Adaptive Multilevel Krylov Methods

Journal Article · 15 December 2019 · Electronic Transactions on Numerical Analysis

DOI: https://doi.org/10.1553/etna_vol51s512 · OSTI ID:1612659

Kehl, René ^[1]; Nabben, Reinhard ^[2]; Szyld, Daniel B. ^[3]

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1. Weierstraß-Inst., Berlin (Germany); DOE/OSTI
2. Technische Univ. Berlin (Germany). Inst. für Mathematik,
3. Temple Univ., Philadelphia, PA (United States)

Inexact (variable) preconditioning of Multilevel Krylov methods (MK methods) for the solution of linear systems of equations is considered. MK methods approximate the solution of the local systems on a subspace using a few, but fixed, number of iteration steps of a preconditioned flexible Krylov method. In this paper, using the philosophy of inexact Krylov subspace methods, we use a theoretically-derived criterion to choose the number of iterations needed on each level to achieve a desired tolerance. We use this criterion on one level and obtain an improved MK method. Inspired by these results, a second ad hoc method is also explored. Numerical experiments for the Poisson, Helmholtz, and the convection-diffusion equations illustrate the efficiency and robustness of this adaptive Multilevel Krylov method.

• Research Organization: Temple Univ., Philadelphia, PA (United States)
• Sponsoring Organization: National Science Foundation (NSF); USDOE Office of Science (SC)
• Grant/Contract Number: SC0016578
• OSTI ID: 1612659
• Journal Information: Electronic Transactions on Numerical Analysis, Journal Name: Electronic Transactions on Numerical Analysis Vol. 51; ISSN 1068-9613
• Publisher: Kent State University - Johann Radon Institute for Computational and Applied Mathematics (RICAM)Copyright Statement
• Country of Publication: United States
• Language: English