uu.seUppsala University Publications

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High Order Finite Difference Methods with Artificial Boundary Treatment in Quantum DynamicsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2011 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Uppsala: Acta Universitatis Upsaliensis , 2011. , p. 48
##### Series

Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 864
##### Keywords [en]

Schrödinger equation, finite difference methods, perfectly matched layer, summation-by-parts operators, adaptive discretization, stability
##### National Category

Computational Mathematics
##### Research subject

Scientific Computing with specialization in Numerical Analysis
##### Identifiers

URN: urn:nbn:se:uu:diva-159856ISBN: 978-91-554-8180-3 (print)OAI: oai:DiVA.org:uu-159856DiVA, id: diva2:447201
##### Public defence

2011-11-25, Room 2446, Polacksbacken, Lägerhyddsvägen 2D, Uppsala, 10:15 (English)
##### Opponent

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##### Supervisors

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#####

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##### Projects

eSSENCEAvailable from: 2011-11-03 Created: 2011-10-11 Last updated: 2011-11-10Bibliographically approved
##### List of papers

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.

1. An optimized perfectly matched layer for the Schrödinger equation$(function(){PrimeFaces.cw("OverlayPanel","overlay337596",{id:"formSmash:j_idt925:0:j_idt935",widgetVar:"overlay337596",target:"formSmash:j_idt925:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Error control for simulations of a dissociative quantum system$(function(){PrimeFaces.cw("OverlayPanel","overlay359737",{id:"formSmash:j_idt925:1:j_idt935",widgetVar:"overlay359737",target:"formSmash:j_idt925:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. A perfectly matched layer applied to a reactive scattering problem$(function(){PrimeFaces.cw("OverlayPanel","overlay337594",{id:"formSmash:j_idt925:2:j_idt935",widgetVar:"overlay337594",target:"formSmash:j_idt925:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. High order stable finite difference methods for the Schrödinger equation$(function(){PrimeFaces.cw("OverlayPanel","overlay420145",{id:"formSmash:j_idt925:3:j_idt935",widgetVar:"overlay420145",target:"formSmash:j_idt925:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

5. Stability at nonconforming grid interfaces for a high order discretization of the Schrödinger equation$(function(){PrimeFaces.cw("OverlayPanel","overlay435011",{id:"formSmash:j_idt925:4:j_idt935",widgetVar:"overlay435011",target:"formSmash:j_idt925:4:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

6. Stable difference methods for block-structured adaptive grids$(function(){PrimeFaces.cw("OverlayPanel","overlay447190",{id:"formSmash:j_idt925:5:j_idt935",widgetVar:"overlay447190",target:"formSmash:j_idt925:5:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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