Domain decomposition methods and fast solvers for PDEs

The research presented here covers:

• fast Fourier-based transforms
• iterative methods for large sparse linear systems of equations
• suitable preconditioners based on Fourier transforms for the above mentioned linear systems
• domain decomposition methods
• the extension of the above methods to suit real-life applications such as fluid flow problems
• high-order methods
• adaptive methods

The work was mainly carried out during 1989-2001.

Note that Lina von Sydow has published papers also under the names Lina Frändén, Lina Hemmingsson, and Lina Hemmingsson-Frändén.

Publications

Refereed

1. Parallelization of iterative solution methods and preconditioners for non-diagonally dominant, block-tridiagonal systems of equations. Sverker Holmgren, Kurt Otto, and Lina Frändén. In Hypercube and Distributed Computers, pp 353-354, Elsevier Science, Amsterdam, The Netherlands, 1989.
2. A fast modified sine transform for solving block-tridiagonal systems with Toeplitz blocks. Lina Hemmingsson. In Numerical Algorithms, volume 7, pp 375-389, 1994. (DOI).
3. A domain decomposition method for first-order PDEs. Lina Hemmingsson. In SIAM Journal on Matrix Analysis and Applications, volume 16, pp 1241-1267, 1995. (DOI).
4. A domain decomposition method for hyperbolic problems in 2D. Lina Hemmingsson. In Parallel Computational Fluid Dynamics: New Trends and Advances, pp 373-380, Elsevier Science, Amsterdam, The Netherlands, 1995. (DOI).
5. Analysis of semi-Toeplitz preconditioners for first-order PDEs. Lina Hemmingsson and Kurt Otto. In SIAM Journal on Scientific Computing, volume 17, pp 47-64, 1996. (DOI).
6. Toeplitz preconditioners with block structure for first-order PDEs. Lina Hemmingsson. In Numerical Linear Algebra with Applications, volume 3, pp 21-44, 1996. (DOI).
7. A domain decomposition method for almost incompressible flow. Lina Hemmingsson. In Computers & Fluids, volume 25, pp 771-789, 1996. (DOI).
8. A semi-circulant preconditioner for the convection-diffusion equation. Lina Hemmingsson. In Numerische Mathematik, volume 81, pp 211-248, 1998. (DOI).
9. A new parallel preconditioner for the Euler equations. Lina Hemmingsson and Andreas Kähäri. In Applied Parallel Computing: Large Scale Scientific and Industrial Problems, volume 1541 of Lecture Notes in Computer Science, pp 230-238, Springer-Verlag, Berlin, 1998. (DOI).
10. A fast domain decomposition high order Poisson solver. Bertil Gustafsson and Lina Hemmingsson-Frändén. In Journal of Scientific Computing, volume 14, pp 223-243, 1999. (DOI).
11. Convergence acceleration for the Euler equations using a parallel semi-Toeplitz preconditioner. Andreas Kähäri and Samuel Sundberg. In Euro-Par'99: Parallel Processing, volume 1685 of Lecture Notes in Computer Science, pp 1124-1127, Springer-Verlag, Berlin, 1999. (DOI).
12. Implicit high-order difference methods and domain decomposition for hyperbolic problems. Bertil Gustafsson and Lina Hemmingsson-Frändén. In Applied Numerical Mathematics, volume 33, pp 493-500, 2000. (DOI).
13. High order methods and domain decomposition. Bertil Gustafsson and Lina Hemmingsson-Frändén. In Absorbing Boundaries and Layers, Domain Decomposition Methods: Applications to Large Scale Computers, pp 341-347, Nova Science Publishers, Huntington, NY, 2001.
14. A nearly optimal preconditioner for the Navier-Stokes equations. Lina Hemmingsson-Frändén and Andrew Wathen. In Numerical Linear Algebra with Applications, volume 8, pp 229-243, 2001. (DOI).
15. Deferred correction in space and time. Bertil Gustafsson and Lina Hemmingsson-Frändén. In Journal of Scientific Computing, volume 17, pp 541-550, 2002. (DOI).
16. Implicit solution of hyperbolic equations with space-time adaptivity. Per Lötstedt, Stefan Söderberg, Alison Ramage, and Lina Hemmingsson-Frändén. In BIT Numerical Mathematics, volume 42, pp 134-158, 2002. (DOI).
17. Preconditioned implicit solution of linear hyperbolic equations with adaptivity. Per Lötstedt, Alison Ramage, Lina von Sydow, and Stefan Söderberg. In Journal of Computational and Applied Mathematics, volume 170, pp 269-289, 2004. (DOI).
18. Semi-Toeplitz preconditioning for the linearized Navier-Stokes equations. Samuel Sundberg and Lina von Sydow. In BIT Numerical Mathematics, volume 44, pp 307-341, 2004. (DOI).

Theses

• Domain Decomposition Methods and Fast Solvers for First-order PDEs. Lina Hemmingsson. Ph.D. thesis, Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology nr 114, Acta Universitatis Upsaliensis, Uppsala, 1995. (KÖP BOKEN / BUY THIS BOOK).
• Semi-Toeplitz preconditioning for linearized boundary layer problems. Samuel Sundberg. Licentiate thesis, IT licentiate theses / Uppsala University, Department of Information Technology nr 2002-007, 2002. (External link).

Supervised Master thesis projects

• An implementation of a new parallel preconditioner for the time dependent Euler equations. Andreas Kähäri. Master thesis, Report nr 96:04, Parallel and Scientific Computing Institute, Royal Institute of Technology, Stockholm, 1996.

• Convergence acceleration for the Euler equations using a parallel semi-Toeplitz preconditioner. Samuel Sundberg. Master thesis, Report nr 98:10, Parallel and Scientific Computing Institute, Royal Institute of Technology, Stockholm, 1998.

Contact information

Lina von Sydow