Simulation Analysis of Electrostatic Field Based on Localized Method of Fundamental Solutions

doi:10.19596/j.cnki.1001-246x.8308

Abstract

Abstract:

Localized method of fundamental solutions is applied to the simulation and analysis of electrostatic field problems. The localized method of fundamental solutions is a meshless algorithm based on local theory and moving least square approximation, which uses fundamental solution of the governing equation. Compared with traditional mesh-type methods such as finite element method and finite difference method, this method needs discrete nodes only, and avoids troublesome mesh generation. As a semi-analytical numerical technique, fundamental solutions of physical problems are used as interpolation basis functions to establish a numerical discrete model, thus ensuring high accuracy of the algorithm. In addition, compared with meshless methods with global discretization scheme, the local fundamental method is more suitable for high-dimensional complex geometry and large-scale simulation. Two- and three-dimensional numerical tests show that this method is convenient, flexible, accurate and fast. It is a new way for electrostatic field simulation. It expands application of localized method of fundamental solutions.

Key words: localized method of fundamental solutions, meshless method, electrostatic field, fundamental solution

CLC Number:

TM151

Chao WANG, Fajie WANG, Yan GU, Xiao WANG. Simulation Analysis of Electrostatic Field Based on Localized Method of Fundamental Solutions[J]. Chinese Journal of Computational Physics, 2021, 38(5): 612-622.

Figures/Tables 16

Fig.1 Schematic of the LMFS for boundary value problem of electrostatic field (a) distribution of nodes; (b) local subdomain

Fig.2 Model of rectangular grounding metal slot

Fig.3 Nodal distribution of the LMFS (a) regular nodal distribution; (b) irregular nodal distribution

Fig.4 Error curves of the LMFS with respect to the number of supporting nodes, under regular and irregular nodal distributions

Fig.5 Error curves of the LMFS with respect to the number of total nodes, under regular and irregular nodal distributions

Fig.6 Exact solution and numerical error of electric potential in the computational domain (a) exact solution; (b) absolute error

Fig.7 Calculation times of LMFS, GFDM and MFS with respect to the total number of nodes

Fig.8 Global errors of LMFS, GFDM and MFS with respect to the total number of nodes

Table 1 Computational errors of MFS, LMFS and GFDM with distrubance

s/%	MFS	LMFS	GFDM
0	2.881×10^-13	3.057×10^-9	9.355×10^-6
1	7.431×10^-3	1.386×10^-3	7.576×10^-3
3	1.966×10^-2	7.725×10^-3	1.593×10^-2
5	4.117×10^-2	8.575×10^-3	4.670×10^-2

Fig.9 Mesh distribution of the FEM

Fig.10 Nodal distribution of the LMFS

Fig.11 Electric potential distributions (a) results of FEM; (b) results of FEM; (c) distribution of relative deviation

Fig.12 An S-shape pipe model

Fig.13 Distribution of FEM mesh

Fig.14 Electric potential simulation results (a) FEM; (b) N=5 443; (c) N=7 649; (d) N=13 375

Table 2 Numerical results obtained with FEM, LMFS and GFDM

坐标	FEM	LMFS	LMFS偏差/10^-3	GFDM	GFDM偏差/10^-2
(0.07, 0, 0)	1.982 01	1.976 05	3.01	1.934 52	2.40
(0.2, 0, 0)	3.871 22	3.863 86	1.90	3.769 14	2.64
(0.3, 0.1, 0)	5.339 76	5.355 57	2.96	5.314 81	0.467
(0.4, 0.2, 0)	7.359 71	7.389 45	4.04	7.885 56	7.14
(0.5, 0.2, 0)	8.563 52	8.578 86	1.79	8.893 10	3.85

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