DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

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:
ORCiD logo [1];  [2];  [3]
  1. Univ. of Colorado, Boulder, CO (United States). Dept. of Applied Mathematics
  2. Southern Methodist Univ., Dallas, TX (United States). Dept. of Mathematics
  3. 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. https://doi.org/10.1137/18M1171072
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.
@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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 3 works
Citation information provided by
Web of Science

Save / Share:

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


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


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


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


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


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

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


Works referencing / citing this record:

Leapfrog Time-Stepping for Hermite Methods
journal, March 2019