2021
DOI: 10.3390/math10010014
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The Improved Element-Free Galerkin Method for 3D Helmholtz Equations

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 parameter… Show more

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Cited by 10 publications
(3 citation statements)
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“…It is found that the motion trajectory of the internal store will change at different time under the same launch conditions, which is caused by the unsteady flow field of the internal bay. Some scholars [7][8][9][10][11][12] have studied the hybrid complex variable element-free Galerkin (HCVEFG) method, which can improve computational efficiency. The research of Westmoreland [13] showed that applying appropriate ejection force to the store is conducive to the separation.…”
Section: Introductionmentioning
confidence: 99%
“…It is found that the motion trajectory of the internal store will change at different time under the same launch conditions, which is caused by the unsteady flow field of the internal bay. Some scholars [7][8][9][10][11][12] have studied the hybrid complex variable element-free Galerkin (HCVEFG) method, which can improve computational efficiency. The research of Westmoreland [13] showed that applying appropriate ejection force to the store is conducive to the separation.…”
Section: Introductionmentioning
confidence: 99%
“…The MLS approximate functions have been improved to accelerate computational speed, including the Improved Moving Least-Squares (IMLS) approximation [6], interpolating MLS approximation [7,8], and complex variable MLS approximation [9,10]. Using these methods to construct shape functions resulted in the presentation of the IEFG method [11][12][13][14], interpolating EFG method [15][16][17][18][19][20], and complex variable EFG method [10,21,22], respectively.…”
Section: Introductionmentioning
confidence: 99%
“…The improved element-free Galerkin (IEFG) method [1], which is based on the improved moving least-squares (IMLS) approximation [2], is an important meshless method. In the paper submitted to this Special Issue by Cheng et al [3], the IEFG method for solving three-dimensional (3D) Helmholtz equations is proposed. The IMLS approximation is used to form the trial function, the penalty method is used to enforce the essential boundary conditions and Galerkin weak form of 3D Helmholtz equations are used to obtain the final discretized equations.…”
mentioning
confidence: 99%