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  • 1.
    Almquist, Martin
    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.
    Efficient Simulation of Wave Phenomena2017Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Wave phenomena appear in many fields of science such as acoustics, geophysics, and quantum mechanics. They can often be described by partial differential equations (PDEs). As PDEs typically are too difficult to solve by hand, the only option is to compute approximate solutions by implementing numerical methods on computers. Ideally, the numerical methods should produce accurate solutions at low computational cost. For wave propagation problems, high-order finite difference methods are known to be computationally cheap, but historically it has been difficult to construct stable methods. Thus, they have not been guaranteed to produce reasonable results.

    In this thesis we consider finite difference methods on summation-by-parts (SBP) form. To impose boundary and interface conditions we use the simultaneous approximation term (SAT) method. The SBP-SAT technique is designed such that the numerical solution mimics the energy estimates satisfied by the true solution. Hence, SBP-SAT schemes are energy-stable by construction and guaranteed to converge to the true solution of well-posed linear PDE. The SBP-SAT framework provides a means to derive high-order methods without jeopardizing stability. Thus, they overcome most of the drawbacks historically associated with finite difference methods.

    This thesis consists of three parts. The first part is devoted to improving existing SBP-SAT methods. In Papers I and II, we derive schemes with improved accuracy compared to standard schemes. In Paper III, we present an embedded boundary method that makes it easier to cope with complex geometries. The second part of the thesis shows how to apply the SBP-SAT method to wave propagation problems in acoustics (Paper IV) and quantum mechanics (Papers V and VI). The third part of the thesis, consisting of Paper VII, presents an efficient, fully explicit time-integration scheme well suited for locally refined meshes.

    List of papers
    1. A solution to the stability issues with block norm summation by parts operators
    Open this publication in new window or tab >>A solution to the stability issues with block norm summation by parts operators
    2013 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 253, p. 418-442Article in journal (Refereed) Published
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-205418 (URN)10.1016/j.jcp.2013.07.013 (DOI)000323610500022 ()
    Available from: 2013-07-24 Created: 2013-08-16 Last updated: 2017-12-06Bibliographically approved
    2. Optimal diagonal-norm SBP operators
    Open this publication in new window or tab >>Optimal diagonal-norm SBP operators
    2014 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 264, p. 91-111Article in journal (Refereed) Published
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-215785 (URN)10.1016/j.jcp.2013.12.041 (DOI)000331717100005 ()
    Available from: 2014-01-15 Created: 2014-01-16 Last updated: 2017-12-06Bibliographically approved
    3. A high-order accurate embedded boundary method for first order hyperbolic equations
    Open this publication in new window or tab >>A high-order accurate embedded boundary method for first order hyperbolic equations
    2017 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 334, p. 255-279Article in journal (Refereed) Published
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-310122 (URN)10.1016/j.jcp.2016.12.034 (DOI)000395210500015 ()
    Available from: 2016-12-28 Created: 2016-12-11 Last updated: 2017-06-30Bibliographically approved
    4. Atmospheric sound propagation over large-scale irregular terrain
    Open this publication in new window or tab >>Atmospheric sound propagation over large-scale irregular terrain
    2014 (English)In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 61, p. 369-397Article in journal (Refereed) Published
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-218680 (URN)10.1007/s10915-014-9830-4 (DOI)000343215600007 ()
    Available from: 2014-02-14 Created: 2014-02-14 Last updated: 2017-12-06Bibliographically approved
    5. High-fidelity numerical solution of the time-dependent Dirac equation
    Open this publication in new window or tab >>High-fidelity numerical solution of the time-dependent Dirac equation
    2014 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 262, p. 86-103Article in journal (Refereed) Published
    National Category
    Computational Mathematics Theoretical Chemistry
    Identifiers
    urn:nbn:se:uu:diva-215119 (URN)10.1016/j.jcp.2013.12.038 (DOI)000330955200006 ()
    Available from: 2014-01-09 Created: 2014-01-10 Last updated: 2017-12-06Bibliographically approved
    6. Realization of adiabatic Aharonov–Bohm scattering with neutrons
    Open this publication in new window or tab >>Realization of adiabatic Aharonov–Bohm scattering with neutrons
    Show others...
    2015 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 92, no 5, p. 052108:1-5, article id 052108Article in journal (Refereed) Published
    National Category
    Atom and Molecular Physics and Optics Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-246721 (URN)10.1103/PhysRevA.92.052108 (DOI)000364468300002 ()
    Funder
    Swedish Research Council, D0413201
    Available from: 2015-11-12 Created: 2015-03-09 Last updated: 2017-12-04Bibliographically approved
    7. Multilevel local time-stepping methods of Runge–Kutta-type for wave equations
    Open this publication in new window or tab >>Multilevel local time-stepping methods of Runge–Kutta-type for wave equations
    2017 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 39, p. A2020-A2048Article in journal (Refereed) Published
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-310123 (URN)10.1137/16M1084407 (DOI)000415797300064 ()
    Available from: 2017-09-14 Created: 2016-12-11 Last updated: 2018-03-02Bibliographically approved
  • 2.
    Almquist, Martin
    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.
    Karasalo, Ilkka
    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.
    Atmospheric sound propagation over large-scale irregular terrain2013Report (Other academic)
  • 3.
    Almquist, Martin
    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.
    Karasalo, Ilkka
    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.
    Atmospheric sound propagation over large-scale irregular terrain2014In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 61, p. 369-397Article in journal (Refereed)
  • 4.
    Almquist, Martin
    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.
    Edvinsson, Tomas
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Chemistry - Ångström, Inorganic Chemistry.
    High-fidelity numerical solution of the time-dependent Dirac equation2014In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 262, p. 86-103Article in journal (Refereed)
  • 5.
    Almquist, Martin
    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.
    Edvinsson, Tomas
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Chemistry - Ångström, Inorganic Chemistry.
    Stable and accurate simulation of phenomena in relativistic quantum mechanics2013In: Proc. 11th International Conference on Mathematical and Numerical Aspects of Waves, Tunisia: ENIT , 2013, p. 213-214Conference paper (Other academic)
  • 6.
    Almquist, Martin
    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.
    Mehlin, Michaela
    Multilevel local time-stepping methods of Runge–Kutta-type for wave equations2017In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 39, p. A2020-A2048Article in journal (Refereed)
  • 7. Almquist, Martin
    et al.
    Wang, Siyang
    Werpers, Jonatan
    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.
    Order-preserving interpolation for summation-by-parts operators at nonconforming grid interfaces2019In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 41, p. A1201-A1227Article in journal (Refereed)
  • 8. Giangaspero, Giorgio
    et al.
    Almquist, Martin
    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.
    van der Weide, Edwin
    Unsteady simulations of rotor stator interactions using SBP-SAT schemes: Status and challenges2015In: Spectral and High Order Methods for Partial Differential Equations: ICOSAHOM 2014, Springer, 2015, p. 247-255Conference paper (Refereed)
  • 9.
    Mattsson, Ken
    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.
    Almquist, Martin
    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.
    A high-order accurate embedded boundary method for first order hyperbolic equations2017In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 334, p. 255-279Article in journal (Refereed)
  • 10.
    Mattsson, Ken
    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.
    Almquist, Martin
    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.
    A solution to the stability issues with block norm summation by parts operators2013In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 253, p. 418-442Article in journal (Refereed)
  • 11.
    Mattsson, Ken
    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.
    Almquist, Martin
    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.
    Carpenter, Mark H.
    Optimal diagonal-norm SBP operators2013Report (Other academic)
  • 12.
    Mattsson, Ken
    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.
    Almquist, Martin
    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.
    Carpenter, Mark H.
    Optimal diagonal-norm SBP operators2014In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 264, p. 91-111Article in journal (Refereed)
  • 13.
    Mattsson, Ken
    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.
    Almquist, Martin
    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.
    Engblom, Stefan
    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.
    Stable and accurate wave simulations in complex geometries and discontinuous media2013In: Proc. 11th International Conference on Mathematical and Numerical Aspects of Waves, Tunisia: ENIT , 2013, p. 201-202Conference paper (Other academic)
  • 14.
    Mattsson, Ken
    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.
    Almquist, Martin
    van der Weide, Edwin
    Boundary optimized diagonal-norm SBP operators2018In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 374, p. 1261-1266Article in journal (Refereed)
  • 15.
    Sjöqvist, Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy.
    Almquist, Martin
    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.
    Gürkan, Zeynep Nilhan
    Hessmo, Björn
    Realization of adiabatic Aharonov–Bohm scattering with neutrons2015In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 92, no 5, p. 052108:1-5, article id 052108Article in journal (Refereed)
1 - 15 of 15
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