کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4641525 | 1341311 | 2009 | 17 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Spectral domain embedding for elliptic PDEs in complex domains Spectral domain embedding for elliptic PDEs in complex domains](/preview/png/4641525.png)
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.
Journal: Journal of Computational and Applied Mathematics - Volume 225, Issue 2, 15 March 2009, Pages 541–557