This course will be held online using Zoom.
The focus of the course is on modern iterative solvers for large linear systems of equations. Thereby, beside classical schemes and fundamentals of multigrid techniques different modern Krylov subspace methods (CG, GMRES, BiCGSTAB ...) as well as highly efficient preconditioning techniques are presented in the context of real life applications. Hands-on sessions (MATLAB and GNU Octave respectively) will allow users to immediately test and understand the basic constructs of iterative solvers. This course provides scientific training in Computational Science, and in addition, the scientific exchange of the participants among themselves. It is organized by HLRS, IAG, and Uni. Kassel.
The guest lecture on Day 2 (slides) is offered in collaboration with HiDALGO, the EU Centre of Excellence for Global Challenges. The method exposed is used in the HiDALGO Social Network Pilot. See also this HiDALGO news.
08:30 - 09:00 on every day: drop in to Zoom
09:00 - 10:00 Introduction, Basics and Practicals (Lecture + Practicals)
10:00 - 11:00 Consistency and Convergence (Lecture)
11:00 - 11:30 Break
11:30 - 12:15 Jacobi Method (Lecture)
12:15 - 13:00 Practicals
13:00 - 14:00 Lunch
14:00 - 14:30 Gauß-Seidel Method (Lecture)
14:30 - 15:00 Practicals
15:00 - 15:15 Q+A
09:00 - 10:00 Relaxation Schemes (Lecture)
10:00 - 10:45 Practicals
10:45 - 11:00 Break
11:00 - 11:30 Method of Steepest Descent (Lecture)
11:30 - 12:00 Practicals
12:00 - 13:00 Lunch
13:00 - 14:00 Method of Conjugate Gradients (Lecture)
14:00 - 14:45 Practicals
14:45 - 15:00 Q+A
15:00 - 15:15 Break
15:15 - 16:00 Guest Lecture by Robert Elsässer (PLUS, Salzburg): slides.
09:00 - 10:00 Introduction to Multigrid Methods (Lecture)
10:00 - 10:30 Practicals
10:30 - 10:45 Break
10:45 - 11:45 GMRES and BICG (Lecture)
11:45 - 12:15 Practicals
12:15 - 13:15 Lunch
13:15 - 13:45 Variants of BICG (Lecture)
13:45 - 14:15 Practicals
14:15 - 15:15 Preconditioning
15:15 - 15:30 Q+A
Guest Lecture by Robert Elsässer (PLUS, Salzburg):
Spectral methods to compute "eigenvalue histograms" (estimates of eigenvalue frequencies) for graph Laplacians and other LA apps that rely on iterative solvers (e.g in PETCs): slides.
Basics of linear algebra
MATLAB or GNU Octave
The course language is English.
Students without Diploma/Master: 30 EUR
Students with Diploma/Master (PhD students) at German universities: 60 EUR
Members of German universities and public research institutes: 60 EUR
Members of universities and public research institutes within EU or PRACE member countries: 120 EUR.
Members of other universities and public research institutes: 240 EUR
Others: 600 EUR
HLRS is part of the Gauss Centre for Supercomputing (GCS), which is one of the six PRACE Advanced Training Centres (PATCs) that started in Feb. 2012.
HLRS is also member of the Baden-Württemberg initiative bwHPC-C5.
This course is provided within the framework of the bwHPC-C5 user support. This course is not part of the PATC curriculum and is not sponsored by the PATC program.