Digiteo Labs
Bâtiment 565
CEA Saclay
91191 Gif-sur-Yvette
Description
This course will present the state of the art in the development of parallel direct methods for sparse linear systems. Some of these methods are being 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)
Parallel methods: data distribution, scheduling of computations and communications
Hands-on with the MUMPS and Pastix solvers
Hybrid methods
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.
Learning outcomes
Participants will understand the main features of the main direct and iterative methofd, their tradeoffs and when using them is most advisable.
They will also gain practical experience with some state of the art solvers
Prerequisites
Basic knowledge of linear algebra and parallel algorithms
Knowledge of a programming language (Fortran, C, C++)
Use of Linux (Unix)
