Finite Difference preconditioning for compact scheme discretizations of the Poisson equation with variable coefficients

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:379

Article

Abide, Stephane¹ 

[1] Univ Perpignan, LAMPS EA 4217, Via Domitia, Perpignan, France

关键词: Compact schemes;    Poisson's equation;    Preconditioned Richardson method;   

DOI  :  10.1016/j.cam.2020.112872

来源: Elsevier

【 摘 要 】

The finite difference preconditioning for higher-order compact scheme discretizations of non separable Poisson's equation is investigated. An eigenvalue analysis of a one-dimensional problem is detailed for compact schemes up to the tenth-order. The analysis concludes that the spectrum is bounded irrespective of the mesh size and the continuous variable coefficient. Hence, combined to a multigrid method, the preconditioned Richardson method shows a convergence rate which is independent from the mesh size and the variable coefficient. Several numerical experiments, including the simulation of a flow with large density variations, confirm that the spectrum of the preconditioned operator remains bounded. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

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