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# Numerical Modelling of Electromagnetic Wave Propagation by Meshless Local Petrov-Galerkin Formulations

Delﬁm Soares Jr. 1
Faculty of Engineering, Federal University of Juiz de Fora, Cidade Universitária, CEP 36036-330, Juiz de Fora, MG, Brazil. Tel: +55 32 2102-3468; E-mail: delﬁm.soares@ufjf.edu.br

Computer Modeling in Engineering & Sciences 2009, 50(2), 97-114. https://doi.org/10.3970/cmes.2009.050.097

### Abstract

In this work, meshless methods based on the local Petrov-Galerkin (MLPG) approach are presented to analyse electromagnetic wave propagation problems. Formulations adopting the Heaviside step function and the Gaussian weight function as the test functions in the local weak form are considered. The moving least square (MLS) method is used to approximate the physical quantities in the local integral equations. After spatial discretization is carried out, a system of ordinary differential equations of second order is obtained. This system is solved in the time-domain by the Houbolt's method, allowing the computation of the so-called primary fields (either the electric or the magnetic field can be selected as the primary field; the complementary field is here referred to as secondary field). The secondary field is obtained following Maxwell's equations, i.e., considering space derivatives of the primary field and time integration procedures. This methodology is more efficient and flexible since fewer systems of equations must be solved along the analysis. At the end of the paper, numerical applications illustrate the accuracy and potentialities of the proposed techniques.

### Keywords

Meshless Local Petrov-Garlekin, Moving Least Square Interpolation, Maxwell's Equations, Wave Propagation Problems, Time-Domain Analysis, Electromagnetic Fields.

### Cite This Article

Jr., D. S. (2009). Numerical Modelling of Electromagnetic Wave Propagation by Meshless Local Petrov-Galerkin Formulations. CMES-Computer Modeling in Engineering & Sciences, 50(2), 97–114.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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