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  • 1. Duru, Kenneth
    et al.
    Virta, Kristoffer
    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.
    Stable and high order accurate difference methods for the elastic wave equation in discontinuous media2013In: Proc. 11th International Conference on Mathematical and Numerical Aspects of Waves, Tunisia: ENIT , 2013, p. 197-198Conference paper (Other academic)
  • 2. Duru, Kenneth
    et al.
    Virta, Kristoffer
    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.
    Stable and high order accurate difference methods for the elastic wave equation in discontinuous media2014In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 279, p. 37-62Article in journal (Refereed)
  • 3. Nissen, Anna
    et al.
    Kormann, Katharina
    Grandin, Magnus
    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, Computational Science.
    Virta, Kristoffer
    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.
    Stable difference methods for block-oriented adaptive grids2015In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 65, p. 486-511Article in journal (Refereed)
  • 4.
    Virta, Kristoffer
    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.
    Difference methods with boundary and interface treatment for wave equations2013Licentiate 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.

    List of papers
    1. 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, 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
    2. Surface waves in almost incompressible elastic materials
    Open this publication in new window or tab >>Surface waves in almost incompressible elastic materials
    2013 (English)In: Proc. 11th International Conference on Mathematical and Numerical Aspects of Waves, Tunisia: ENIT , 2013, p. 375-376Conference paper, Published paper (Other academic)
    Place, publisher, year, edition, pages
    Tunisia: ENIT, 2013
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-207279 (URN)
    Conference
    WAVES 2013
    Available from: 2013-06-07 Created: 2013-09-11 Last updated: 2014-06-16Bibliographically approved
    3. 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, 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
  • 5.
    Virta, Kristoffer
    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.
    Numerics of Elastic and Acoustic Wave Motion2016Doctoral 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.

    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, 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
    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, 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
    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, 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
    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, 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
  • 6.
    Virta, Kristoffer
    et al.
    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.
    Appelö, Daniel
    Formulae and software for particular solutions to the elastic wave equation in curved geometries2015In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716Article in journal (Other academic)
    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.

  • 7.
    Virta, Kristoffer
    et al.
    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.
    Juhlin, Christopher
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
    Kreiss, Gunilla
    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.
    Elastic wave propagation in complex geometries: A qualitative comparison between two high order finite difference methods2015In: Computing Research Repository, no 1511.07596Article in journal (Other academic)
  • 8.
    Virta, Kristoffer
    et al.
    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.
    Kreiss, Gunilla
    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.
    Interface waves in almost incompressible elastic materials2015In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 303, p. 313-330Article in journal (Refereed)
  • 9.
    Virta, Kristoffer
    et al.
    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.
    Kreiss, Gunilla
    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.
    Surface waves in almost incompressible elastic materials2013In: Proc. 11th International Conference on Mathematical and Numerical Aspects of Waves, Tunisia: ENIT , 2013, p. 375-376Conference paper (Other academic)
  • 10.
    Virta, Kristoffer
    et al.
    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.
    Mattsson, Ken
    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.
    Acoustic wave propagation in complicated geometries and heterogeneous media2014In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 61, p. 90-118Article in journal (Refereed)
  • 11.
    Wang, Siyang
    et al.
    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.
    Virta, Kristoffer
    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.
    Kreiss, Gunilla
    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.
    High order finite difference methods for the wave equation with non-conforming grid interfaces2016In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 68, p. 1002-1028Article in journal (Refereed)
1 - 11 of 11
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