[petsc-users] solveBackward in parallel

[Barry Smith]

  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 <petsc-users at mcs.anl.gov> 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

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