Numerical Solution of Maxwell Equations Using Local Weak Form Meshless Techniques

Volume 13, Issue 2, pp 168-185 http://dx.doi.org/10.22436/jmcs.013.02.08

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Authors

S. Sarabadan - Department of Mathematics, Imam Hossein University, P.O. Box 16895-198, Tehran, Iran. M. Shahrezaee - Department of Mathematics, Imam Hossein University, P.O. Box 16895-198, Tehran, Iran. J. A. Rad - Department of Computer Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, Evin, P.O. Box 198396-3113,Tehran,Iran. K. Parand - Department of Computer Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, Evin, P.O. Box 198396-3113,Tehran,Iran.

Abstract

The aim of this work is to propose a numerical approach based on the local weak formulations and finite difference scheme to solve the Maxwell equation, especially in this paper we select and analysis local radial point interpolation (LRPI) based on multiquadrics radial basis functions (MQ-RBFs). LRPI scheme is the truly meshless method, because, a traditional non-overlapping, continuous mesh is not required, either for the construction of the shape functions, or for the integration of the local sub-domains. These shape functions which are constructed by point interpolation method using the radial basis functions have delta function property which allows one to easily impose essential boundary conditions. One numerical example is presented showing the behavior of the solution and the efficiency of the proposed method.

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Keywords

• Meshless weak form
• Maxwell equation
• Finite differences
• Local radial point interpolation.

MSC

•  35Q61
•  74S30
•  65M99

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