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Workshop Recent Developments in the Solution of Indefinite Systems

1 day workshop, TU Eindhoven, April 17, 2012


  • Wil Schilders (TU Eindhoven)
  • Kees Vuik (TU Delft)
  • Mike Botchev (Univ. Twente)


The numerical approximation of several important scientific and engineering problems leads to block-structured indefinite linear systems in saddle point form. These problems arise in systems of PDEs with conservation laws, in constrained optimization problems, in mixed finite element discretizations, and in generalized least squares problems. Their efficient numerical solution is the subject of much research. The successful design of robust, scalable, and efficient preconditioners is intimately connected with an understanding of the structure of the resulting block matrix system, and relies heavily on exploiting this structure. Effective preconditioners are often based on an approximate block decomposition of the system that derives from a careful consideration of the spectral properties of the component block operators and the Schur complement operators. Through this purely algebraic view of preconditioning, a simplified system of block component equations is developed that encodes a specific "physics based" decomposition. Recent progress based on these ideas has led to the construction of a number of effective preconditioners with optimal or nearly optimal convergence rates for several applications. However, to compute accurate solutions to saddle point problems at a reasonable cost has proved difficult. As a consequence, a significant effort has been devoted to define proper formulations, discretizations, and fast solution methods for discretized saddle point problems and their generalizations.

This workshop brings together experts on the continuous and discrete formulation of saddle point problems from several areas of computational science, both for specific and general problems, and on efficient (parallel) solution techniques for the resulting systems of equations. This workshop will be useful both to researchers dealing with applications that give rise to saddle point problems and to developers of effective solution techniques for the resulting equations.

Invited speakers:


Participation is free of charge, but registration is mandatory. Please send an e-mail to w.h.a.schilders@tue.nl before April 10, 2012. There is a limited number of time slots available for short (5, 10 or 15 minute) presentations, please include your proposal (title, abstract, duration) in the e-mail.


10.25-10.30: Opening and word of welcome: Introduction
10.30-11.15: Michele Benzi: “New block preconditioners for saddle point problems
11.15-11.30: Coffee break
11.30-12.15: Andy Wathen: “Combination Preconditioning of saddle-point systems for positive definiteness
12.15-12.30: Jos Maubach: “Micro- and macro-block factorizations for regularized saddle point systems
12.30-12.45: Karl Meerbergen: “A shifted preconditioner for the damped Helmholtz equation
12.45-13.45: Lunch
13.45-14.30: Miroslav Rozloznik: “Implementation and numerical stability of saddle point solvers
14.30-14.45: Fred Wubs: “Structure preserving preconditioner for the incompressible Navier-Stokes equations
14.45-15.00: Christiaan Klaij: The use of SIMPLE-type preconditioners in maritime CFD applications
15.00-15.30: Coffee/tea
15.30-16.15: Marc Baboulin: “A parallel tiled solver for dense symmetric indefinite systems on multicore architectures"
16.15-17.00: Luca Bergamaschi: “Relaxed mixed constraint preconditioners for Ill-conditioned symmetric saddle point linear systems
17.00-17.15: Pawan Kumar: “A Purely algebraic domain decomposition method for the incompressible Navier-Stokes equation
17.15-17.30: Sebastiaan Breedveld: "Optimization in cancer treatment: indefinitely a problem?"
17.30: Closing
18.00: Dinner for invited speakers


De Zwarte Doos, in the cinema ("filmzaal") at the TU/e campus (http://www.dezwartedoos.nl/).

© Centre for Analysis, Scientific Computing and Applications. For questions please refer to the editor.
This page modified: Mon Apr 23 15:10:06 CEST 2012