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

2004/06/16 by Alfonso Bueno‐Orovio, Víctor M. Pérez‐García, Bueno-Orovio, Alfonso +3 · 4 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.math/0406327

openalex publication_date 2004/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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