
Workshop Recent Developments in the Solution of Indefinite Systems
1 day workshop, TU Eindhoven, April 17, 2012
Organizers
 Wil Schilders (TU Eindhoven)
 Kees Vuik (TU Delft)
 Mike Botchev (Univ. Twente)
Topics
The numerical approximation of several important scientific and
engineering problems leads to blockstructured 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:
Registration
Participation is free of charge, but registration is mandatory. Please send an email 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 email.
Programme
10.2510.30: Opening and word of welcome: Introduction
10.3011.15: Michele Benzi: “New block preconditioners for saddle point problems”
11.1511.30: Coffee break
11.3012.15: Andy Wathen: “Combination Preconditioning of saddlepoint systems for positive definiteness”
12.1512.30: Jos Maubach: “Micro and macroblock factorizations for regularized saddle point systems”
12.3012.45: Karl Meerbergen: “A shifted preconditioner for the damped Helmholtz equation”
12.4513.45: Lunch
13.4514.30: Miroslav Rozloznik: “Implementation and numerical stability of saddle point solvers”
14.3014.45: Fred Wubs: “Structure preserving preconditioner for the incompressible NavierStokes equations”
14.4515.00: Christiaan Klaij: The use of SIMPLEtype preconditioners in maritime CFD applications”
15.0015.30: Coffee/tea
15.3016.15: Marc Baboulin: “A parallel tiled solver for dense symmetric indefinite systems on multicore architectures"
16.1517.00: Luca Bergamaschi: “Relaxed mixed constraint
preconditioners for Illconditioned symmetric saddle point linear
systems”
17.0017.15: Pawan Kumar: “A Purely algebraic domain decomposition method for the incompressible NavierStokes equation”
17.1517.30: Sebastiaan Breedveld: "Optimization in cancer treatment: indefinitely a problem?"
17.30: Closing
18.00: Dinner for invited speakers
Location
De Zwarte Doos, in the cinema ("filmzaal") at the TU/e campus (http://www.dezwartedoos.nl/).
