Annals of Mathematical Sciences and Applications

Volume 5 (2020)

Number 1

Mathematical sciences related to theoretical physics, engineering, biology and economics

Guest Editor: Tony Wen-Hann Sheu, National Taiwan University

Fast spectral solver for Poisson equation in an annular domain

Pages: 65 – 74

DOI: https://dx.doi.org/10.4310/AMSA.2020.v5.n1.a3

Authors

T.-S. Lin (Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan)

C.-Y. He (Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan)

W.-F. Hu (Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan)

Abstract

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 $O(NM \operatorname{log}_2 N)$ arithmetic operations.

Keywords

fast Fourier transform, ultraspherical spectral method, fast Poisson solver, annular domain

2010 Mathematics Subject Classification

65N35

Full Text (PDF format)

Received 20 August 2019

Accepted 28 October 2019

Published 27 February 2020