Discretizing singular point sources in hyperbolic wave propagation problems
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 1D advection equation (both in the interior and near a boundary), the 3D elastic wave equation, and the 3D linearized Euler equations.
 Authors:

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 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Stanford Univ., Stanford, CA (United States)
 Publication Date:
 Report Number(s):
 LLNLJRNL679293
Journal ID: ISSN 00219991
 Grant/Contract Number:
 AC5207NA27344
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 321; Journal Issue: C; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Research Org:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org:
 USDOE
 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
 OSTI Identifier:
 1343000
 Alternate Identifier(s):
 OSTI ID: 1329335
Petersson, N. Anders, O'Reilly, Ossian, Sjogreen, Bjorn, and Bydlon, Samuel. Discretizing singular point sources in hyperbolic wave propagation problems. United States: N. p.,
Web. doi: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. doi:10.1016/j.jcp.2016.05.060.
Petersson, N. Anders, O'Reilly, Ossian, Sjogreen, Bjorn, and Bydlon, Samuel. 2016.
"Discretizing singular point sources in hyperbolic wave propagation problems". United States.
doi: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 1D advection equation (both in the interior and near a boundary), the 3D elastic wave equation, and the 3D 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}
}