Parallel calculation

The aim of this course is to introduce students to the complete implementation of a parallel algorithm by domain decomposition of a 2D problem, and to compare this technique with the operator parallelism covered in the 2nd year option.
The difficulty, in the case of solution schemes applied to unstructured meshes, is to reconcile load balance and communication structure (simple and as small as possible). Solutions based on graph partitioning (METIS, SCOTCH) will be discussed. The use of these partitionings in a finite element code (provided) for unstructured meshes will be explained and used for a speed-up study of the code. After a reminder of the main functions of the MPI communication interface, optimization in parallel programming will be considered (use of non-blocking communication subroutines, overlapping of communication with computation).
Domain decomposition methods (additive and multiplicative Schwarz) will be presented, and their numerical application will be made on a 2D equation for structured meshes. If time permits, an introduction to PETSC (open source library for scientific computing based on MPI for parallelism) will be offered.

Module AN202