Spectral Methods for Partial Differential Equations in Irregular Domains: The Spectral Smoothed Boundary Method

Details Spectral Methods for Partial Differential Equations in Irregular Domains: The Spectral Smoothed Boundary Method Spectral Methods for Partial Differential Equations in Irregular Domains: The Spectral Smoothed Boundary Method

2004-06-16

arxiv.org/abs/math/0406327v1

Mathematics

Numerical Analysis

15 pages, 11 figures

Scientific paper

In this paper, we propose a numerical method to approximate the solution of partial differential equations in irregular domains with no-flux boundary conditions by means of spectral methods. The main features of this method are its capability to deal with domains of arbitrary shape and its easy implementation via Fast Fourier Transform routines. We discuss several examples of practical interest and test the results against exact solutions and standard numerical methods.

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