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A Study of Boundary Conditions in the Meshless Local Petrov-Galerkin (MLPG) Method for Electromagnetic Field Computations

Meiling Zhao1, Yufeng Nie2
Department of Mathematics, Beijing University of Aeronautics & Astronautics, Beijing, 100083, P. R. China.
Department of Applied Mathematics, Northwestern Polytechnic University, Xi’an, Shaanxi, 710072, P. R. China.

Computer Modeling in Engineering & Sciences 2008, 37(2), 97-112.


Meshless local Petrov-Galerkin (MLPG) method is successfully applied for electromagnetic field computations. The moving least square technique is used to interpolate the trial and test functions. More attention is paid to imposing the essential boundary conditions of electromagnetic equations. A new coupled meshless local Petrov-Galerkin and finite element (MLPG-FE) method is presented to enforce the essential boundary conditions. Unlike the conventional coupled technique, this approach can ensure the smooth blending of the potential variables as well as their derivatives in the transition region between the meshless and finite element domains. Then the boundary singular weight method is proposed to enforce the boundary conditions for electromagnetic field equations accurately. Practical examples in engineering, including the computations of the electric-field intensity of the cross section of long straight metal slot, the end region of a power transformer and axisymmetric problem in the electromagnetic field, are solved by the presented approaches. All numerical verification and all kinds of comparison analysis show that the MLPG method is a promising alternative numerical approach for electromagnetic field computations, and the proposed techniques can be good candidates for imposing essential boundary conditions.


Meshless local Petrov-Galerkin (MLPG) method, electromagnetic field computation, essential boundary, coupled method.

Cite This Article

Zhao, M., Nie, Y. (2008). A Study of Boundary Conditions in the Meshless Local Petrov-Galerkin (MLPG) Method for Electromagnetic Field Computations. CMES-Computer Modeling in Engineering & Sciences, 37(2), 97–112.

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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