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Virta, Kristoffer
Publications (10 of 11) Show all publications
Wang, S., Virta, K. & Kreiss, G. (2016). High order finite difference methods for the wave equation with non-conforming grid interfaces. Journal of Scientific Computing, 68, 1002-1028
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, p. 1002-1028Article 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
Virta, K. (2016). Numerics of Elastic and Acoustic Wave Motion. (Doctoral dissertation). Uppsala: Acta Universitatis Upsaliensis
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. p. 32
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1322
Keywords
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
Virta, K., Juhlin, C. & Kreiss, G. (2015). Elastic wave propagation in complex geometries: A qualitative comparison between two high order finite difference methods. Computing Research Repository (1511.07596)
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
Virta, K. & Appelö, D. (2015). Formulae and software for particular solutions to the elastic wave equation in curved geometries. Journal of Computational Physics
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
Virta, K. & Kreiss, G. (2015). Interface waves in almost incompressible elastic materials. Journal of Computational Physics, 303, 313-330
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, p. 313-330Article 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
Nissen, A., Kormann, K., Grandin, M. & Virta, K. (2015). Stable difference methods for block-oriented adaptive grids. Journal of Scientific Computing, 65, 486-511
Open this publication in new window or tab >>Stable difference methods for block-oriented adaptive grids
2015 (English)In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 65, p. 486-511Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-234977 (URN)10.1007/s10915-014-9969-z (DOI)000362911900003 ()
Projects
eSSENCE
Available from: 2014-12-18 Created: 2014-10-27 Last updated: 2017-12-05Bibliographically approved
Virta, K. & Mattsson, K. (2014). Acoustic wave propagation in complicated geometries and heterogeneous media. Journal of Scientific Computing, 61, 90-118
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, p. 90-118Article 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
Duru, K. & Virta, K. (2014). Stable and high order accurate difference methods for the elastic wave equation in discontinuous media. Journal of Computational Physics, 279, 37-62
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, p. 37-62Article 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
Virta, K. (2013). Difference methods with boundary and interface treatment for wave equations. (Licentiate dissertation). Uppsala University
Open this publication in new window or tab >>Difference methods with boundary and interface treatment for wave equations
2013 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Wave motion in acoustic and elastic media is highly influenced by the presence of outer boundaries and media interfaces. The solutions to the equations governing the wave motion at any point in the domain as a function of time can be sought either through analytical or numerical techniques.

This thesis proposes provably stable finite difference schemes to accurately investigate wave interaction with boundaries and interfaces. Schemes for the acoustic wave equation in three spatial coordinates, general domains and heterogeneous media and the elastic wave equation in two spatial dimensions and layered media are presented. A study of the Rayleigh surface wave in almost incompressible media is carried through. Extensive numerical experiments designed to verify stability and accuracy as well as applicability to nontrivial boundary and interface phenomena are given.

Place, publisher, year, edition, pages
Uppsala University, 2013
Series
Information technology licentiate theses: Licentiate theses from the Department of Information Technology, ISSN 1404-5117 ; 2013-006
National Category
Computational Mathematics
Research subject
Scientific Computing
Identifiers
urn:nbn:se:uu:diva-209139 (URN)
Supervisors
Available from: 2013-10-22 Created: 2013-10-14 Last updated: 2017-08-31Bibliographically approved
Duru, K. & Virta, K. (2013). Stable and high order accurate difference methods for the elastic wave equation in discontinuous media. In: Proc. 11th International Conference on Mathematical and Numerical Aspects of Waves: . Paper presented at WAVES 2013 (pp. 197-198). Tunisia: ENIT
Open this publication in new window or tab >>Stable and high order accurate difference methods for the elastic wave equation in discontinuous media
2013 (English)In: Proc. 11th International Conference on Mathematical and Numerical Aspects of Waves, Tunisia: ENIT , 2013, p. 197-198Conference paper, Published paper (Other academic)
Place, publisher, year, edition, pages
Tunisia: ENIT, 2013
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-207272 (URN)
Conference
WAVES 2013
Available from: 2013-06-04 Created: 2013-09-11 Last updated: 2013-09-11Bibliographically approved
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