Keywords: electromagnetic metamaterials, topology optimization, binary particle swarm optimization, finite element method..

This paper presents a particle swarm optimization-based topology optimization method for the design of negative permeability dielectric metamaterials. As the electromagnetic metamaterials have some physical properties not available in nature, they have attracted a significant scientific research interest for decades. In fact, electromagnetic metamaterials can exhibit simultaneously negative permeability and negative permittivity. The aim of the work, described in this paper, is to find an optimal topology of a dielectric metamaterial that achieves negative permeability at a given frequency. A binary particle swarm optimization is developed and applied to a negative permeability dielectric metamaterial topology design problem.

The optimization process is achieved using a developed numerical model of the studied metamaterial, which is solved by the finite element method.

First, a review of the literature concerning the electromagnetic metamaterials and the particle swarm optimization algorithm is presented. Secondly, the governing equations and the weak formulation of the electromagnetic problem are presented. Then, the optimization problem to be solved is formulated. The binary particle swarm optimization method and the developed interfacing method are explained. A numerical example is presented to demonstrate that the binary particle swarm optimization is adapted to the topology optimization of negative permeability dielectric metamaterials at given frequencies, to agree the utility and validity of the presented method.

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