## This content will become publicly available on November 9, 2020

# 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. (SNL-NM), Albuquerque, NM (United States); Univ. of Illinois at Urbana-Champaign, IL (United States)
- Univ. of Illinois at Urbana-Champaign, IL (United States); Purdue Univ., West Lafayette, IN (United States)

- Publication Date:

- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF)

- OSTI Identifier:
- 1595015

- Report Number(s):
- SAND-2019-14970J

Journal ID: ISSN 0021-9991; 682269

- Grant/Contract Number:
- AC04-94AL85000; ECCS-169195; NA0003525

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Computational Physics

- Additional Journal Information:
- Journal Volume: 408; Journal Issue: C; Journal ID: ISSN 0021-9991

- 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.
```

```
@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}

}