, using "mumps" or "superlu_dist" prevents us from using "solveForward" or "solveBackward". Is there a way of using solveBackward in parallel with a distributed matrix (MPI)?