Engineering with Computers

, Volume 33, Issue 4, pp 897–918 | Cite as

The local radial point interpolation meshless method for solving Maxwell equations

  • Mehdi DehghanEmail author
  • Mina Haghjoo-Saniji
Original Article


The Maxwell equations are basic equations of electromagnetic. In this paper we employed ADI–LRPIM (alternative direction implicit method is applied for approximating the time variable and the local radial point interpolation meshless method is used for space variable) to solve the two-dimensional time dependent Maxwell equations. This method consists of two stages for each time step implemented in alternative directions which are simple in computations. Local radial point interpolation method is a type of meshless method which uses a set of nodes scattered within the domain of the problem as well as a set of nodes scattered on the boundaries of the domain instead of using a predefined mesh to represent the problem domain and its boundaries, this feature makes, LRPIM to be flexible. Also it produces acceptable results for solving many partial differential equations. The proposed method is accurate and efficient, these features are illustrated by solving numerical examples in transverse magnetic and transverse electric fields. We used a kind of finite difference scheme for approximation of derivative terms in main relations to reduce errors and computational cost and eliminate integrals of weak form on internal boundaries by suitable selection of test function.


Time-dependent partial differential equation Maxwell equations Meshless method and local weak form Local radial point interpolation method (LRPIM) Radial basis functions Alternative direction implicit (ADI) method 



The authors thank one of the reviewers for his useful comments. Also authors would like to thank Mostafa Abbaszadeh for his useful suggestions and nice comments that improved the paper.


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Copyright information

© Springer-Verlag London 2017

Authors and Affiliations

  1. 1.Department of Applied Mathematics, Faculty of Mathematics and Computer SciencesAmirkabir University of TechnologyTehranIran

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