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Title: Discretizing singular point sources in hyperbolic wave propagation problems

Abstract

Here, we develop high order accurate source discretizations for hyperbolic wave propagation problems in first order formulation that are discretized by finite difference schemes. By studying the Fourier series expansions of the source discretization and the finite difference operator, we derive sufficient conditions for achieving design accuracy in the numerical solution. Only half of the conditions in Fourier space can be satisfied through moment conditions on the source discretization, and we develop smoothness conditions for satisfying the remaining accuracy conditions. The resulting source discretization has compact support in physical space, and is spread over as many grid points as the number of moment and smoothness conditions. In numerical experiments we demonstrate high order of accuracy in the numerical solution of the 1-D advection equation (both in the interior and near a boundary), the 3-D elastic wave equation, and the 3-D linearized Euler equations.

Authors:
 [1];  [2];  [1];  [2]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  2. Stanford Univ., Stanford, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1343000
Alternate Identifier(s):
OSTI ID: 1329335
Report Number(s):
LLNL-JRNL-679293
Journal ID: ISSN 0021-9991
Grant/Contract Number:  
AC52-07NA27344; LLNL-JRNL-679293
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 321; Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
58 GEOSCIENCES; 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; singular sources; hyperbolic wave propagation; moment conditions; smoothness conditions; summation by parts

Citation Formats

Petersson, N. Anders, O'Reilly, Ossian, Sjogreen, Bjorn, and Bydlon, Samuel. Discretizing singular point sources in hyperbolic wave propagation problems. United States: N. p., 2016. Web. https://doi.org/10.1016/j.jcp.2016.05.060.
Petersson, N. Anders, O'Reilly, Ossian, Sjogreen, Bjorn, & Bydlon, Samuel. Discretizing singular point sources in hyperbolic wave propagation problems. United States. https://doi.org/10.1016/j.jcp.2016.05.060
Petersson, N. Anders, O'Reilly, Ossian, Sjogreen, Bjorn, and Bydlon, Samuel. Wed . "Discretizing singular point sources in hyperbolic wave propagation problems". United States. https://doi.org/10.1016/j.jcp.2016.05.060. https://www.osti.gov/servlets/purl/1343000.
@article{osti_1343000,
title = {Discretizing singular point sources in hyperbolic wave propagation problems},
author = {Petersson, N. Anders and O'Reilly, Ossian and Sjogreen, Bjorn and Bydlon, Samuel},
abstractNote = {Here, we develop high order accurate source discretizations for hyperbolic wave propagation problems in first order formulation that are discretized by finite difference schemes. By studying the Fourier series expansions of the source discretization and the finite difference operator, we derive sufficient conditions for achieving design accuracy in the numerical solution. Only half of the conditions in Fourier space can be satisfied through moment conditions on the source discretization, and we develop smoothness conditions for satisfying the remaining accuracy conditions. The resulting source discretization has compact support in physical space, and is spread over as many grid points as the number of moment and smoothness conditions. In numerical experiments we demonstrate high order of accuracy in the numerical solution of the 1-D advection equation (both in the interior and near a boundary), the 3-D elastic wave equation, and the 3-D linearized Euler equations.},
doi = {10.1016/j.jcp.2016.05.060},
journal = {Journal of Computational Physics},
number = C,
volume = 321,
place = {United States},
year = {2016},
month = {6}
}

Journal Article:

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Cited by: 6 works
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