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Matrices, Moments, Quadrature and PDEs

Banff International Research Station for Mathematical Innovation and Discovery

Krylov subspace spectral (KSS) methods are high-order accurate, explicit time-stepping methods with stability characteristic of implicit methods. This "best-of-both-worlds" compromise is achieved by computing each Fourier coefficient of the solution using an individualized approximation, based on techniques from "matrices, moments and quadrature" due to Golub and Meurant for computing bilinear forms involving matrix functions. The result is superior scalability to that of other time-stepping approaches, which motivates continued development of KSS methods for high-resolution simulation. Through combination with EPI methods due to Tokman, et al., KSS methods have been shown to be applicable to nonlinear PDEs as well. This talk will present an overview of their derivation and essential properties, including new theoretical results, and also highlight ongoing projects aimed at enhancing their performance and applicability.

Mathematics; Numerical analysis; Partial differential equations; Scientific computing

video/mp4

Author affiliation: University of Southern Mississippi

2019-06-03

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/70457

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/