Developing a leap-frog meshless methods with radial basis functions for modeling of electromagnetic concentrator

Bin He; Bin He

doi:10.3934/math.2022943

AIMS Mathematics

2022, Volume 7, Issue 9: 17133-17149. doi: 10.3934/math.2022943

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Research article

Developing a leap-frog meshless methods with radial basis functions for modeling of electromagnetic concentrator

Bin He ^,

Department of Mathematics, Lanzhou Jiaotong University Lanzhou, Gansu 730070, China

Received: 14 June 2022 Revised: 07 July 2022 Accepted: 12 July 2022 Published: 21 July 2022
MSC : 35L05

The main goal of this paper is to develop a fast and effective meshless method by using radial basis function (RBF) for the time domain model equations of electromagnetic wave concentration device. This is mainly because the complex model equations involve different partial differential equations in different subdomains, which makes the meshless method very attractive and also very challenging. In order to simulate the propagation of electromagnetic waves in the electromagnetic concentrator, perfect matching layer technology was used to reduce an unbounded domain problem into a bounded domain problem. Borrowing the idea of the leap-frog finite-difference time-domain scheme, I develop the leap-frog RBF meshless method to solve the coupled complex modeling equations. The numerical results obtained by using a multiquadric RBF and Gaussian RBF demonstrate that our RBF method is very effective.
- time domain Maxwell equations,
- metamaterial,
- radial basis function,
- meshless methods
Citation: Bin He. Developing a leap-frog meshless methods with radial basis functions for modeling of electromagnetic concentrator[J]. AIMS Mathematics, 2022, 7(9): 17133-17149. doi: 10.3934/math.2022943

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Abstract

The main goal of this paper is to develop a fast and effective meshless method by using radial basis function (RBF) for the time domain model equations of electromagnetic wave concentration device. This is mainly because the complex model equations involve different partial differential equations in different subdomains, which makes the meshless method very attractive and also very challenging. In order to simulate the propagation of electromagnetic waves in the electromagnetic concentrator, perfect matching layer technology was used to reduce an unbounded domain problem into a bounded domain problem. Borrowing the idea of the leap-frog finite-difference time-domain scheme, I develop the leap-frog RBF meshless method to solve the coupled complex modeling equations. The numerical results obtained by using a multiquadric RBF and Gaussian RBF demonstrate that our RBF method is very effective.

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