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arXiv · 2111.04585

Fast global spectral methods for three-dimensional partial differential equations

Christoph Strössner·Daniel Kressner
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Abstract

Global spectral methods offer the potential to compute solutions of partial differential equations numerically to very high accuracy. In this work, we develop a novel global spectral method for linear partial differential equations on cubes by extending ideas of Chebop2 [Townsend and Olver, J. Comput. Phys., 299 (2015)] to the three-dimensional setting utilizing expansions in tensorized polynomial bases. Solving the discretized PDE involves a linear system that can be recast as a linear tensor equation. Under suitable additional assumptions, the structure of these equations admits for an efficient solution via the blocked recursive solver [Chen and Kressner, Numer. Algorithms, 84 (2020)]. In the general case, when these assumptions are not satisfied, this solver is used as a preconditioner to speed up computations.

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Christoph Strössner, Daniel Kressner. 2021-11-08. Fast global spectral methods for three-dimensional partial differential equations. https://doi.org/10.1093/imanum%2Fdrac030

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