A Hybrid Chebyshev Pseudo-Spectral Finite-Difference Time-Domain Method for Numerical Simulation of 2D Acoustic Wave Propagation

Abstract

In this study, a hybrid Chebyshev pseudo-spectral finite-difference time-domain (CPS-FDTD) algorithm is proposed for simulating 2D acoustic wave propagation in heterogeneous media, which is different from the other traditional numerical schemes such as finite element and finite difference. This proposed hybrid method integrates the efficiency of the FDTD approach in the time domain and the high accuracy of the CPS technique in the spatial domain. We present the calculation formulas of this novel approach and conduct simulation experiments to test it. The biconjugate gradient is solved by combining the large symmetric sparse systems stabilized algorithm with an incomplete LU factorization. Three numerical experiments are further presented to illustrate the accuracy, efficiency, and flexibility of the hybrid CPS-FDTD algorithm.

Accurate Nonstandard Path Integral Models for Arbitrary Dielectric Boundaries in 2-D NS-FDTD Domains

“…Therefore, the discrete space treatment is unsuitable for realistic problems with arbitrarily shaped objects and fine details, not aligned to the grid axes [4,5,[7][8][9][10][11], owing to the use of the insufficient staircase approximation on orthogonal grids in an effort to model the realistic object under study. Such structures can be, frequently, encountered in various applications, ranging from electromagnetic compatibility configurations [12][13][14] and microwave devices [15][16][17] to antennas [18][19][20], optical arrangements [21][22][23][24][25], and designs of low observability, including RCS scenarios. To circumvent such a drawback, a path integral (PI) model, based on the path integral form of Ampere's and Faraday's laws, has been previously presented [26][27][28].…”