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A perfectly matched layer-boundary integral equation method for wave scattering in a two-layer medium of a step-like
Wangtao Lu1,2, Zhilin Li2
1Center for Interdisciplinary Applied Mathematics, Zhejiang University, Hangzhou, Zhejiang, People's Republic of China.
Summary
This study introduces a novel method for analyzing wave scattering in a two-layer medium with a step-like interface. The approach ensures accurate radiation behavior analysis using a transition curve and perfectly matched layers (PML).
Area of Science:
- Computational Electromagnetics
- Wave Scattering Theory
- Numerical Analysis
Background:
- Wave scattering in layered media presents challenges in characterizing scattered fields at infinity.
- Step-like interfaces in two-layer media complicate the analysis of reflected and transmitted waves.
Purpose of the Study:
- To develop a robust method for analyzing wave scattering in a two-layer medium with a step-like interface.
- To accurately model the radiation behavior of scattered fields satisfying the Sommerfeld radiation condition.
- To introduce a numerical solver for wave scattering problems in complex layered media.
Main Methods:
- Introduction of a transition curve to define outgoing waves satisfying the Sommerfeld radiation condition.
- Utilization of a uniaxial perfectly matched layer (PML) for wave truncation.
- Derivation of boundary integral equations (BIEs) using PML-transformed Green's functions.
- Discretization of BIEs with high-accuracy quadrature and assembly into a linear system.
Main Results:
- The proposed method effectively handles wave scattering from step-like interfaces in two-layer media.
- Numerical experiments validate the accuracy of the Sommerfeld radiation condition and the proposed solver.
- The approach accurately approximates the outgoing wave behavior.
Conclusions:
- The developed technique provides a valid and accurate solution for wave scattering problems in layered media with complex interfaces.
- The integration of transition curves and PML offers a powerful tool for computational electromagnetics.
- This work advances the understanding and numerical treatment of wave phenomena in stratified media.
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