A multi-domain spectral collocation method for PDEs in curved domains with holes

Chuan Wang, Zhongqing Wang and Chao Zhang

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 239, issue C, 629-645

Abstract: This paper presents a novel spectral collocation method that combines domain decomposition and mapping techniques for solving second-order elliptic equations with variable coefficients, as well as time-dependent advection–diffusion–reaction equations in a curved domain with holes. The process begins by partitioning the curved domain with holes into several subdomains. Each subdomain is then mapped to a regular domain through a polar coordinate transformation. Following this, linear transformations are applied to map these subdomains onto the reference element (−1,1)×(−1,1). Numerical simulations are performed on each reference element using the classical spectral collocation method. The numerical results demonstrate the high accuracy of the proposed approach.

Keywords: Second-order elliptic equations; Advection–diffusion–reaction equations; Curved domains with holes; Coordinate transformations; Multi-domain spectral collocation method (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:239:y:2026:i:c:p:629-645

DOI: 10.1016/j.matcom.2025.07.017

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