Seminars at the Faculty of Informatics

Usage and improvement of Krylov subspace recycling methods

The Faculty of Informatics is pleased to announce a seminar given by Matthias Bolten

DATE: Tuesday, May 15th, 2012
PLACE: USI Università della Svizzera italiana, room SI-006, Informatics building  (Via G. Buffi 13)
TIME: 14.00

Many problems in numerical simulations in science and engineering require the solution of long sequences of slowly changing linear systems. One example problem that is of interest to us arises in Lattice QCD simulations, e.g., while computing masses of elementary particles.

Here, a hybrid Monte-Carlo approach is applied that introduces the calculation of an artificial trajectory using molecular dynamics.  In each time step, a linear system with a Dirac operator that changes slightly from time step to time step has to be solved.

In the talk we will introduce the idea Krylov recycling methods and the method GCRO-DR by M. Parks and E. de Sturler [1] that is similar to GCRO, GCROT and GMRES-DR. We will then present recent simple ideas on improving the method by enriching them with further knowledge about the subspaces.

Results for QCD simulations and electronic structure calculations in comparison to algorithms solving each system separately and numerical examples for our new approaches will be presented.

[1] Michael L. Parks, Eric de Sturler, Greg Mackey, Duane D. Johnson and Spandan Maiti, Recycling Krylov subspaces for sequences of linear systems, SIAM Journal on Scientific Computing, 28 (2006), 1651-1674

Prof. Dr. Matthias Bolten currently holds the position of a Juniorprofessor for Applied Mathematics/Computer Science in the group for Applied Computer Science ( at the University of Wuppertal. After finishing his diploma degree in Computer Science at the University of Lübeck in 2005 he worked as a doctoral student at the Jülich Supercomputing Centre where he continued to work as a postdoc after obtaining his doctor in science degree from the University of Wuppertal. He holds his current position since 2009.

His research interests are:
- Numerical linear algebra, especially iterative solvers and structured matrices, including multigrid methods and Krylov subspace methods
- Particle simulation methods, e.g., for long-ranged interactions arising in biophysics or plasma physics or for short-ranged interactions for simulating granular matter
- Parallel numerical algorithms

HOST: Prof. Rolf Krause, Dr. Robert Speck

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