Polynomial Preconditioned Arnoldi with Stability Control

Embree, Mark; Loe, Jennifer A.; Morgan, Ronald

doi:10.1137/19m1302430

Polynomial Preconditioned Arnoldi with Stability Control

Journal Article · Mon Jan 04 00:00:00 EST 2021 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/19m1302430· OSTI ID:1760458

Embree, Mark ^[1]; Loe, Jennifer A. ^[2]; Morgan, Ronald ^[3]

Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)
Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States). Center for Computing Research
Baylor Univ., Waco, TX (United States)

Polynomial preconditioning can improve the convergence of the Arnoldi method for computing eigenvalues. Such preconditioning significantly reduces the cost of orthogonalization; for difficult problems, it can also reduce the number of matrix-vector products. Parallel computations can particularly benefit from the reduction of communication-intensive operations. Additoinally, the GMRES algorithm provides a simple and effective way of generating the preconditioning polynomial. For some problems high degree polynomials are especially effective, but they can lead to stability problems that must be mitigated. A two-level “double polynomial preconditioning” strategy provides an effective way to generate high-degree preconditioners.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

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

Grant/Contract Number:: AC04-94AL85000; NA0003525

OSTI ID:: 1760458

Report Number(s):: SAND--2020-10340J; 690950

Journal Information:: SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 1 Vol. 43; ISSN 1064-8275

Publisher:: SIAMCopyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
Arnoldi
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Polynomial Preconditioned Arnoldi with Stability Control

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