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Accelerated convergence for Schrödinger equations with non-smooth potentials
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.
2013 (English)Report (Other academic)
Place, publisher, year, edition, pages
2013.
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2013-007
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-198253OAI: oai:DiVA.org:uu-198253DiVA: diva2:615535
Projects
eSSENCE
Available from: 2013-04-10 Created: 2013-04-10 Last updated: 2013-10-08Bibliographically approved
In thesis
1. Numerical Quantum Dynamics
Open this publication in new window or tab >>Numerical Quantum Dynamics
2013 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

We consider computational methods for simulating the dynamics of molecular systems governed by the time-dependent Schrödinger equation. Solving the Schrödinger equation numerically poses a challenge due to its often highly oscillatory solutions, and to the exponential growth of work and memory with the number of particles in the system.

Two different classes of problems are studied: the dynamics of the nuclei in a molecule and the dynamics of an electron in orbit around a nucleus. For the first class of problems we present new computational methods which exploit the relation between quantum and classical dynamics in order to make the computations more efficient. For the second class of problems, the lack of regularity in the solution poses a computational challenge. Using knowledge of the non-smooth features of the solution we construct a new method with two orders higher accuracy than what is achieved by direct application of a difference stencil.

Place, publisher, year, edition, pages
Uppsala University, 2013
Series
Information technology licentiate theses: Licentiate theses from the Department of Information Technology, ISSN 1404-5117 ; 2013-005
National Category
Computational Mathematics
Research subject
Scientific Computing
Identifiers
urn:nbn:se:uu:diva-208837 (URN)
Supervisors
Projects
eSSENCE
Available from: 2013-10-15 Created: 2013-10-08 Last updated: 2017-08-31Bibliographically approved

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Kieri, Emil

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