On the evaluation of general sparse hybrid linear solvers

Farea A., Çelebi M. S.

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, vol.30, no.2, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.1002/nla.2469
  • Journal Name: NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Computer & Applied Sciences, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: additive Schwarz, direct methods, high performance computing, HIPS, iterative methods, LU factorization, Maphys, parallel sparse hybrid linear solver, partitioning, PDSLin, preconditioners, preconditioning, scalability, Schur complement, sparse matrix, SuperLU_DIST, PERFORMANCE
  • Istanbul Technical University Affiliated: Yes

Abstract

General sparse hybrid solvers are commonly used kernels for solving wide range of scientific and engineering problems. This work addresses the current problems of efficiently solving general sparse linear equations with direct/iterative hybrid solvers on many core distributed clusters. We briefly discuss the solution stages of Maphys, HIPS, and PDSLin hybrid solvers for large sparse linear systems with their major algorithmic differences. In this category of solvers, different methods with sophisticated preconditioning algorithms are suggested to solve the trade off between memory and convergence. Such solutions require a certain hierarchical level of parallelism more suitable for modern supercomputers that allow to scale for thousand numbers of processors using Schur complement framework. We study the effect of reordering and analyze the performance, scalability as well as memory for each solve phase of PDSLin, Maphys, and HIPS hybrid solvers using large set of challenging matrices arising from different actual applications and compare the results with SuperLU_DIST direct solver. We specifically focus on the level of parallel mechanisms used by the hybrid solvers and the effect on scalability. Tuning and Analysis Utilities (TAU) is employed to assess the efficient usage of heap memory profile and measuring communication volume. The tests are run on high performance large memory clusters using up to 512 processors.