On the evaluation of general sparse hybrid linear solvers

Afrah Farea*, M. Serdar Çelebi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article numbere2469
JournalNumerical Linear Algebra with Applications
Issue number2
Publication statusPublished - Mar 2023

Bibliographical note

Publisher Copyright:
© 2022 John Wiley & Sons Ltd.


Computing resources used in this work were provided by the National Center for High Performance Computing of Turkey (UHeM) under grant number 4005142018.

FundersFunder number
National Center for High Performance Computing of Turkey
Ulusal Yüksek Başarımlı Hesaplama Merkezi, Istanbul Teknik Üniversitesi4005142018


    • 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


    Dive into the research topics of 'On the evaluation of general sparse hybrid linear solvers'. Together they form a unique fingerprint.

    Cite this