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- Title
Fast global spectral methods for three-dimensional partial differential equations.
- Authors
Strössner, Christoph; Kressner, Daniel
- 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 the ideas of Chebop2 (Townsend, A. & Olver, S. (2015) The automatic solution of partial differential equations using a global spectral method. J. Comput. Phys. , 299 , 106–123) to the three-dimensional setting utilizing expansions in tensorized polynomial bases. Solving the discretized partial differential equation involves a linear system that can be recast as a linear tensor equation. Under suitable additional assumptions, the structure of these equations admits an efficient solution via the blocked recursive solver (Chen, M. & Kressner, D. (2020) Recursive blocked algorithms for linear systems with Kronecker product structure. Numer. Algorithms , 84 , 1199–1216). In the general case, when these assumptions are not satisfied, this solver is used as a preconditioner to speed up computations.
- Subjects
LINEAR differential equations; KRONECKER products; LINEAR equations; LINEAR systems; SPECTRAL element method
- Publication
IMA Journal of Numerical Analysis, 2023, Vol 43, Issue 3, p1519
- ISSN
0272-4979
- Publication type
Article
- DOI
10.1093/imanum/drac030