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)?
