The Improved Element-Free Galerkin Method for 3D Helmholtz Equations

Heng Cheng and Miaojuan Peng
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Heng Cheng: School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, China
Miaojuan Peng: Department of Civil Engineering, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200444, China

Mathematics, 2021, vol. 10, issue 1, 1-20

Abstract: The improved element-free Galerkin (IEFG) method is proposed in this paper for solving 3D Helmholtz equations. The improved moving least-squares (IMLS) approximation is used to establish the trial function, and the penalty technique is used to enforce the essential boundary conditions. Thus, the final discretized equations of the IEFG method for 3D Helmholtz equations can be derived by using the corresponding Galerkin weak form. The influences of the node distribution, the weight functions, the scale parameters of the influence domain, and the penalty factors on the computational accuracy of the solutions are analyzed, and the numerical results of three examples show that the proposed method in this paper can not only enhance the computational speed of the element-free Galerkin (EFG) method but also eliminate the phenomenon of the singular matrix.

Keywords: improved element-free Galerkin method; Helmholtz equation; penalty method; improved moving least-squares approximation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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