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Publications (10 of 15) Show all publications
Almquist, M., Wang, S. & Werpers, J. (2019). Order-preserving interpolation for summation-by-parts operators at nonconforming grid interfaces. SIAM Journal on Scientific Computing, 41, A1201-A1227
Open this publication in new window or tab >>Order-preserving interpolation for summation-by-parts operators at nonconforming grid interfaces
2019 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 41, p. A1201-A1227Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-387569 (URN)10.1137/18M1191609 (DOI)000469225300021 ()
Available from: 2019-04-18 Created: 2019-06-24 Last updated: 2019-06-24Bibliographically approved
Mattsson, K., Almquist, M. & van der Weide, E. (2018). Boundary optimized diagonal-norm SBP operators. Journal of Computational Physics, 374, 1261-1266
Open this publication in new window or tab >>Boundary optimized diagonal-norm SBP operators
2018 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 374, p. 1261-1266Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-354575 (URN)10.1016/j.jcp.2018.06.010 (DOI)000447904200059 ()
Available from: 2018-06-05 Created: 2018-06-20 Last updated: 2019-06-27Bibliographically approved
Mattsson, K. & Almquist, M. (2017). A high-order accurate embedded boundary method for first order hyperbolic equations. Journal of Computational Physics, 334, 255-279
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
Almquist, M. (2017). Efficient Simulation of Wave Phenomena. (Doctoral dissertation). Uppsala: Acta Universitatis Upsaliensis
Open this publication in new window or tab >>Efficient Simulation of Wave Phenomena
2017 (English)Doctoral 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.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2017. p. 42
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1463
Keywords
finite difference method, high-order accuracy, stability, summation by parts, simultaneous approximation term, quantum mechanics, Dirac equation, local time-stepping
National Category
Computational Mathematics
Research subject
Scientific Computing with specialization in Numerical Analysis
Identifiers
urn:nbn:se:uu:diva-310124 (URN)978-91-554-9777-4 (ISBN)
Public defence
2017-02-10, Room 2446, ITC, Lägerhyddsvägen 2, Uppsala, 10:15 (English)
Opponent
Supervisors
Available from: 2017-01-19 Created: 2016-12-11 Last updated: 2017-01-25
Almquist, M. & Mehlin, M. (2017). Multilevel local time-stepping methods of Runge–Kutta-type for wave equations. SIAM Journal on Scientific Computing, 39, A2020-A2048
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
Sjöqvist, E., Almquist, M., Mattsson, K., Gürkan, Z. N. & Hessmo, B. (2015). Realization of adiabatic Aharonov–Bohm scattering with neutrons. Physical Review A. Atomic, Molecular, and Optical Physics, 92(5), 052108:1-5, Article ID 052108.
Open this publication in new window or tab >>Realization of adiabatic Aharonov–Bohm scattering with neutrons
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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
Giangaspero, G., Almquist, M., Mattsson, K. & van der Weide, E. (2015). Unsteady simulations of rotor stator interactions using SBP-SAT schemes: Status and challenges. In: Spectral and High Order Methods for Partial Differential Equations: ICOSAHOM 2014. Paper presented at ICOSAHOM 2014 (pp. 247-255). Springer
Open this publication in new window or tab >>Unsteady simulations of rotor stator interactions using SBP-SAT schemes: Status and challenges
2015 (English)In: Spectral and High Order Methods for Partial Differential Equations: ICOSAHOM 2014, Springer, 2015, p. 247-255Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
Springer, 2015
Series
Lecture Notes in Computational Science and Engineering ; 106
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-281562 (URN)10.1007/978-3-319-19800-2_21 (DOI)000368440400021 ()978-3-319-19799-9 (ISBN)
Conference
ICOSAHOM 2014
Available from: 2015-03-24 Created: 2016-03-24 Last updated: 2016-03-31Bibliographically approved
Almquist, M., Karasalo, I. & Mattsson, K. (2014). Atmospheric sound propagation over large-scale irregular terrain. Journal of Scientific Computing, 61, 369-397
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
Almquist, M., Mattsson, K. & Edvinsson, T. (2014). High-fidelity numerical solution of the time-dependent Dirac equation. Journal of Computational Physics, 262, 86-103
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
Mattsson, K., Almquist, M. & Carpenter, M. H. (2014). Optimal diagonal-norm SBP operators. Journal of Computational Physics, 264, 91-111
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
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-8012-5860

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