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Simplified Boundary Knot Method with Ghost Points for High-Order Harmonic-Type PDEs

L. Liu

https://orcid.org/0009-0008-1392-7864

College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, P. R. China

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M. Lei

https://orcid.org/0000-0002-1900-3223

College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, P. R. China

E-mail Address: leimin@tyut.edu.cn

Corresponding author.

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J. H. Yue

https://orcid.org/0000-0002-0042-7376

College of Data Science, Taiyuan University of Technology, Taiyuan 030024, P. R. China

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, and

S. Q. Li

https://orcid.org/0000-0003-3325-1263

College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, P. R. China

E-mail Address: lisiqing@tyut.edu.cn

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https://doi.org/10.1142/S0219876223420112Cited by:0 (Source: Crossref)

This article is part of the issue:

Special Issue: Recent Advances in Computational Methods (ICCM 2023)
Guest Editor: Zhen Wang

Abstract

In this paper, a new approach named simplified boundary knot method with ghost points (SBKM-G) is proposed to improve the performance of SBKM in solving high-order harmonic-type partial differential equations (PDEs). In contrast to the traditional SBKM where the source points are coincident with the collocation nodes on the boundary, the SBKM-G removes the source/ghost nodes to an arbitrary area like a circle (sphere) which covers the original problem domain in 2D (3D). This modification leads to higher accuracy without sacrificing simplicity and efficiency. In addition, the effect of free parameters in SBKM-G has also been studied. Numerical examples in 2D and 3D show the superiority of SBKM-G to SBKM and the performance of SBKM-G in solving this type of high-order PDEs is highlighted.

This work is further developed based on the original work presented at ICCM 2023.

Keywords:

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