It appears that only MATSOLVERMKL_CPARDISO provides a parallel backward solve currently.
The only seperation of forward and backward solves in MUMPS appears to be provided with (from its users manual) A special case is the one where the forward elimination step is performed during factorization (see Subsection 3.8), instead of during the solve phase. This allows accessing the L factors right after they have been computed, with a better locality, and can avoid writing the L factors to disk in an out-of-core context. In this case (forward > On Nov 15, 2025, at 9:17 AM, Yin Shi via petsc-users > <[email protected]> wrote: > > Dear Developers, > > In short, I need to explicitly use A.solveBackward(b, x) in parallel with > petsc4py, where A is a Cholesky factored matrix, but it seems that this is > not supported (e.g., for mumps and superlu_dist factorization solver > backend). Is it possible to work around this? > > In detail, the problem I need to solve is to generate a set of correlated > random numbers (denoted by a vector, w) from an uncorrelated one (denoted by > a vector n). Denote the covariance matrix of n as C (symmetric). One needs to > first factorize C, C = L L^T, and then solve the linear system L^T w = n for > w in parallel. Is it possible to reformulate this problem for it to be > implemented using petsc4py? > > Thank you! > Yin
