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Kieri, Emil
Publications (10 of 13) Show all publications
Sørensen, L. K., Kieri, E., Srivastav, S., Lundberg, M. & Lindh, R. (2019). Implementation of a semiclassical light-matter interaction using the Gauss–Hermite quadrature: A simple alternative to the multipole expansion. Physical Review A: covering atomic, molecular, and optical physics and quantum information, 99(1), Article ID 013419.
Open this publication in new window or tab >>Implementation of a semiclassical light-matter interaction using the Gauss–Hermite quadrature: A simple alternative to the multipole expansion
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2019 (English)In: Physical Review A: covering atomic, molecular, and optical physics and quantum information, ISSN 2469-9926, E-ISSN 2469-9934, Vol. 99, no 1, article id 013419Article in journal (Refereed) Published
National Category
Theoretical Chemistry
Identifiers
urn:nbn:se:uu:diva-375867 (URN)10.1103/PhysRevA.99.013419 (DOI)000455815000010 ()
Available from: 2019-01-16 Created: 2019-02-04 Last updated: 2019-02-14Bibliographically approved
Brumm, B. & Kieri, E. (2016). A matrix-free Legendre spectral method for initial–boundary value problems. Electronic Transactions on Numerical Analysis, 45, 283-304
Open this publication in new window or tab >>A matrix-free Legendre spectral method for initial–boundary value problems
2016 (English)In: Electronic Transactions on Numerical Analysis, ISSN 1068-9613, E-ISSN 1068-9613, Vol. 45, p. 283-304Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-267728 (URN)000393415700015 ()
Projects
eSSENCE
Available from: 2016-07-29 Created: 2015-11-25 Last updated: 2017-12-01Bibliographically approved
Kieri, E., Lubich, C. & Walach, H. (2016). Discretized dynamical low-rank approximation in the presence of small singular values. SIAM Journal on Numerical Analysis, 54, 1020-1038
Open this publication in new window or tab >>Discretized dynamical low-rank approximation in the presence of small singular values
2016 (English)In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 54, p. 1020-1038Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-267729 (URN)10.1137/15M1026791 (DOI)000375488100021 ()
Projects
eSSENCE
Available from: 2016-04-05 Created: 2015-11-25 Last updated: 2017-12-01Bibliographically approved
Kieri, E. (2016). Numerical Methods for Wave Propagation: Analysis and Applications in Quantum Dynamics. (Doctoral dissertation). Uppsala: Acta Universitatis Upsaliensis
Open this publication in new window or tab >>Numerical Methods for Wave Propagation: Analysis and Applications in Quantum Dynamics
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

We study numerical methods for time-dependent partial differential equations describing wave propagation, primarily applied to problems in quantum dynamics governed by the time-dependent Schrödinger equation (TDSE). We consider both methods for spatial approximation and for time stepping. In most settings, numerical solution of the TDSE is more challenging than solving a hyperbolic wave equation. This is mainly because the dispersion relation of the TDSE makes it very sensitive to dispersion error, and infers a stringent time step restriction for standard explicit time stepping schemes. The TDSE is also often posed in high dimensions, where standard methods are intractable.

The sensitivity to dispersion error makes spectral methods advantageous for the TDSE. We use spectral or pseudospectral methods in all except one of the included papers. In Paper III we improve and analyse the accuracy of the Fourier pseudospectral method applied to a problem with limited regularity, and in Paper V we construct a matrix-free spectral method for problems with non-trivial boundary conditions. Due to its stiffness, the TDSE is most often solved using exponential time integration. In this thesis we use exponential operator splitting and Krylov subspace methods. We rigorously prove convergence for force-gradient operator splitting methods in Paper IV. One way of making high-dimensional problems computationally tractable is low-rank approximation. In Paper VI we prove that a splitting method for dynamical low-rank approximation is robust to singular values in the approximation approaching zero, a situation which is difficult to handle since it implies strong curvature of the approximation space.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2016. p. 33
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1330
Keywords
computational wave propagation, quantum dynamics, time-dependent Schrödinger equation, spectral methods, Gaussian beams, splitting methods, low-rank approximation
National Category
Computational Mathematics
Research subject
Scientific Computing
Identifiers
urn:nbn:se:uu:diva-268625 (URN)978-91-554-9437-7 (ISBN)
Public defence
2016-02-12, ITC 2446, Lägerhyddsvägen 2, Uppsala, 10:15 (English)
Opponent
Supervisors
Projects
eSSENCE
Available from: 2016-01-19 Created: 2015-12-08 Last updated: 2016-02-12
Kieri, E., Kreiss, G. & Runborg, O. (2015). Coupling of Gaussian beam and finite difference solvers for semiclassical Schrödinger equations. Advances in Applied Mathematics and Mechanics, 7, 687-714
Open this publication in new window or tab >>Coupling of Gaussian beam and finite difference solvers for semiclassical Schrödinger equations
2015 (English)In: Advances in Applied Mathematics and Mechanics, ISSN 2070-0733, E-ISSN 2075-1354, Vol. 7, p. 687-714Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-262240 (URN)10.4208/aamm.2013.m411 (DOI)000361055400001 ()
Projects
eSSENCE
Available from: 2015-09-09 Created: 2015-09-10 Last updated: 2017-12-04Bibliographically approved
Kieri, E., Lubich, C. & Walach, H. (2015). Discretised dynamical low-rank approximation in the presence of small singular values. In: Mathematical Methods in Quantum Molecular Dynamics: (pp. 1516-1517). Zürich, Switzerland: EMS Publishing House
Open this publication in new window or tab >>Discretised dynamical low-rank approximation in the presence of small singular values
2015 (English)In: Mathematical Methods in Quantum Molecular Dynamics, Zürich, Switzerland: EMS Publishing House , 2015, p. 1516-1517Conference paper, Published paper (Other academic)
Place, publisher, year, edition, pages
Zürich, Switzerland: EMS Publishing House, 2015
Series
Oberwolfach Reports ; 12
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-266311 (URN)10.4171/OWR/2015/27 (DOI)
Projects
eSSENCE
Available from: 2015-11-06 Created: 2015-11-06 Last updated: 2016-02-16Bibliographically approved
Kieri, E. (2015). Stiff convergence of force-gradient operator splitting methods. Applied Numerical Mathematics, 94, 33-45
Open this publication in new window or tab >>Stiff convergence of force-gradient operator splitting methods
2015 (English)In: Applied Numerical Mathematics, ISSN 0168-9274, E-ISSN 1873-5460, Vol. 94, p. 33-45Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-248024 (URN)10.1016/j.apnum.2015.03.005 (DOI)000355498600003 ()
Projects
eSSENCE
Available from: 2015-03-18 Created: 2015-03-26 Last updated: 2017-12-04Bibliographically approved
Kieri, E. (2014). Accelerated convergence for Schrödinger equations with non-smooth potentials. BIT Numerical Mathematics, 54, 729-748
Open this publication in new window or tab >>Accelerated convergence for Schrödinger equations with non-smooth potentials
2014 (English)In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 54, p. 729-748Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-214685 (URN)10.1007/s10543-013-0465-x (DOI)000342210300009 ()
Projects
eSSENCE
Available from: 2014-01-01 Created: 2014-01-09 Last updated: 2017-12-06Bibliographically approved
Kieri, E. (2014). Stiff convergence of force-gradient operator splitting methods.
Open this publication in new window or tab >>Stiff convergence of force-gradient operator splitting methods
2014 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2014-004
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-220197 (URN)
Projects
eSSENCE
Available from: 2014-02-28 Created: 2014-03-12 Last updated: 2014-03-17Bibliographically approved
Kieri, E. (2013). Accelerated convergence for Schrödinger equations with non-smooth potentials.
Open this publication in new window or tab >>Accelerated convergence for Schrödinger equations with non-smooth potentials
2013 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2013-007
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-198253 (URN)
Projects
eSSENCE
Available from: 2013-04-10 Created: 2013-04-10 Last updated: 2013-10-08Bibliographically approved
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