Here, we report multiple physical time-scales can arise in electromagnetic simulations when dissipative effects are introduced through boundary conditions, when currents follow external time-scales, and when material parameters vary spatially. In such scenarios, the time-scales of interest may be much slower than the fastest time-scales supported by the Maxwell equations, therefore making implicit time integration an efficient approach. The use of implicit temporal discretizations results in linear systems in which fast time-scales, which severely constrain the stability of an explicit method, can manifest as so-called stiff modes. This study proposes a new block preconditioner for structure preserving (also termed physics compatible) discretizations of the Maxwell equations in first order form. The intent of the preconditioner is to enable the efficient solution of multiple-time-scale Maxwell type systems. An additional benefit of the developed preconditioner is that it requires only a traditional multigrid method for its subsolves and compares well against alternative approaches that rely on specialized edge-based multigrid routines that may not be readily available. Lastly, results demonstrate parallel scalability at large electromagnetic wave CFL numbers on a variety of test problems.

- Publication Date:

- Report Number(s):
- SAND-2018-4332J

Journal ID: ISSN 1064-8275; 662668

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

- Type:
- Accepted Manuscript

- Journal Name:
- SIAM Journal on Scientific Computing

- Additional Journal Information:
- Journal Volume: 40; Journal Issue: 3; Journal ID: ISSN 1064-8275

- Publisher:
- SIAM

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

- Sponsoring Org:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); USDOE National Nuclear Security Administration (NNSA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; Maxwell equations; preconditioning; compatible discretization

- OSTI Identifier:
- 1441484

```
Phillips, Edward Geoffrey, Shadid, John N., and Cyr, Eric C..
```*Scalable Preconditioners for Structure Preserving Discretizations of Maxwell Equations in First Order Form*. United States: N. p.,
Web. doi:10.1137/17M1135827.

```
Phillips, Edward Geoffrey, Shadid, John N., & Cyr, Eric C..
```*Scalable Preconditioners for Structure Preserving Discretizations of Maxwell Equations in First Order Form*. United States. doi:10.1137/17M1135827.

```
Phillips, Edward Geoffrey, Shadid, John N., and Cyr, Eric C.. 2018.
"Scalable Preconditioners for Structure Preserving Discretizations of Maxwell Equations in First Order Form". United States.
doi:10.1137/17M1135827.
```

```
@article{osti_1441484,
```

title = {Scalable Preconditioners for Structure Preserving Discretizations of Maxwell Equations in First Order Form},

author = {Phillips, Edward Geoffrey and Shadid, John N. and Cyr, Eric C.},

abstractNote = {Here, we report multiple physical time-scales can arise in electromagnetic simulations when dissipative effects are introduced through boundary conditions, when currents follow external time-scales, and when material parameters vary spatially. In such scenarios, the time-scales of interest may be much slower than the fastest time-scales supported by the Maxwell equations, therefore making implicit time integration an efficient approach. The use of implicit temporal discretizations results in linear systems in which fast time-scales, which severely constrain the stability of an explicit method, can manifest as so-called stiff modes. This study proposes a new block preconditioner for structure preserving (also termed physics compatible) discretizations of the Maxwell equations in first order form. The intent of the preconditioner is to enable the efficient solution of multiple-time-scale Maxwell type systems. An additional benefit of the developed preconditioner is that it requires only a traditional multigrid method for its subsolves and compares well against alternative approaches that rely on specialized edge-based multigrid routines that may not be readily available. Lastly, results demonstrate parallel scalability at large electromagnetic wave CFL numbers on a variety of test problems.},

doi = {10.1137/17M1135827},

journal = {SIAM Journal on Scientific Computing},

number = 3,

volume = 40,

place = {United States},

year = {2018},

month = {5}

}