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Formulae and software for particular solutions to the elastic wave equation in curved geometries
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.
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.

Place, publisher, year, edition, pages
2015.
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-267124OAI: oai:DiVA.org:uu-267124DiVA: diva2:872264
Available from: 2015-08-28 Created: 2015-11-18 Last updated: 2017-12-01Bibliographically approved
In thesis
1. Numerics of Elastic and Acoustic Wave Motion
Open this publication in new window or tab >>Numerics of Elastic and Acoustic Wave Motion
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
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:nbn:se:uu:diva-267135 (URN)978-91-554-9418-6 (ISBN)
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

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Virta, Kristoffer

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