LinearSolve.jl
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Strumpack wrapper?
Strumpack (https://github.com/pghysels/STRUMPACK) contains dense and sparse linear solvers, with OpenMP/MPI/CUDA backends. It is a relatively new package written by SuperLU developers. It implements a variety of hierarchical low-rank compression algorithms to achieve lower O(n^k) complexity than exact factorization. It is more robust for indefinite matrix where fast AMG solvers fail (as shown in this paper, TABLE IV)
There is an unofficial, un-maintained Python interface: https://github.com/sshiraiwa/PySTRUMPACK
@Wimmerer what's the status of https://github.com/JuliaSparse/SuperLUBase.jl and https://github.com/JuliaSparse/SuperLUDIST.jl ?