Stability analysis and discretization of A-Φ time domain integral equations for multiscale electromagnetics

• Published in: Journal of computational physics 2020-05, Vol.408, p.109102, Article 109102
• Main Authors: Roth, Thomas E., Chew, Weng C.
• Format: Article
• Language: English
• Subjects: Computational physics; Discretization; Electromagnetics; Integral equations; Mathematical analysis; Quantum theory; Solvers; Stability analysis; Time domain analysis; Time domain integral equations
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2019.109102

•Time domain integral equation stability depends on the integral's domain and range.•New electromagnetic potential-based time domain integral equations are derived.•Potential-based time domain integral equations are suitable for multiscale systems.•New equations can be more easily coupled to quantum physics calculations. The growth of applications at the intersection between electromagnetic and quantum physics is necessitating the creation of novel computational electromagnetic solvers. This work presents a new set of time domain integral equations (TDIEs) formulated directly in terms of the magnetic vector and electric scalar potentials that can be used to meet many of the requirements of this emerging area. Stability for this new set of TDIEs is achieved by leveraging an existing rigorous functional framework that can be used to determine suitable discretization approaches to yield stable results in practice. The basics of this functional framework are reviewed before it is shown in detail how it may be applied in developing the TDIEs of this work. Numerical results are presented which validate the claims of stability and accuracy of this method over a wide range of frequencies where traditional methods would fail.