Hermite Methods for the Scalar Wave Equation

doi:10.1137/18M1171072

Title: Hermite Methods for the Scalar Wave Equation

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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:

^[1]; Hagstrom, Thomas ^[2]; Vargas, Arturo ^[3]

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:: 2018-11-27

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.

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

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                    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.

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@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}

}

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DOI: 10.1137/18M1171072

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