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parGeMSLR: A parallel multilevel Schur complement low-rank preconditioning and solution package for general sparse matrices.

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Title: parGeMSLR: A parallel multilevel Schur complement low-rank preconditioning and solution package for general sparse matrices.
Authors: Xu, Tianshi1 (AUTHOR) xuxx1180@umn.edu, Kalantzis, Vassilis2 (AUTHOR) vkal@ibm.com, Li, Ruipeng3 (AUTHOR) li50@llnl.gov, Xi, Yuanzhe4 (AUTHOR) yxi26@emory.edu, Dillon, Geoffrey5 (AUTHOR) dillong@math.sc.edu, Saad, Yousef1 (AUTHOR) saad@cs.umn.edu
Source: Parallel Computing. Oct2022, Vol. 113, pN.PAG-N.PAG. 1p.
Subjects: Schur complement, Sparse matrices, Algebraic equations, Matrix inversion, Graphics processing units, Graph algorithms
Abstract: This paper discusses parGeMSLR, a C++/MPI software library for the solution of sparse systems of linear algebraic equations via preconditioned Krylov subspace methods in distributed-memory computing environments. The preconditioner implemented in parGeMSLR is based on algebraic domain decomposition and partitions the symmetrized adjacency graph recursively into several non-overlapping partitions via a p -way vertex separator, where p is an integer multiple of the total number of MPI processes. From a numerical perspective, parGeMSLR builds a Schur complement approximate inverse preconditioner as the sum between the matrix inverse of the interface coupling matrix and a low-rank correction term. To reduce the cost associated with the computation of the approximate inverse matrices, parGeMSLR exploits a multilevel partitioning of the algebraic domain. The parGeMSLR library is implemented on top of the Message Passing Interface and can solve both real and complex linear systems. Furthermore, parGeMSLR can take advantage of hybrid computing environments with in-node access to one or more Graphics Processing Units. Finally, the parallel efficiency (weak and strong scaling) of parGeMSLR is demonstrated on a few model problems arising from discretizations of 3D Partial Differential Equations. • Our library is publicly available at https://github.com/Hitenze/pargemslr. • The preconditioner featured in parGeMSLR is less sensitive to indefiniteness. • parGeMSLR supports both single and double precision real and complex arithmetic. • parGeMSLR can accelerate parts of the preconditioner via GPU-based matrix kernels. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
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Abstract:This paper discusses parGeMSLR, a C++/MPI software library for the solution of sparse systems of linear algebraic equations via preconditioned Krylov subspace methods in distributed-memory computing environments. The preconditioner implemented in parGeMSLR is based on algebraic domain decomposition and partitions the symmetrized adjacency graph recursively into several non-overlapping partitions via a p -way vertex separator, where p is an integer multiple of the total number of MPI processes. From a numerical perspective, parGeMSLR builds a Schur complement approximate inverse preconditioner as the sum between the matrix inverse of the interface coupling matrix and a low-rank correction term. To reduce the cost associated with the computation of the approximate inverse matrices, parGeMSLR exploits a multilevel partitioning of the algebraic domain. The parGeMSLR library is implemented on top of the Message Passing Interface and can solve both real and complex linear systems. Furthermore, parGeMSLR can take advantage of hybrid computing environments with in-node access to one or more Graphics Processing Units. Finally, the parallel efficiency (weak and strong scaling) of parGeMSLR is demonstrated on a few model problems arising from discretizations of 3D Partial Differential Equations. • Our library is publicly available at https://github.com/Hitenze/pargemslr. • The preconditioner featured in parGeMSLR is less sensitive to indefiniteness. • parGeMSLR supports both single and double precision real and complex arithmetic. • parGeMSLR can accelerate parts of the preconditioner via GPU-based matrix kernels. [ABSTRACT FROM AUTHOR]
ISSN:01678191
DOI:10.1016/j.parco.2022.102956