uu.seUppsala University Publications
Change search
ReferencesLink to record
Permanent link

Direct link
Composable difference operators for coordinate invariant partial differential equations
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. (Software Aspects of High-Performance Computing)
2007 (English)Report (Other academic)
Place, publisher, year, edition, pages
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2007-007
National Category
Software Engineering Computational Mathematics
URN: urn:nbn:se:uu:diva-10383OAI: oai:DiVA.org:uu-10383DiVA: diva2:38151
Available from: 2007-03-20 Created: 2007-03-20 Last updated: 2011-11-18Bibliographically approved
In thesis
1. Design of High Performance Computing Software for Genericity and Variability
Open this publication in new window or tab >>Design of High Performance Computing Software for Genericity and Variability
2007 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Computer simulations have emerged as a cost efficient complement to laboratory experiments, as computers have become increasingly powerful.

The aim of the present work is to explore the ideas of some state of the art software development practices, and ways in which these can be useful for developing high performance research codes.

The introduction of these practices, and the modular designs that they give rise to, raises issues regarding a potential conflict between runtime efficiency on one hand and development efficiency on the other. Flexible software modules, based on mathematical abstractions, will provide support for convenient implementation and modification of numerical operators. Questions still remain about whether such modules will provide the efficiency which is required for high performance applications.

To answer these questions, investigations were performed within two different problem domains. The first domain consisted of modular frameworks for the numerical solution of Partial Differential Equations. Such frameworks proved a suitable setting, since several of my research questions revolved around the issue of modularity.

The second problem domain was that of symmetry exploiting algorithms. These algorithms are based on group theory, and make ample use of mathematical abstractions from that field. The domain of symmetry exploiting algorithms gave us opportunities to investigate difficulties in combining modularity based on high level abstractions with low level optimizations using data layout and parallelization.

In conclusion, my investigation of software development practices for the area of high performance computing has proved very fruitful indeed. I have found that none of the concerns that were raised should lead us to refrain from the use of the practices that I have considered. On the contrary, in the two case studies presented here, these practices lead to designs that perform well in terms of usability as well as runtime efficiency.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2007. 29 p.
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 285
PDE solver, high-performance, coordinate invariant, curvilinear coordinates, symmetry exploiting, generalized Fourier transform, finite difference, expression templates, feature modeling, variability
National Category
Software Engineering
Research subject
Scientific Computing
urn:nbn:se:uu:diva-7768 (URN)978-91-554-6837-8 (ISBN)
Public defence
2007-04-20, Room 2446, Polacksbacken, Lägerhyddsvägen 2D, Uppsala, 10:15 (English)
Available from: 2007-03-30 Created: 2007-03-30 Last updated: 2011-10-26Bibliographically approved

Open Access in DiVA

No full text

Other links


Search in DiVA

By author/editor
Ljungberg, Malin
By organisation
Division of Scientific ComputingNumerical Analysis
Software EngineeringComputational Mathematics

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 138 hits
ReferencesLink to record
Permanent link

Direct link