Unsplit complex frequency shifted perfectly matched layer for second-order wave equation using auxiliary differential...

Area of Science:

• Computational Electromagnetics
• Wave Propagation Modeling

Background:

• Traditional Perfectly Matched Layers (PML) and Complex Frequency Shifted PML (CFS-PML) are primarily designed for first-order wave equations.
• These existing methods exhibit limitations when applied to second-order wave equations, particularly for absorbing waves at nearly grazing incidence.

Purpose of the Study:

• To develop and implement an effective CFS-PML for second-order wave equations.
• To address the limitations of existing PML techniques in handling nearly grazing incident waves in second-order formulations.

Main Methods:

• An auxiliary differential equation approach is utilized for the implementation of CFS-PML.
• The proposed method avoids computationally intensive convolution calculations and third-order temporal derivatives.
• It is presented as an unsplit CFS-PML, simplifying the numerical scheme.

Main Results:

• The implemented CFS-PML demonstrates superior absorbing performance compared to conventional PML methods for second-order wave equations.
• Numerical experiments validate the effectiveness of the proposed technique in reducing reflections for nearly grazing incident waves.
• The method successfully handles second-order wave equations without requiring convolution or higher-order derivatives.

Conclusions:

• The developed unsplit CFS-PML is a robust and efficient method for second-order wave equations.
• This technique significantly improves the absorption of waves, particularly at challenging nearly grazing incidence angles.
• The findings offer a valuable advancement for electromagnetic wave simulations involving complex geometries and incidence conditions.