Complex variable element-free Galerkin method for Helmholtz equations with variable wave numbers

Jiao Zhang; Zebin Xing; Heng Cheng

doi:10.1117/12.3025915

8 April 2024 Complex variable element-free Galerkin method for Helmholtz equations with variable wave numbers

Jiao Zhang, Zebin Xing, Heng Cheng

Proceedings Volume 13090, International Conference on Computer Application and Information Security (ICCAIS 2023); 1309028 (2024) https://doi.org/10.1117/12.3025915
Event: International Conference on Computer Application and Information Security (ICCAIS 2023), 2023, Wuhan, China

Abstract

This study introduces complex variable element-free Galerkin (CVEFG) method to analyze Helmholtz equation with variable wave numbers. Approximation functions are established by applying complex variable moving least-squares (CVMLS) approximation, thus Lagrange multiplier method is chosen for the enforcement of Dirichlet boundary condition. As a result, ultimate solution equation for CVEFG method applied to 2D Helmholtz equation is obtained through the utilization of the corresponding Galerkin weak form. The astringency of CVEFG method is examined in numerical examples through an analysis of the impact of nodes on relative errors. And CVEFG method has high accuracy and speed.

(2024) Published by SPIE. Downloading of the abstract is permitted for personal use only.

Citation Download Citation

Jiao Zhang, Zebin Xing, and Heng Cheng "Complex variable element-free Galerkin method for Helmholtz equations with variable wave numbers", Proc. SPIE 13090, International Conference on Computer Application and Information Security (ICCAIS 2023), 1309028 (8 April 2024); https://doi.org/10.1117/12.3025915

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