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Kormann, Katharina

Open this publication in new window or tab >>Stable difference methods for block-oriented adaptive grids### Nissen, Anna

### Kormann, Katharina

### Grandin, Magnus

### Virta, Kristoffer

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_some",{id:"formSmash:j_idt184:0:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_otherAuthors",{id:"formSmash:j_idt184:0:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_otherAuthors",multiple:true}); 2015 (English)In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 65, p. 486-511Article in journal (Refereed) Published
##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:uu:diva-234977 (URN)10.1007/s10915-014-9969-z (DOI)000362911900003 ()
#####

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##### Projects

eSSENCE
Available from: 2014-12-18 Created: 2014-10-27 Last updated: 2017-12-05Bibliographically approved

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.

Open this publication in new window or tab >>A Galerkin radial basis function method for the Schrödinger equation### Kormann, Katharina

### Larsson, Elisabeth

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_some",{id:"formSmash:j_idt184:1:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_otherAuthors",{id:"formSmash:j_idt184:1:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_otherAuthors",multiple:true}); 2013 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 35, p. A2832-A2855Article in journal (Refereed) Published
##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:uu:diva-212482 (URN)10.1137/120893975 (DOI)000330028400018 ()
#####

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##### Projects

eSSENCE
Available from: 2013-12-05 Created: 2013-12-10 Last updated: 2017-12-06Bibliographically approved

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.

Open this publication in new window or tab >>A generic interface for parallel cell-based finite element operator application### Kronbichler, Martin

### Kormann, Katharina

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_some",{id:"formSmash:j_idt184:2:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_otherAuthors",{id:"formSmash:j_idt184:2:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_otherAuthors",multiple:true}); 2012 (English)In: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 63, p. 135-147Article in journal (Refereed) Published
##### National Category

Computational Mathematics Software Engineering
##### Identifiers

urn:nbn:se:uu:diva-174401 (URN)10.1016/j.compfluid.2012.04.012 (DOI)000307093500010 ()
#####

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##### Projects

eSSENCE
Available from: 2012-04-21 Created: 2012-05-15 Last updated: 2018-01-12Bibliographically approved

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.

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.

Open this publication in new window or tab >>A time–space adaptive method for the Schrödinger equation### Kormann, Katharina

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.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); 2012 (English)Report (Other academic)
##### Series

Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2012-023
##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:uu:diva-180182 (URN)
#####

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##### Projects

eSSENCE
Available from: 2012-08-31 Created: 2012-08-31 Last updated: 2012-09-27Bibliographically approved

Open this publication in new window or tab >>An RBF–Galerkin approach to the time-dependent Schrödinger equation### Kormann, Katharina

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.### Larsson, Elisabeth

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.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); 2012 (English)Report (Other academic)
##### Series

Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2012-024
##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:uu:diva-180388 (URN)
#####

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##### Projects

eSSENCE
Available from: 2012-09-05 Created: 2012-09-05 Last updated: 2012-09-27Bibliographically approved

Open this publication in new window or tab >>Communication-efficient algorithms for numerical quantum dynamics### Gustafsson, Magnus

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.### Kormann, Katharina

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.### Holmgren, Sverker

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.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_some",{id:"formSmash:j_idt184:5:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_otherAuthors",{id:"formSmash:j_idt184:5:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_otherAuthors",multiple:true}); 2012 (English)In: Applied Parallel and Scientific Computing: Part II, Berlin: Springer-Verlag , 2012, p. 368-378Conference paper, Published paper (Refereed)
##### Place, publisher, year, edition, pages

Berlin: Springer-Verlag, 2012
##### Series

Lecture Notes in Computer Science ; 7134
##### National Category

Computer Sciences Computational Mathematics
##### Identifiers

urn:nbn:se:uu:diva-135980 (URN)10.1007/978-3-642-28145-7_36 (DOI)000309716000036 ()978-3-642-28144-0 (ISBN)
##### Conference

PARA 2010: State of the Art in Scientific and Parallel Computing
#####

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##### Projects

eSSENCEUPMARC
Available from: 2012-02-16 Created: 2010-12-09 Last updated: 2018-01-12Bibliographically approved

Open this publication in new window or tab >>Derivation of strictly stable high order difference approximations for variable-coefficient PDE### Kormann, Katharina

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.### Kronbichler, Martin

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.### Müller, Bernhard

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_some",{id:"formSmash:j_idt184:6:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_otherAuthors",{id:"formSmash:j_idt184:6:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_otherAuthors",multiple:true}); 2012 (English)In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 50, p. 167-197Article in journal (Refereed) Published
##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:uu:diva-156537 (URN)10.1007/s10915-011-9479-1 (DOI)000298862000008 ()
#####

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#####

##### Projects

eSSENCE
Available from: 2011-03-17 Created: 2011-07-31 Last updated: 2017-12-08Bibliographically approved

Open this publication in new window or tab >>Efficient and Reliable Simulation of Quantum Molecular Dynamics### Kormann, Katharina

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.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_some",{id:"formSmash:j_idt184:7:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_otherAuthors",{id:"formSmash:j_idt184:7:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_otherAuthors",multiple:true}); 2012 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

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

Uppsala: Acta Universitatis Upsaliensis, 2012. p. 52
##### Series

Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 970
##### Keywords

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

### Lubich, Christian

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##### Supervisors

### Holmgren, Sverker

### Kreiss, Gunilla

### Karlsson, Hans O.

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##### Projects

eSSENCE
##### Funder

eSSENCE - An eScience Collaboration
Available from: 2012-09-27 Created: 2012-09-01 Last updated: 2013-01-23Bibliographically approved

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.

Universität Tübingen, Mathematisches Institut.

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, Division of Scientific Computing.

Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Chemistry - Ångström, Theoretical Chemistry.

Open this publication in new window or tab >>A generic interface for parallel cell-based finite element operator application### Kronbichler, Martin

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.### Kormann, Katharina

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.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_some",{id:"formSmash:j_idt184:8:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_otherAuthors",{id:"formSmash:j_idt184:8:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_otherAuthors",multiple:true}); 2011 (English)Report (Other academic)
##### Series

Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2011-025
##### National Category

Computational Mathematics Software Engineering
##### Identifiers

urn:nbn:se:uu:diva-162214 (URN)
#####

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##### Projects

eSSENCE
Available from: 2011-11-27 Created: 2011-11-27 Last updated: 2018-01-12Bibliographically approved

Open this publication in new window or tab >>Global error control of the time-propagation for the Schrödinger equation with a time-dependent Hamiltonian### Kormann, Katharina

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.### Holmgren, Sverker

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.### Karlsson, Hans O.

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##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:uu:diva-156538 (URN)10.1016/j.jocs.2011.02.003 (DOI)000208808200011 ()
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##### Projects

eSSENCE
Available from: 2011-02-18 Created: 2011-07-31 Last updated: 2017-12-08Bibliographically approved

Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical and Analytical Chemistry, Quantum Chemistry.