2D Efficient Unconditionally Stable Meshless FDTD Algorithm

Abstract

This paper presents an efficient weighted Laguerre polynomials based meshless finite-difference time domain (WLP-MFDTD). By decomposing the coefficients of the system matrix and adding a perturbation term, a factorization-splitting scheme is introduced. The huge sparse matrix is transformed into two N×N matrices with 9 unknown elements in each row regardless of the duplicated ones. Consequently, compared with the conventional implementation, the CPU time and memory requirement can be saved greatly. The perfectly matched layer absorbing boundary condition is also extended to this approach. A numerical example demonstrates the capability and efficiency of the proposed method.

ADI-MRTD Algorithm for Periodic Structures Analysis

“…Furthermore, the alternating direction implicit finite-difference time-domain (ADI-FDTD) method incorporates the advantages of both the explicit and implicit formats, namely, relatively simple calculation and unconditional stability [8]. Although the weighted Laguerre polynomials based spectral finite-difference time-domain (WLP-SFDTD) scheme for periodic structure analysis is efficient, solving the correspondingly huge banded system matrix is time-consuming [9]. One has to use the sparse lower-upper (LU) factorization packages or add a perturbation term.…”