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Numerics of Elastic and Acoustic Wave Motion
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The elastic wave equation describes the propagation of elastic disturbances produced by seismic events in the Earth or vibrations in plates and beams. The acoustic wave equation governs the propagation of sound. The description of the wave fields resulting from an initial configuration or time dependent forces is a valuable tool when gaining insight into the effects of the layering of the Earth, the propagation of earthquakes or the behavior of underwater sound. In the most general case exact solutions to both the elastic wave equation and the acoustic wave equation are impossible to construct. Numerical methods that produce approximative solutions to the underlaying equations now become valuable tools. In this thesis we construct numerical solvers for the elastic and acoustic wave equations with focus on stability, high order of accuracy, boundary conditions and geometric flexibility. The numerical solvers are used to study wave boundary interactions and effects of curved geometries. We also compare the methods that we have constructed to other methods for the simulation of elastic and acoustic wave motion.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2016. , 32 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1322
Keyword [en]
finite differences, stability, high order accuracy, elastic wave equation, acoustic wave equation
National Category
Computational Mathematics
Research subject
Scientific Computing with specialization in Numerical Analysis
Identifiers
URN: urn:nbn:se:uu:diva-267135ISBN: 978-91-554-9418-6 (print)OAI: oai:DiVA.org:uu-267135DiVA: diva2:872294
Public defence
2016-01-18, 2446, Polacksbacken, Lägerhyddsvägen 2, Uppsala, 10:00 (English)
Opponent
Supervisors
Available from: 2015-12-17 Created: 2015-11-18 Last updated: 2016-01-13
List of papers
1. Stable and high order accurate difference methods for the elastic wave equation in discontinuous media
Open this publication in new window or tab >>Stable and high order accurate difference methods for the elastic wave equation in discontinuous media
2014 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 279, 37-62 p.Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-226424 (URN)10.1016/j.jcp.2014.08.046 (DOI)000342750100003 ()
Available from: 2014-09-06 Created: 2014-06-16 Last updated: 2017-12-05Bibliographically approved
2. Interface waves in almost incompressible elastic materials
Open this publication in new window or tab >>Interface waves in almost incompressible elastic materials
2015 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 303, 313-330 p.Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-264771 (URN)10.1016/j.jcp.2015.09.051 (DOI)000364886900020 ()
Available from: 2015-10-09 Created: 2015-10-16 Last updated: 2017-12-01Bibliographically approved
3. Formulae and software for particular solutions to the elastic wave equation in curved geometries
Open this publication in new window or tab >>Formulae and software for particular solutions to the elastic wave equation in curved geometries
2015 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716Article in journal (Other academic) Submitted
Abstract [en]

We present formulae for particular solutions to the elastic wave equation in cylindrical geometries. We consider scattering and diffraction from a cylinder and inclusion and surface waves exterior and interior to a cylindrical boundary. The solutions are used to compare two modern numerical methods for the elastic wave equation. Associated to this paper is the free software PeWe that implements the exact solutions.

National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-267124 (URN)
Available from: 2015-08-28 Created: 2015-11-18 Last updated: 2017-12-01Bibliographically approved
4. Elastic wave propagation in complex geometries: A qualitative comparison between two high order finite difference methods
Open this publication in new window or tab >>Elastic wave propagation in complex geometries: A qualitative comparison between two high order finite difference methods
2015 (English)In: Computing Research Repository, no 1511.07596Article in journal (Other academic) Submitted
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-267133 (URN)
Available from: 2015-11-24 Created: 2015-11-18 Last updated: 2017-01-25Bibliographically approved
5. Acoustic wave propagation in complicated geometries and heterogeneous media
Open this publication in new window or tab >>Acoustic wave propagation in complicated geometries and heterogeneous media
2014 (English)In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 61, 90-118 p.Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-217300 (URN)10.1007/s10915-014-9817-1 (DOI)000341627100005 ()
Available from: 2014-01-29 Created: 2014-01-31 Last updated: 2017-12-06Bibliographically approved
6. High order finite difference methods for the wave equation with non-conforming grid interfaces
Open this publication in new window or tab >>High order finite difference methods for the wave equation with non-conforming grid interfaces
2016 (English)In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 68, 1002-1028 p.Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-264754 (URN)10.1007/s10915-016-0165-1 (DOI)000380693700006 ()
External cooperation:
Available from: 2016-01-27 Created: 2015-10-16 Last updated: 2017-12-01Bibliographically approved

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