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Received Oct 23, 2017; Revised Dec 22, 2017; Accepted Jan 23, 2018
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1. Introduction
Computational electromagnetics is a science, which spans many subjects. It is an organic combination of mathematical theory, electromagnetic theory, and computer science. Electromagnetism is the classical dynamics theory. Electromagnetic phenomena are also closely related to eigenvalue problems and essentially can be deduced by Maxwell eigenvalue equation. The typical eigenvalue problem of the electromagnetic field is the resonant problem of the cavity and the guide wave problem of the waveguide. No matter the resonance problem of closed cavity, or the propagation problem of uniform guided waves, the wave equation is homogeneous without considering any source or field excitation process. For simplification, the conductors that constitute the cavity are idealized. So the field satisfies the homogeneous boundary condition on the boundary. There are many methods for solving computational electromagnetics, such as finite difference method and finite element method; see literatures [1–7] for details. In recent years, various methods in computational electromagnetics have been continuously improved. However, the input data are usually affected by many uncertain factors, such as the environment, which often results in the difference between calculation and measurement. So, we consider establishing a new model to solve some related electromagnetics problems. This is also the motivation of this paper.
Among the optimization model, as we all know, the eigenvalue complementarity problem arises from several important applications in engineering and physics, such as the study of the resonance frequency and the stability of dynamic systems. In the last few years, the eigenvalue complementarity problem has drawn increasing attention, in many literature systems, such as [8–13] and the references therein. Among them, in [8], the authors study an eigenvalue complementarity problem and find its origins in the solution of a contract problem in mechanics. In [9], the eigenvalue complementarity problems with symmetric real matrices are considered. The authors transform this problem into a differentiable optimization program involving the Rayleigh quotient on a simplex and find its stationary point by the spectral projected gradient algorithm. In [10–13], many methods are proposed to solve the...