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Parallel finite element operator application: Graph partitioning and coloring
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.
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.
2011 (English)In: Proc. 7th International Conference on e-Science, Los Alamitos, CA: IEEE Computer Society, 2011, 332-339 p.Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
Los Alamitos, CA: IEEE Computer Society, 2011. 332-339 p.
National Category
Computer Science Computational Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-166267DOI: 10.1109/eScience.2011.53ISBN: 978-1-4577-2163-2 (print)OAI: oai:DiVA.org:uu-166267DiVA: diva2:475824
Projects
eSSENCE
Available from: 2012-01-09 Created: 2012-01-11 Last updated: 2014-03-14Bibliographically approved
In thesis
1. Efficient and Reliable Simulation of Quantum Molecular Dynamics
Open this publication in new window or tab >>Efficient and Reliable Simulation of Quantum Molecular Dynamics
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The time-dependent Schrödinger equation (TDSE) models the quantum nature of molecular processes.  Numerical simulations based on the TDSE help in understanding and predicting the outcome of chemical reactions. This thesis is dedicated to the derivation and analysis of efficient and reliable simulation tools for the TDSE, with a particular focus on models for the interaction of molecules with time-dependent electromagnetic fields.

Various time propagators are compared for this setting and an efficient fourth-order commutator-free Magnus-Lanczos propagator is derived. For the Lanczos method, several communication-reducing variants are studied for an implementation on clusters of multi-core processors. Global error estimation for the Magnus propagator is devised using a posteriori error estimation theory. In doing so, the self-adjointness of the linear Schrödinger equation is exploited to avoid solving an adjoint equation. Efficiency and effectiveness of the estimate are demonstrated for both bounded and unbounded states. The temporal approximation is combined with adaptive spectral elements in space. Lagrange elements based on Gauss-Lobatto nodes are employed to avoid nondiagonal mass matrices and ill-conditioning at high order. A matrix-free implementation for the evaluation of the spectral element operators is presented. The framework uses hybrid parallelism and enables significant computational speed-up as well as the solution of larger problems compared to traditional implementations relying on sparse matrices.

As an alternative to grid-based methods, radial basis functions in a Galerkin setting are proposed and analyzed. It is found that considerably higher accuracy can be obtained with the same number of basis functions compared to the Fourier method. Another direction of research presented in this thesis is a new algorithm for quantum optimal control: The field is optimized in the frequency domain where the dimensionality of the optimization problem can drastically be reduced. In this way, it becomes feasible to use a quasi-Newton method to solve the problem.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2012. 52 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 970
Keyword
time-dependent Schrödinger equation, quantum optimal control, exponential integrators, spectral elements, radial basis functions, global error control and adaptivity, high-performance computing implementation
National Category
Computational Mathematics
Research subject
Scientific Computing with specialization in Numerical Analysis
Identifiers
urn:nbn:se:uu:diva-180251 (URN)978-91-554-8466-8 (ISBN)
Public defence
2012-10-19, Room 2446, Polacksbacken, Lägerhyddsvägen 2D, Uppsala, 10:00 (English)
Opponent
Supervisors
Projects
eSSENCE
Funder
eSSENCE - An eScience Collaboration
Available from: 2012-09-27 Created: 2012-09-01 Last updated: 2013-01-23Bibliographically approved

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Kormann, KatharinaKronbichler, Martin

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