Implementation of Parallel Adaptive-Krylov Exponential Solvers for Stiff Problems

Loffeld, J.; Tokman, M.

doi:10.1137/13094462x

Title: Implementation of Parallel Adaptive-Krylov Exponential Solvers for Stiff Problems

Journal Article · Thu Oct 30 00:00:00 EDT 2014 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/13094462x· OSTI ID:1860891

Loffeld, J. ^[1]; Tokman, M. ^[1]

Univ. of California, Merced, CA (United States)

Recently exponential integrators have been receiving increased attention as a means of solving large stiff systems of ODEs. Preliminary performance analysis demonstrated that exponential integrators hold promise compared to state-of-the-art implicit methods. However, much work remains to be done to understand in detail possible computational advantages these methods may offer in practice. This is particularly true for supercomputer-scale problems as there has been very little work on parallelizing exponential methods. In this paper we describe an implementation of a suite of parallel exponential solvers. Additionally, we present some performance tests on four stiff benchmark problems of a particular adaptive-Krylov exponential propagation iterative Runge--Kutta (EPIRK) method from the suite, and compare efficiency with the Newton--Krylov implicit solver CVODE.

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Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF)

Grant/Contract Number:: AC52-07NA27344; 1115978

OSTI ID:: 1860891

Report Number(s):: LLNL-JRNL-645881; 765819

Journal Information:: SIAM Journal on Scientific Computing, Vol. 36, Issue 5; ISSN 1064-8275

Publisher:: Society for Industrial and Applied Mathematics (SIAM)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited By (3)

Nonoverlapping Localized Exponential Time Differencing Methods for Diffusion Problems Hoang, Thi-Thao-Phuong; Ju, Lili; Wang, Zhu Journal of Scientific Computing, Vol. 82, Issue 2 https://doi.org/10.1007/s10915-020-01136-w	journal	February 2020
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Preconditioned Implicit-Exponential (IMEXP) Time Integrators for Stiff Differential Equations Luan, Vu Thai; Tokman, Mayya; Rainwater, Greg arXiv https://doi.org/10.48550/arxiv.1605.02858	preprint	January 2016

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