Multiscale Structure Simulation Using Adaptive Mesh in DGTD Method

Abstract

This paper presents an adaptive mesh methodology to construct simulation source which has unlimited spectrum coverage for the discontinuous Galerkin time-domain (DGTD) method. The limitation of grid size (i.e., λ/20) for the construction of time-domain signal is relaxed by using a nonuniform sampling technique. The excitation source is modeled by using a standard gauss pulse with a nonuniform sampling rate. The modeling is tested for broadband spectrum coverage of up to hypothetical frequencies (e.g., X-ray: $\text{10}^{\text{18}}$ Hz and Gamma-ray: $\text{10}^{\text{20}}$ Hz). The problem of memory for dealing with such a high frequency during fast Fourier transform (FFT) analysis is resolved by reducing the number of points used for calculating the FFT. Then, multiscale structures composed of contrasting thicknesses (small thickness and ultrasmall thickness with wide thickness) are analyzed for the input reflection coefficients up to 10 GHz. The improvement in computational resources of the adaptive mesh techniques in terms of execution time is compared with that of the uniform mesh technique. The adaptive mesh technique uses an optimal number of finite elements for the discretization of the computational domain, hence, saving plenty of time while finding the numerical solutions. The whole analysis is performed by using the DGTD method in one dimension and the truncation of the boundary for the normally incident wave is achieved by employing the first-order Silver-Muller absorbing boundary condition (SM-ABC).