Random-Order Alternating Schwarz for Sparse Triangular Solves

TitleRandom-Order Alternating Schwarz for Sparse Triangular Solves
Publication TypeConference Paper
Year of Publication2015
AuthorsAnzt, H., E. Chow, D. Szyld, and J. Dongarra
Conference Name2015 SIAM Conference on Applied Linear Algebra (SIAM LA)
Date Published2015-10
Conference LocationAtlanta, GA
AbstractBlock-asynchronous Jacobi is an iteration method where a locally synchronous iteration is embedded in an asynchronous global iteration. The unknowns are partitioned into small subsets, and while the components within the same subset are iterated in Jacobi fashion, no update order in-between the subsets is enforced. The values of the non-local entries remain constant during the local iterations, which can result in slow inter-subset information propagation and slow convergence. Interpreting of the subsets as subdomains allows to transfer the concept of domain overlap typically enhancing the information propagation to block-asynchronous solvers. In this talk we explore the impact of overlapping domains to convergence and performance of block-asynchronous Jacobi iterations, and present results obtained by running this solver class on state-of-the-art HPC systems.