Hermite Methods for the Scalar Wave Equation

Appelö, Daniel; Hagstrom, Thomas; Vargas, Arturo

doi:10.1137/18M1171072

Title: 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:

^[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.  https://doi.org/10.1137/18M1171072

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                    Appelö, Daniel, Hagstrom, Thomas, and Vargas, Arturo. Tue .  
"Hermite Methods for the Scalar Wave Equation".  United States.  https://doi.org/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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https://doi.org/10.1137/18M1171072

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Works referenced in this record:

A New Discontinuous Galerkin Formulation for Wave Equations in Second-Order Form
journal, January 2015

Appelö, Daniel; Hagstrom, Thomas
SIAM Journal on Numerical Analysis, Vol. 53, Issue 6
DOI: 10.1137/140973517

On Galerkin difference methods
journal, May 2016

Banks, J. W.; Hagstrom, T.
Journal of Computational Physics, Vol. 313
DOI: 10.1016/j.jcp.2016.02.042

Upwind schemes for the wave equation in second-order form
journal, July 2012

Banks, Jeffrey W.; Henshaw, William D.
Journal of Computational Physics, Vol. 231, Issue 17
DOI: 10.1016/j.jcp.2012.05.012

Piecewise Hermite interpolation in one and two variables with applications to partial differential equations
journal, March 1968

Birkhoff, G.; Schultz, M. H.; Varga, R. S.
Numerische Mathematik, Vol. 11, Issue 3
DOI: 10.1007/BF02161845

High-order unconditionally stable FC-AD solvers for general smooth domains I. Basic elements
journal, March 2010

Bruno, Oscar P.; Lyon, Mark
Journal of Computational Physics, Vol. 229, Issue 6
DOI: 10.1016/j.jcp.2009.11.020

P -adaptive Hermite methods for initial value problems
journal, January 2012

Chen, Ronald; Hagstrom, Thomas
ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 46, Issue 3
DOI: 10.1051/m2an/2011050

Optimal energy conserving local discontinuous Galerkin methods for second-order wave equation in heterogeneous media
journal, September 2014

Chou, Ching-Shan; Shu, Chi-Wang; Xing, Yulong
Journal of Computational Physics, Vol. 272
DOI: 10.1016/j.jcp.2014.04.009

Hermite methods for hyperbolic initial-boundary value problems
journal, December 2005

Goodrich, John; Hagstrom, Thomas; Lorenz, Jens
Mathematics of Computation, Vol. 75, Issue 254
DOI: 10.1090/S0025-5718-05-01808-9

Discontinuous Galerkin Finite Element Method for the Wave Equation
journal, January 2006

Grote, Marcus J.; Schneebeli, Anna; Schötzau, Dominik
SIAM Journal on Numerical Analysis, Vol. 44, Issue 6
DOI: 10.1137/05063194X

A High‐Order Accurate Parallel Solver for Maxwell’s Equations on Overlapping Grids
journal, January 2006

Henshaw, William D.
SIAM Journal on Scientific Computing, Vol. 28, Issue 5
DOI: 10.1137/050644379

High-order unconditionally stable FC-AD solvers for general smooth domains II. Elliptic, parabolic and hyperbolic PDEs; theoretical considerations
journal, May 2010

Lyon, Mark; Bruno, Oscar P.
Journal of Computational Physics, Vol. 229, Issue 9
DOI: 10.1016/j.jcp.2010.01.006

Summation by parts operators for finite difference approximations of second derivatives
journal, September 2004

Mattsson, Ken; Nordström, Jan
Journal of Computational Physics, Vol. 199, Issue 2
DOI: 10.1016/j.jcp.2004.03.001

Works referencing / citing this record:

Leapfrog Time-Stepping for Hermite Methods
journal, March 2019

Vargas, Arturo; Hagstrom, Thomas; Chan, Jesse
Journal of Scientific Computing, Vol. 80, Issue 1
DOI: 10.1007/s10915-019-00938-x

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Similar Records

Title: Hermite Methods for the Scalar Wave Equation

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Citation Formats

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