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Stable difference methods for block-oriented adaptive grids
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Tillämpad beräkningsvetenskap.
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
2015 (engelsk)Inngår i: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 65, s. 486-511Artikkel i tidsskrift (Fagfellevurdert) Published
sted, utgiver, år, opplag, sider
2015. Vol. 65, s. 486-511
HSV kategori
Identifikatorer
URN: urn:nbn:se:uu:diva-234977DOI: 10.1007/s10915-014-9969-zISI: 000362911900003OAI: oai:DiVA.org:uu-234977DiVA, id: diva2:758564
Prosjekter
eSSENCETilgjengelig fra: 2014-12-18 Laget: 2014-10-27 Sist oppdatert: 2017-12-05bibliografisk kontrollert
Inngår i avhandling
1. Adaptive Solvers for High-Dimensional PDE Problems on Clusters of Multicore Processors
Åpne denne publikasjonen i ny fane eller vindu >>Adaptive Solvers for High-Dimensional PDE Problems on Clusters of Multicore Processors
2014 (engelsk)Doktoravhandling, med artikler (Annet vitenskapelig)
Abstract [en]

Accurate numerical solution of time-dependent, high-dimensional partial differential equations (PDEs) usually requires efficient numerical techniques and massive-scale parallel computing. In this thesis, we implement and evaluate discretization schemes suited for PDEs of higher dimensionality, focusing on high order of accuracy and low computational cost.

Spatial discretization is particularly challenging in higher dimensions. The memory requirements for uniform grids quickly grow out of reach even on large-scale parallel computers. We utilize high-order discretization schemes and implement adaptive mesh refinement on structured hyperrectangular domains in order to reduce the required number of grid points and computational work. We allow for anisotropic (non-uniform) refinement by recursive bisection and show how to construct, manage and load balance such grids efficiently. In our numerical examples, we use finite difference schemes to discretize the PDEs. In the adaptive case we show how a stable discretization can be constructed using SBP-SAT operators. However, our adaptive mesh framework is general and other methods of discretization are viable.

For integration in time, we implement exponential integrators based on the Lanczos/Arnoldi iterative schemes for eigenvalue approximations. Using adaptive time stepping and a truncated Magnus expansion, we attain high levels of accuracy in the solution at low computational cost. We further investigate alternative implementations of the Lanczos algorithm with reduced communication costs.

As an example application problem, we have considered the time-dependent Schrödinger equation (TDSE). We present solvers and results for the solution of the TDSE on equidistant as well as adaptively refined Cartesian grids.

sted, utgiver, år, opplag, sider
Uppsala: Acta Universitatis Upsaliensis, 2014. s. 34
Serie
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1199
Emneord
adaptive mesh refinement, anisotropic refinement, exponential integrators, Lanczos' algorithm, hybrid parallelization, time-dependent Schrödinger equation
HSV kategori
Forskningsprogram
Beräkningsvetenskap
Identifikatorer
urn:nbn:se:uu:diva-234984 (URN)978-91-554-9095-9 (ISBN)
Disputas
2014-12-12, Room 2446, Polacksbacken, Lägerhyddsvägen 2, Uppsala, 10:15 (engelsk)
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Veileder
Prosjekter
eSSENCEUPMARC
Tilgjengelig fra: 2014-11-21 Laget: 2014-10-27 Sist oppdatert: 2019-02-25bibliografisk kontrollert

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