High Order Solution to Exterior 3D Wave Equation by the Method of Difference Potentials

Fouché Frantz Smith; Semyon Tsynkov; Eli Turkel

doi:10.1007/978-3-031-20432-6_30

High Order Solution to Exterior 3D Wave Equation by the Method of Difference Potentials

Fouché Frantz Smith^*, Semyon Tsynkov, Eli Turkel

^*Corresponding author for this work

School of Mathematical Sciences

North Carolina State University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We solve the 3D acoustic wave equation with variable propagation speed in an unbounded domain with fourth order accuracy in time and space. The unbounded domain is truncated with a spherical artificial outer boundary, and an artificial boundary condition (ABC) is imposed to absorb the outgoing waves. In time, we discretize the wave equation using the θ-scheme. The resulting one parameter family of elliptic PDEs, which contain three levels in time, are discretized in space using a compact finite difference scheme on a 3 × 3 × 3 stencil. The method of difference potentials (MDP) allows us to solve this discrete elliptic PDE (EPDE) fast on a Cartesian grid despite the spherical domain not conforming to the grid.

Original language	English
Title of host publication	Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 - Selected Papers from the ICOSAHOM Conference 2021
Editors	Jens M. Melenk, Joachim Schöberl, Ilaria Perugia, Christoph Schwab
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	455-467
Number of pages	13
ISBN (Print)	9783031204319
DOIs	https://doi.org/10.1007/978-3-031-20432-6_30
State	Published - 2023
Event	13th International Conference on Spectral and High Order Methods, ICOSAHOM 2021 - Vienna, Austria Duration: 12 Jul 2021 → 16 Jul 2021

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	137
ISSN (Print)	1439-7358
ISSN (Electronic)	2197-7100

Conference

Conference	13th International Conference on Spectral and High Order Methods, ICOSAHOM 2021
Country/Territory	Austria
City	Vienna
Period	12/07/21 → 16/07/21

Funding

Funders	Funder number
Army Research Office	W911NF-16-1-0115
Bloom's Syndrome Foundation	2014048, 2020128
United States-Israel Binational Science Foundation

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10.1007/978-3-031-20432-6_30

Cite this

Smith, F. F., Tsynkov, S., & Turkel, E. (2023). High Order Solution to Exterior 3D Wave Equation by the Method of Difference Potentials. In J. M. Melenk, J. Schöberl, I. Perugia, & C. Schwab (Eds.), Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 - Selected Papers from the ICOSAHOM Conference 2021 (pp. 455-467). (Lecture Notes in Computational Science and Engineering; Vol. 137). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-20432-6_30

Smith, Fouché Frantz ; Tsynkov, Semyon ; Turkel, Eli. / High Order Solution to Exterior 3D Wave Equation by the Method of Difference Potentials. Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 - Selected Papers from the ICOSAHOM Conference 2021. editor / Jens M. Melenk ; Joachim Schöberl ; Ilaria Perugia ; Christoph Schwab. Springer Science and Business Media Deutschland GmbH, 2023. pp. 455-467 (Lecture Notes in Computational Science and Engineering).

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abstract = "We solve the 3D acoustic wave equation with variable propagation speed in an unbounded domain with fourth order accuracy in time and space. The unbounded domain is truncated with a spherical artificial outer boundary, and an artificial boundary condition (ABC) is imposed to absorb the outgoing waves. In time, we discretize the wave equation using the θ-scheme. The resulting one parameter family of elliptic PDEs, which contain three levels in time, are discretized in space using a compact finite difference scheme on a 3 × 3 × 3 stencil. The method of difference potentials (MDP) allows us to solve this discrete elliptic PDE (EPDE) fast on a Cartesian grid despite the spherical domain not conforming to the grid.",

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Smith, FF, Tsynkov, S & Turkel, E 2023, High Order Solution to Exterior 3D Wave Equation by the Method of Difference Potentials. in JM Melenk, J Schöberl, I Perugia & C Schwab (eds), Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 - Selected Papers from the ICOSAHOM Conference 2021. Lecture Notes in Computational Science and Engineering, vol. 137, Springer Science and Business Media Deutschland GmbH, pp. 455-467, 13th International Conference on Spectral and High Order Methods, ICOSAHOM 2021, Vienna, Austria, 12/07/21. https://doi.org/10.1007/978-3-031-20432-6_30

High Order Solution to Exterior 3D Wave Equation by the Method of Difference Potentials. / Smith, Fouché Frantz; Tsynkov, Semyon; Turkel, Eli.
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 - Selected Papers from the ICOSAHOM Conference 2021. ed. / Jens M. Melenk; Joachim Schöberl; Ilaria Perugia; Christoph Schwab. Springer Science and Business Media Deutschland GmbH, 2023. p. 455-467 (Lecture Notes in Computational Science and Engineering; Vol. 137).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Smith FF, Tsynkov S, Turkel E. High Order Solution to Exterior 3D Wave Equation by the Method of Difference Potentials. In Melenk JM, Schöberl J, Perugia I, Schwab C, editors, Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 - Selected Papers from the ICOSAHOM Conference 2021. Springer Science and Business Media Deutschland GmbH. 2023. p. 455-467. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-031-20432-6_30

High Order Solution to Exterior 3D Wave Equation by the Method of Difference Potentials

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