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This paper discusses parGeMSLR, a C++/MPI software library for the solutionof sparse systems of linear algebraic equations via preconditioned Krylovsubspace methods in distributed-memory computing environments. Thepreconditioner implemented in parGeMSLR is based on algebraic domaindecomposition and partitions the symmetrized adjacency graph recursively intoseveral non-overlapping partitions via a p-way vertex separator, where p is aninteger multiple of the total number of MPI processes. From a numericalperspective, parGeMSLR builds a Schur complement approximate inversepreconditioner as the sum between the matrix inverse of the interface couplingmatrix and a low-rank correction term. To reduce the cost associated with thecomputation of the approximate inverse matrices, parGeMSLR exploits amultilevel partitioning of the algebraic domain. The parGeMSLR library isimplemented on top of the Message Passing Interface and can solve both real andcomplex linear systems. Furthermore, parGeMSLR can take advantage of hybridcomputing environments with in-node access to one or more Graphics ProcessingUnits. Finally, the parallel efficiency (weak and strong scaling) of parGeMSLRis demonstrated on a few model problems arising from discretizations of 3DPartial Differential Equations.

parGeMSLR: A Parallel Multilevel Schur Complement Low-Rank Preconditioning and Solution Package for General Sparse Matrices