From multi-layered problems to multiple two-layered problems: a novel frequency-time hybrid multiple-scattering integral equation solver
Abstract
This paper proposes a novel frequency-time hybrid multiple scattering (FTH-MS) integral equation solver for time-dependent wave equation problems in general multi-layered media, with remarkable scalability with respect to the number of layers N. In light of the finite speed of wave propagation, the new methodology provides an innovative multiple-scattering idea of re-modeling the original N-layered problem into a sequence of N−1 two-layered sub-problems, for which the main advantages lie in that (i) each sub-problem enjoys much simpler wave scattering properties compared with the complicated problem in a multi-layered medium, (ii) it enables to develop high-accuracy solver utilizing Fourier transform and frequency-domain boundary integral equation (BIE) method; and (iii) numerical evaluation of the sub-problems in each multiple scattering step can be parallelized. Both multiplicative- and additive-type strategies are developed and equivalence results, which indicate that the M-th order multiple scattering sums can provide equivalent representations of the solutions up to a certain time T(M), are rigorously derived. Owing to the existed result of exponential convergence of the perfectly-matched-layer (PML) truncation for two-layered problem, all the sub-problems is numerically resolved by means of the FTH method based on the Fourier transform and the PML-BIE method whose numerical evaluation is addressed utilizing the Chebyshev-based rectangular-polar solver with high accuracy. Numerical examples are presented to validate the efficiency and accuracy of the proposed method.
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BibTeX
@misc{pan2026from,
title = {{From multi-layered problems to multiple two-layered problems: a novel frequency-time hybrid multiple-scattering integral equation solver}},
author = {Shuai Pan and Tao Yin and Lu Zhang},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30287},
eprint = {2608.30287},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30287},
}
RIS
TY - UNPB
TI - From multi-layered problems to multiple two-layered problems: a novel frequency-time hybrid multiple-scattering integral equation solver
AU - Shuai Pan
AU - Tao Yin
AU - Lu Zhang
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30287
UR - https://arxiv.org/abs/2608.30287
AB - This paper proposes a novel frequency-time hybrid multiple scattering (FTH-MS) integral equation solver for time-dependent wave equation problems in general multi-layered media, with remarkable scalability with respect to the number of layers N. In light of the finite speed of wave propagation, the new methodology provides an innovative multiple-scattering idea of re-modeling the original N-layered problem into a sequence of N−1 two-layered sub-problems, for which the main advantages lie in that (i) each sub-problem enjoys much simpler wave scattering properties compared with the complicated problem in a multi-layered medium, (ii) it enables to develop high-accuracy solver utilizing Fourier transform and frequency-domain boundary integral equation (BIE) method; and (iii) numerical evaluation of the sub-problems in each multiple scattering step can be parallelized. Both multiplicative- and additive-type strategies are developed and equivalence results, which indicate that the M-th order multiple scattering sums can provide equivalent representations of the solutions up to a certain time T(M), are rigorously derived. Owing to the existed result of exponential convergence of the perfectly-matched-layer (PML) truncation for two-layered problem, all the sub-problems is numerically resolved by means of the FTH method based on the Fourier transform and the PML-BIE method whose numerical evaluation is addressed utilizing the Chebyshev-based rectangular-polar solver with high accuracy. Numerical examples are presented to validate the efficiency and accuracy of the proposed method.
ER -