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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
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Parallelization of iterative solution methods and preconditioners for non-diagonally dominant, block-tridiagonal systems of equations
. In Hypercube and Distributed Computers, pp 353-354, Elsevier Science, Amsterdam, The Netherlands, 1989.
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A fast modified sine transform for solving block-tridiagonal systems with Toeplitz blocks
. In Numerical Algorithms, volume 7, pp 375-389, 1994. (DOI
).
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A domain decomposition method for first-order PDEs
. In SIAM Journal on Matrix Analysis and Applications, volume 16, pp 1241-1267, 1995. (DOI
).
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A domain decomposition method for hyperbolic problems in 2D
. In Parallel Computational Fluid Dynamics: New Trends and Advances, pp 373-380, Elsevier Science, Amsterdam, The Netherlands, 1995. (DOI
).
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Analysis of semi-Toeplitz preconditioners for first-order PDEs
. In SIAM Journal on Scientific Computing, volume 17, pp 47-64, 1996. (DOI
).
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Toeplitz preconditioners with block structure for first-order PDEs
. In Numerical Linear Algebra with Applications, volume 3, pp 21-44, 1996. (DOI
).
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A domain decomposition method for almost incompressible flow
. In Computers & Fluids, volume 25, pp 771-789, 1996. (DOI
).
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A semi-circulant preconditioner for the convection-diffusion equation
. In Numerische Mathematik, volume 81, pp 211-248, 1998. (DOI
).
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A new parallel preconditioner for the Euler equations
. 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
).
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A fast domain decomposition high order Poisson solver
. In Journal of Scientific Computing, volume 14, pp 223-243, 1999. (DOI
).
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Convergence acceleration for the Euler equations using a parallel semi-Toeplitz preconditioner
. In Euro-Par'99: Parallel Processing, volume 1685 of Lecture Notes in Computer Science, pp 1124-1127, Springer-Verlag, Berlin, 1999. (DOI
).
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Implicit high-order difference methods and domain decomposition for hyperbolic problems
. In Applied Numerical Mathematics, volume 33, pp 493-500, 2000. (DOI
).
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High order methods and domain decomposition
. In Absorbing Boundaries and Layers, Domain Decomposition Methods: Applications to Large Scale Computers, pp 341-347, Nova Science Publishers, Huntington, NY, 2001.
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A nearly optimal preconditioner for the Navier-Stokes equations
. In Numerical Linear Algebra with Applications, volume 8, pp 229-243, 2001. (DOI
).
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Deferred correction in space and time
. In Journal of Scientific Computing, volume 17, pp 541-550, 2002. (DOI
).
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Implicit solution of hyperbolic equations with space-time adaptivity
. In BIT Numerical Mathematics, volume 42, pp 134-158, 2002. (DOI
).
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Preconditioned implicit solution of linear hyperbolic equations with adaptivity
. In Journal of Computational and Applied Mathematics, volume 170, pp 269-289, 2004. (DOI
).
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Semi-Toeplitz preconditioning for the linearized Navier-Stokes equations
. In BIT Numerical Mathematics, volume 44, pp 307-341, 2004. (DOI
).
Theses
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Semi-Toeplitz preconditioning for linearized boundary layer problems
. Licentiate thesis, IT licentiate theses / Uppsala University, Department of Information Technology nr 2002-007, Uppsala University, 2002. (fulltext
).
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Domain Decomposition Methods and Fast Solvers for First-order PDEs
. Ph.D. thesis, Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology nr 114, Acta Universitatis Upsaliensis, Uppsala, 1995.
Supervised Master thesis projects
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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.
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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.