Scientific Progress (Goes Boink)

The overall theme for my research is and has been the construction of software for scientific computing, particularly regarding the numerical simulation of PDEs (partial differential equations). As a graduate student at the Department of Scientific Computing, Uppsala University, I worked in the group Software aspects of high-performance computing, led by my thesis advisor Prof. Michael Thune. My first project, which led to my licentiate degree, concerned a project where object-orientation was used for modeling PDEs and numerical methods for PDEs. In addition, an object-oriented database was used to provide a persistent plug-and-play interface to the objects. Thereafter, I had the opportunity to spend six months at Los Alamos National Laboratories, New Mexico, USA. Using software tools and experience from this period, I developed Compose, an object-oriented C++ framework for PDE solvers, capable of addressing more complicated PDEs such as the incompressible Navier--Stokes equations on overlapping grids. The main part of my Ph.D. thesis An Object-Oriented Framework for PDE Solvers, defended in 1999, presents research related to Compose.

After the dissertation, I was involved in a joint project with the Chalmers Finite Element Centre, Goethenburg, Sweden. We developed and investigated a numerical approach for simulating a wave equation in several dimensions, which combined finite elements and finite differences. Thus, we obtained the flexibility of finite elements together with the efficiency of finite differences.

In year 2000 and the first half of 2001, I was a post doc in Bergen. Particularly, I became interested in software for tensor support and for coordinate free numerics.

In July 2001, I returned back to base where I now have a research position. My research has focused on software support for mathematical groups in conjunction with the Generalized Fourier Transform.

In April 2006, I left the IT department for a position at TietoEnator. This page will nevertheless be maintained at least for a while.

Publications

Publications related to research on Generalized Fourier Transforms

Eigenvalues for equivariant matrices
KÅ and Hans Munthe-Kaas. Journal of Computational and Applied Mathematics 192 (2006) pp. 89-99. An extended abstract appeared in Proceedings of CMMSE 2004, International Conference on Computational and Mathematical Methods in Science and Engineering, pp. 1-5, Uppsala, June 4-8, 2004.

Mesh Generation for Symmetrical Geometries
KÅ. Proceedings of International Conference on Computational Science and its Applications 2005, Singapore: Gervasi et al. (Eds.): ICCSA 2005, LNCS 3840, pp. 657-668, 2005.

Applications of the Generalized Fourier Transform in Numerical Linear Algebra
KÅ and Hans Munthe-Kaas. BIT numerical mathematics 45 (2005) pp. 819-850. Earlier version available as Technical Report 2004-029, Department of Information Technology, Uppsala University, Uppsala Sweden, 2004.

Generic Programming Aspects of Symmetry Exploiting Numerical Software
Malin Ljungberg and KÅ. Proceedings of ECCOMAS 2004, the European Congress on Computational Methods in Applied Science and Engineering, Neittaanmäki et al. (eds.), Jyväskylä, Finland, 24-28 July 2004. Also available as Technical Report 2004-020, Department of Information Technology, Uppsala University, Uppsala Sweden, 2004.

Sparse Generalized Fourier Transforms
KÅ and Daniel Henriksson. BIT numerical mathematics 47 (2007). E-publication. Earlier verion available as Technical Report 2005-043, Department of Information Technology, Uppsala University, Uppsala Sweden, 2005.

Designing for Geometrical Symmetry Exploitation
André Yamba Yamba, KÅ, and Malin Ljungberg. Scientific Programming 14 (2006) pp. 61-80. Earlier version available as Technical Report 2006-017, Department of Information Technology, Uppsala University, Uppsala Sweden, 2006.

Multi-Dimensional Option Pricing using Radial Basis Functions and the Generalized Fourier Transform
Elisabeth Larsson, KÅ and Andreas Hall. Technical Report 2006-037, Department of Information Technology, Uppsala University, Uppsala Sweden, 2006.

Publications related to Computational databases

Computational Database Technology Applied to Option Pricing via Finite Differences
Jöns Åkerlund KÅ and Kjell Orsborn. In Proceedings of ADBIS 2006, Tenth East-European Conference on Advances in Databases and Information Systems. LNCS 4152, 367--382. 2006.

Publications related to Generic Programming
Sorting out the relationships between pairs of iterators, values, and references
In Proceedings of Fourth International Conference on Generative Programming and Component Engineering (GPCE'05), pp 342 - 356, Tallinn, Estonia, Sep 29 - Oct 1, 2005.

Publications related to research in Bergen
Einstein summation for Multi-dimensional arrays
Computers and Mathematics with Applications 44 (2002) 1007-1017. Earlier version available in proceedings of NIK 2000, Norsk Informatikk Konferanse, Bodø, Norway, 20 - 22 November 2000, pp 67 - 78, Tapir, Norway, 2000.

Support for tensor symmetries in EinSum
Computers and Mathematics with Applications 45 (2003) 789-803. Also available as Technical Report 212, Dept. of Informatics, University of Bergen, Norway, June, 2001.

Mathematical Abstractions for Scientific Computing
KÅ, Magne Haveraaen and Hans Munthe-Kaas. In R. Boisvert and P. Tang, editors, The architecture of Scientific Software, pp. 145-158, Kluwer Academic Publishers, Boston, 2001.

On OO Frameworks and coordinate free formulations for PDEs
KÅ, Magne Haveraaen and Hans Munthe-Kaas. Engineering with Computers (2002) 18:285-294. Springer-Verlag London. (Presented at the minisymposium Advances in Software Technology for Computational Mechanics, held at the sixth Congress of the US Association for Computational Mechanics, Dearborn, Michigan, August 1-4, 2001.)

Software design for finite difference schemes based on index notation
KÅ and Kurt Otto. Future Generation Computer Systems, Volume 22, Issues 1-2, January 2006, pp. 102-109. (Electronic publication October 2003.) Earlier version appeared in Computational science -- ICCS 2002, part III, LNCS 2331.

Publications related to my joint research with Chalmers

A hybrid method for the wave equation
Larisa Beilina, Klas Samuelsson, KÅ. Technical Report 2001-024, Department of Information Technology, Uppsala University, Uppsala Sweden, 2001. Also available as Technical Report 2001-14, Finite Element Center, Chalmers University of Technology, Göteborg, Sweden, 2001.

Efficiency of a Hybrid Method for the Wave Equation
Larisa Beilina, Klas Samuelsson, KÅ. In proceedings of FEM3D, Finite Element Methods for Three-dimensional Problems, Jyväskylä, Finland, June 28 - July 1, 2000.

Publications closely related to thesis research

Object-oriented Modeling of Parallel PDE Solvers
Michael Thuné, KÅ, Malin Ljungberg, Markus Nordén, Kurt Otto, Jarmo Rantakokko. In R. Boisvert and P. Tang, editors, The architecture of Scientific Software, pp. 159-174, Kluwer Academic Publishers, Boston, 2001.

Verifying Extensions of OO Frameworks: An Example from Scientific Computing
In B. Sanchez et al., editors, Information Systems Development, Volume II, pp. 375 - 378, IIIS, 2000.

Thesis summary
The summary of my thesis, an object-oriented framework for PDE solvers.

An extendable PDE solver with reusable components, Read abstract
Accepted for presentation and publication at the ASME 2nd International Symposium on Computational Technologies for Fluid/Thermal/Chemical Systems with Industrial Applications, August 1­5, 1999, Boston, USA.

Rapid Development of PDE Solvers, Read abstract
Report 212, Department of Scientific Computing, Uppsala University, Uppsala, 1999.

Implementing Runge--Kutta schemes for reusability, Read abstract
Report 211, Department of Scientific Computing, Uppsala University, Uppsala, 1999.

An extendable PDE solver framework, Read abstract
Report 197, Department of Scientific Computing, Uppsala University, Uppsala, 1997.

An Object-oriented Approach to Construct PDE Solvers, Read abstract
Report 180, Department of Scientific Computing, Uppsala University, Uppsala, 1996.

Towards an Expressive Language for PDE Solvers
Michael Thune, KÅ. Presented and published at the European Symposium on Programming (ESOP'96), Linköping University, April 22 - 26, 1996

krister@user.it.uu.se