Efficient DG-SETD Method for Multiscale Nanostructures

An efficient discontinuous Galerkin spectral element time-domain(DG-SETD) method is proposed to calculate the electromagnetic scattering problem. Compared with the traditional continuous Galerkin time-domain spectral element method, the DG-SETD method discretizing the structure with small cell in the fine, irregular, high-dielectric-characteristic parts and coarse elements in the regular or simple smooth regions (e.g., air, PML, etc.)by nonconformal mesh, so the spatial discretization is more flexible. The upwind flux is introduced to ensure the continuity of the unknowns at the interface and the Gaussian integration is used to obtain the total surface integration. In addition, the proposed method adopts the Gauss-Lobatto-Legendre(GLL) basis function, which forms a mass matrix with orthogonal properties, so it can realize fast operations such as matrix multiplication and inverse. For-multi-scale complex electromagnetic models, the SETD method uses conformal-mesh for the entire region, which leads to a significant increase in the number of unknown quantities, prolonging the computation time, resulting in a waste of computational resources. In this case, the DG-SETD method uses non-conformal mesh splitting, which greatly reduces the number of cells and thus the number of unknown quantities, thus shortening the calculation time. At the same time, the use of fine dissection for fine regions ensures that the computational efficiency is improved without compromising the accuracy of the results. In this paper, the accuracy and efficiency of the above algorithm will be verified by calculating the scattering characteristics of a dispersive medium cube in the optical frequency band, providing a theoretical basis for calculating electromagnetic problems of multi-scale complex structures in the optical frequency band.