Spectral domain embedding for elliptic PDEs in complex domains

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:225

Article

Lui, S. H.

关键词: Spectral method;    Spectral collocation;    Pseudospectral method;    Irregular domain;    Fictitious domain;    Domain embedding;   

DOI  :  10.1016/j.cam.2008.08.034

来源: Elsevier

【 摘 要 】

Spectral methods are a class of methods for solving partial differential equations (PDEs). When the solution of the PDE is analytic, it is known that the spectral solutions converge exponentially as a function of the number of modes used. The basic spectral method works only for regular domains such as rectangles or disks. Domain decomposition methods/spectral element methods extend the applicability of spectral methods to more complex geometries. An alternative is to embed the irregular domain into a regular one. This paper uses the spectral method with domain embedding to solve PDEs on complex geometry. The running time of the new algorithm has the same order as that for the usual spectral collocation method for PDEs on regular geometry. The algorithm is extremely simple and can handle Dirichlet, Neumann boundary conditions as well as nonlinear equations. (c) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

Free