# Hermite Methods for the Scalar Wave Equation

## Abstract

Arbitrary order dissipative and conservative Hermite methods for the scalar wave equation are presented here. Both methods use $(m+1)^d$ degrees of freedom per node for the displacement in $d$ dimensions; the dissipative and conservative methods achieve orders of accuracy $(2m-1)$ and $2m$, respectively. Stability and error analyses as well as implementation strategies for accelerators are also given.

- Authors:

- Univ. of Colorado, Boulder, CO (United States). Dept. of Applied Mathematics
- Southern Methodist Univ., Dallas, TX (United States). Dept. of Mathematics
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Univ. of Colorado, Boulder, CO (United States); Southern Methodist Univ., Dallas, TX (United States)

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

- OSTI Identifier:
- 1497298

- Report Number(s):
- LLNL-JRNL-746059

Journal ID: ISSN 1064-8275; 930652

- Grant/Contract Number:
- AC52-07NA27344; DMS-1319054; DMS-1418871

- Resource Type:
- Accepted Manuscript

- Journal Name:
- SIAM Journal on Scientific Computing

- Additional Journal Information:
- Journal Volume: 40; Journal Issue: 6; Journal ID: ISSN 1064-8275

- Publisher:
- SIAM

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; wave equation; Hermite methods

### Citation Formats

```
Appelö, Daniel, Hagstrom, Thomas, and Vargas, Arturo. Hermite Methods for the Scalar Wave Equation. United States: N. p., 2018.
Web. doi:10.1137/18M1171072.
```

```
Appelö, Daniel, Hagstrom, Thomas, & Vargas, Arturo. Hermite Methods for the Scalar Wave Equation. United States. doi:10.1137/18M1171072.
```

```
Appelö, Daniel, Hagstrom, Thomas, and Vargas, Arturo. Tue .
"Hermite Methods for the Scalar Wave Equation". United States. doi:10.1137/18M1171072. https://www.osti.gov/servlets/purl/1497298.
```

```
@article{osti_1497298,
```

title = {Hermite Methods for the Scalar Wave Equation},

author = {Appelö, Daniel and Hagstrom, Thomas and Vargas, Arturo},

abstractNote = {Arbitrary order dissipative and conservative Hermite methods for the scalar wave equation are presented here. Both methods use $(m+1)^d$ degrees of freedom per node for the displacement in $d$ dimensions; the dissipative and conservative methods achieve orders of accuracy $(2m-1)$ and $2m$, respectively. Stability and error analyses as well as implementation strategies for accelerators are also given.},

doi = {10.1137/18M1171072},

journal = {SIAM Journal on Scientific Computing},

number = 6,

volume = 40,

place = {United States},

year = {2018},

month = {11}

}

Other availability

Cited by: 3 works

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