环域泊松方程的快速谱解

IF 0.4 Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Annals of Mathematical Sciences and Applications Pub Date : 2020-01-01 DOI:10.4310/amsa.2020.v5.n1.a3

Te-Sheng Lin, C-Y. He, Wei-Fan Hu

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引用次数: 0

摘要

提出了一种简单有效的求解环域泊松方程的谱法。求解器依赖于傅里叶展开，其中傅里叶系数的微分方程是用超球面光谱方法求解的。对于极方向有N个网格点，径向有M个网格点的域，求解器只需要O (NM log 2 N)次算术运算。

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Fast spectral solver for Poisson equation in an annular domain

A simple and eﬃcient spectral method is formulated to solve Poisson equation in an annular domain. The solver relies on the Fourier expansion, where the diﬀerential equations for the Fourier coeﬃcients are solved using an ultraspherical spectral method. For a domain with N grid points in the polar direction and M grid points in the radial direction, the solver only requires O ( NM log 2 N ) arith-metic operations.

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Annals of Mathematical Sciences and Applications MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

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