This course will present the state of the art in the development of parallel direct methods for sparse linear systems.
It is organized in conection with IT4Innovations, Ostrava, Czech Republic. The course will be held jointly with the Seminar on Numerical Analysis and Winter School 2017 (SNA), held on 30 January - 3 February 2017. See the PLA web page at IT4Innovations for further details.
Some of these methods presented are implemented as black box solvers; the corresponding toolkits will be experimented in dedicated hand-on sessions.
The course will also present recent work on hybrid (direct / iterative) methods that better exploit the two-level structure of current parallel architectures.
- Direct solvers:
- Dense matrices (serial and parallel, 1D and 2D distributions)
- Sparse matrices (graph model, renumbering, elimination graph, symbolic and numeric factorizations)
- Parallel methods: data distribution, scheduling of computations and communications
- Hands-on with the MUMPS and Pastix solvers
- Basics on Krylov subspace methods
- Basics on algebraic domain decomposition methods (Schur/Schwarz)
- Hybrid direct/iterative methods: motivation and description of methods
- Hierarchical parallel implementation and scalability issues
Hands-on session with the MaPhys and HIPS solvers.
M. Faverge (Bordeaux INP, Bordeaux), L. Giraud (Inria, Bordeaux), Z. Strakos (Charles University, Prague)
Understand the main features of the direct and iterative methods, their tradeoffs and when using them is most advisable.
Gain practical experience with some state of the art solvers.
Basic knowledge of linear algebra and parallel algorithms
Knowledge of a programming language (Fortran, C, C++)
Ability to use Linux (Unix)