Fast global spectral methods for three-dimensional partial differential equations
| Autor: | Christoph Strössner, Daniel Kressner |
|---|---|
| Rok vydání: | 2022 |
| Předmět: |
linear-systems
Applied Mathematics General Mathematics solvers Numerical Analysis (math.NA) 65N35 35C11 47A80 65F05 65N25 65M70 wave-propagation simulation Computational Mathematics numerical-solution automatic solution FOS: Mathematics Mathematics - Numerical Analysis helmholtz-equation approximation least-squares porous-media |
| Zdroj: | IMA Journal of Numerical Analysis. |
| ISSN: | 1464-3642 0272-4979 |
| DOI: | 10.1093/imanum/drac030 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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