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  • 1.
    Gustafsson, Magnus
    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, Computational Science.
    Nissen, Anna
    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.
    Kormann, Katharina
    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 difference methods for block-structured adaptive grids2011Report (Other academic)
  • 2.
    Kormann, Katharina
    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, Computational Science.
    Nissen, Anna
    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.
    Error control for simulations of a dissociative quantum system2010In: Numerical Mathematics and Advanced Applications: 2009, Berlin: Springer-Verlag , 2010, p. 523-531Conference paper (Refereed)
  • 3.
    Nissen, Anna
    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.
    Absorbing boundary techniques for the time-dependent Schrödinger equation2010Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    Chemical dissociation processes are important in quantum dynamics. Such processes can be investigated theoretically and numerically through the time-dependent Schrödinger equation, which gives a quantum mechanical description of molecular dynamics.

    This thesis discusses the numerical simulation of chemical reactions involving dissociation. In particular, an accurate boundary treatment in terms of artificial, absorbing boundaries of the computational domain is considered. The approach taken here is based on the perfectly matched layer technique in a finite difference framework. The errors introduced due to the perfectly matched layer can be divided into two categories, the modeling error from the continuous model and numerical reflections that arise for the discretized problem. We analyze the different types of errors using plane wave analysis, and parameters of the perfectly matched layer are optimized so that the modeling error and the numerical reflections are of the same order. The level of accuracy is determined by estimating the order of the spatial error in the interior domain. Numerical calculations show that this procedure enables efficient calculations within a given accuracy. We apply our perfectly matched layer to a three-state system describing a one-dimensional IBr molecule subjected to a laser field and to a two-dimensional model problem treating dissociative adsorbtion and associative desorption of an H2 molecule on a solid surface. Comparisons made to standard absorbing layers in chemical physics prove our approach to be efficient, especially when high accuracy is of importance.

    List of papers
    1. An optimized perfectly matched layer for the Schrödinger equation
    Open this publication in new window or tab >>An optimized perfectly matched layer for the Schrödinger equation
    2011 (English)In: Communications in Computational Physics, ISSN 1815-2406, E-ISSN 1991-7120, Vol. 9, p. 147-179Article in journal (Refereed) Published
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-129182 (URN)10.4208/cicp.010909.010410a (DOI)000287557000007 ()
    Projects
    eSSENCE
    Available from: 2010-08-05 Created: 2010-08-06 Last updated: 2017-12-12Bibliographically approved
    2. Error control for simulations of a dissociative quantum system
    Open this publication in new window or tab >>Error control for simulations of a dissociative quantum system
    2010 (English)In: Numerical Mathematics and Advanced Applications: 2009, Berlin: Springer-Verlag , 2010, p. 523-531Conference paper, Published paper (Refereed)
    Place, publisher, year, edition, pages
    Berlin: Springer-Verlag, 2010
    National Category
    Computational Mathematics Computer Sciences
    Identifiers
    urn:nbn:se:uu:diva-132929 (URN)10.1007/978-3-642-11795-4_56 (DOI)000395207900056 ()978-3-642-11794-7 (ISBN)
    Projects
    eSSENCE
    Available from: 2010-10-29 Created: 2010-10-29 Last updated: 2018-06-16Bibliographically approved
    3. A perfectly matched layer applied to a reactive scattering problem
    Open this publication in new window or tab >>A perfectly matched layer applied to a reactive scattering problem
    2010 (English)In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 133, p. 054306:1-11Article in journal (Refereed) Published
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-129174 (URN)10.1063/1.3458888 (DOI)000281215000013 ()
    Projects
    eSSENCE
    Available from: 2010-08-04 Created: 2010-08-06 Last updated: 2017-12-12Bibliographically approved
  • 4.
    Nissen, Anna
    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 with Artificial Boundary Treatment in Quantum Dynamics2011Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    The investigation of the dynamics of chemical reactions, both from the theoretical and experimental side, has drawn an increasing interest since Ahmed H. Zewail was awarded the 1999 Nobel Prize in Chemistry for his work on femtochemistry. On the experimental side, new techniques such as femtosecond lasers and attosecond lasers enable laser control of chemical reactions. Numerical simulations serve as a valuable complement to experimental techniques, not only for validation of experimental results, but also for simulation of processes that cannot be investigated through experiments. With increasing computer capacity, more and more physical phenomena fall within the range of what is possible to simulate. Also, the development of new, efficient numerical methods further increases the possibilities.

    The focus of this thesis is twofold; numerical methods for chemical reactions including dissociative states and methods that can deal with coexistence of spatial regions with very different physical properties. Dissociative chemical reactions are reactions where molecules break up into smaller components. The dissociation can occur spontaneously, e.g. by radioactive decay, or be induced by adding energy to the system, e.g. in terms of a laser field. Quantities of interest can for instance be the reaction probabilities of possible chemical reactions. This thesis discusses a boundary treatment model based on the perfectly matched layer (PML) approach to accurately describe dynamics of chemical reactions including dissociative states. The limitations of the method are investigated and errors introduced by the PML are quantified.

    The ability of a numerical method to adapt to different scales is important in the study of more complex chemical systems. One application of interest is long-range molecules, where the atoms are affected by chemical attractive forces that lead to fast movement in the region where they are close to each other and exhibits a relative motion of the atoms that is very slow in the long-range region. A numerical method that allows for spatial adaptivity is presented, based on the summation-by-parts-simultaneous approximation term (SBP-SAT) methodology. The accuracy and the robustness of the numerical method are investigated.

    List of papers
    1. An optimized perfectly matched layer for the Schrödinger equation
    Open this publication in new window or tab >>An optimized perfectly matched layer for the Schrödinger equation
    2011 (English)In: Communications in Computational Physics, ISSN 1815-2406, E-ISSN 1991-7120, Vol. 9, p. 147-179Article in journal (Refereed) Published
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-129182 (URN)10.4208/cicp.010909.010410a (DOI)000287557000007 ()
    Projects
    eSSENCE
    Available from: 2010-08-05 Created: 2010-08-06 Last updated: 2017-12-12Bibliographically approved
    2. Error control for simulations of a dissociative quantum system
    Open this publication in new window or tab >>Error control for simulations of a dissociative quantum system
    2010 (English)In: Numerical Mathematics and Advanced Applications: 2009, Berlin: Springer-Verlag , 2010, p. 523-531Conference paper, Published paper (Refereed)
    Place, publisher, year, edition, pages
    Berlin: Springer-Verlag, 2010
    National Category
    Computational Mathematics Computer Sciences
    Identifiers
    urn:nbn:se:uu:diva-132929 (URN)10.1007/978-3-642-11795-4_56 (DOI)000395207900056 ()978-3-642-11794-7 (ISBN)
    Projects
    eSSENCE
    Available from: 2010-10-29 Created: 2010-10-29 Last updated: 2018-06-16Bibliographically approved
    3. A perfectly matched layer applied to a reactive scattering problem
    Open this publication in new window or tab >>A perfectly matched layer applied to a reactive scattering problem
    2010 (English)In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 133, p. 054306:1-11Article in journal (Refereed) Published
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-129174 (URN)10.1063/1.3458888 (DOI)000281215000013 ()
    Projects
    eSSENCE
    Available from: 2010-08-04 Created: 2010-08-06 Last updated: 2017-12-12Bibliographically approved
    4. High order stable finite difference methods for the Schrödinger equation
    Open this publication in new window or tab >>High order stable finite difference methods for the Schrödinger equation
    2011 (English)Report (Other academic)
    Series
    Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2011-014
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-154360 (URN)
    Projects
    eSSENCE
    Available from: 2011-05-28 Created: 2011-05-31 Last updated: 2011-11-18Bibliographically approved
    5. Stability at nonconforming grid interfaces for a high order discretization of the Schrödinger equation
    Open this publication in new window or tab >>Stability at nonconforming grid interfaces for a high order discretization of the Schrödinger equation
    2011 (English)Report (Other academic)
    Series
    Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2011-017
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-157120 (URN)
    Projects
    eSSENCE
    Available from: 2011-08-16 Created: 2011-08-16 Last updated: 2011-11-18Bibliographically approved
    6. Stable difference methods for block-structured adaptive grids
    Open this publication in new window or tab >>Stable difference methods for block-structured adaptive grids
    2011 (English)Report (Other academic)
    Series
    Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2011-022
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-159854 (URN)
    Projects
    eSSENCE
    Available from: 2011-10-11 Created: 2011-10-11 Last updated: 2013-11-29Bibliographically approved
  • 5.
    Nissen, Anna
    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.
    Karlsson, Hans O.
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical and Analytical Chemistry, Quantum Chemistry.
    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.
    A perfectly matched layer applied to a reactive scattering problem2010In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 133, p. 054306:1-11Article in journal (Refereed)
  • 6. 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)
  • 7.
    Nissen, Anna
    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.
    An optimized perfectly matched layer for the Schrödinger equation2009Report (Other academic)
  • 8.
    Nissen, Anna
    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.
    An optimized perfectly matched layer for the Schrödinger equation2011In: Communications in Computational Physics, ISSN 1815-2406, E-ISSN 1991-7120, Vol. 9, p. 147-179Article in journal (Refereed)
  • 9.
    Nissen, Anna
    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.
    Gerritsen, Margot
    High order stable finite difference methods for the Schrödinger equation2011Report (Other academic)
  • 10. Nissen, Anna
    et al.
    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.
    Gerritsen, Margot
    High order stable finite difference methods for the Schrödinger equation2013In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 55, p. 173-199Article in journal (Refereed)
  • 11.
    Nissen, Anna
    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.
    Gerritsen, Margot
    Stability at nonconforming grid interfaces for a high order discretization of the Schrödinger equation2011Report (Other academic)
  • 12. Nissen, Anna
    et al.
    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.
    Gerritsen, Margot
    Stability at nonconforming grid interfaces for a high order discretization of the Schrödinger equation2012In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 53, p. 528-551Article in journal (Refereed)
  • 13.
    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.
    Nissen, Anna
    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.
    Convergence of finite difference methods for the wave equation in two space dimensions2018In: Mathematics of Computation, ISSN 0025-5718, E-ISSN 1088-6842, Vol. 87, no 314, p. 2737-2763Article in journal (Refereed)
1 - 13 of 13
CiteExportLink to result list
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Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
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Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
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  • html
  • text
  • asciidoc
  • rtf