"云计算中波导计算的新方法：改进束传播法及其应用"

The research paper "An Improvement to the Beam Propagation Method in Waveguide Computing" explores the challenges of wave propagation in various fields such as acoustics, electromagnetics, and seismology, where the distribution of wave fields needs to be calculated over an area much larger than the wavelength. In cases where the wave number is strongly dependent on the direction of propagation, such as in the transmission of lasers and the design of optical instruments, there is a need for improved algorithms to address these issues. Building upon previous research, this paper presents a better approximation of the DtN operator Q, leading to a more efficient algorithm. The main contributions include discussing the numerical solution of the two-dimensional Helmholtz equation model for wave propagation and exploring modern methods for solving large-scale waveguide problems. By utilizing the Riccati equation satisfied by the DtN operator Q, a new and more precise improvement to the Beam Propagation Method (BPM) is proposed, which does not impose restrictions on the wave number and can satisfy scattering boundary conditions. The new algorithm directly employs rational Pade approximations of exponential operator functions to obtain approximate solutions, significantly reducing computational and storage requirements while achieving more accurate results. It is an effective approach for solving large-scale waveguide problems. Furthermore, by introducing Perfectly Matched Layers (PML), the new algorithm can also handle waveguide problems in unbounded domains. Keywords: Helmholtz equation, Riccati method, one-way waveguide, Beam Propagation Method Overall, this research paper presents a novel approach to improving the Beam Propagation Method for waveguide computing, addressing the challenges of large-scale wave propagation problems and offering a more efficient and accurate algorithm for various applications.