Stability analysis and discretization of A–$Φ$ time domain integral equations for multiscale electromagnetics
Abstract
The growth of applications at the intersection between electromagnetic and quantum physics is necessitating the creation of novel computational electromagnetic solvers. Work in this paper 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.
 Authors:

 Sandia National Lab. (SNLNM), Albuquerque, NM (United States); Univ. of Illinois at UrbanaChampaign, IL (United States)
 Univ. of Illinois at UrbanaChampaign, IL (United States); Purdue Univ., West Lafayette, IN (United States)
 Publication Date:
 Research Org.:
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF)
 OSTI Identifier:
 1595015
 Alternate Identifier(s):
 OSTI ID: 1691938
 Report Number(s):
 SAND201914970J
Journal ID: ISSN 00219991; 682269
 Grant/Contract Number:
 AC0494AL85000; ECCS169195; NA0003525; AF Sub RRI PO0539
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 408; Journal Issue: C; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Electromagnetics; Time domain integral equations; Stability analysis
Citation Formats
Roth, Thomas E., and Chew, Weng C. Stability analysis and discretization of A–$Φ$ time domain integral equations for multiscale electromagnetics. United States: N. p., 2019.
Web. doi:10.1016/j.jcp.2019.109102.
Roth, Thomas E., & Chew, Weng C. Stability analysis and discretization of A–$Φ$ time domain integral equations for multiscale electromagnetics. United States. doi:10.1016/j.jcp.2019.109102.
Roth, Thomas E., and Chew, Weng C. Sat .
"Stability analysis and discretization of A–$Φ$ time domain integral equations for multiscale electromagnetics". United States. doi:10.1016/j.jcp.2019.109102. https://www.osti.gov/servlets/purl/1595015.
@article{osti_1595015,
title = {Stability analysis and discretization of A–$Φ$ time domain integral equations for multiscale electromagnetics},
author = {Roth, Thomas E. and Chew, Weng C.},
abstractNote = {The growth of applications at the intersection between electromagnetic and quantum physics is necessitating the creation of novel computational electromagnetic solvers. Work in this paper 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.},
doi = {10.1016/j.jcp.2019.109102},
journal = {Journal of Computational Physics},
number = C,
volume = 408,
place = {United States},
year = {2019},
month = {11}
}