Localized Chebyshev collocation method for solving elliptic partial differential equations in arbitrary 2D domains

作者：

Highlights：

• Proposing a new framework for large-scale simulations of 2D boundary value problems.

• Chebyshev polynomials are employed to ensure the pseudo-spectral convergence of the new method.

• Numerical examples with up to 500,000 unknowns are solved successfully on a desktop computer without any difficulty .

摘要

•Proposing a new framework for large-scale simulations of 2D boundary value problems.•Chebyshev polynomials are employed to ensure the pseudo-spectral convergence of the new method.•Numerical examples with up to 500,000 unknowns are solved successfully on a desktop computer without any difficulty .

论文关键词：Meshless method,Chebyshev polynomials,Large-scale problem,Poisson equation,Helmholtz-type equation

论文评审过程：Received 18 August 2020, Revised 2 December 2020, Accepted 13 December 2020, Available online 12 January 2021, Version of Record 12 January 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2020.125903