FRONTIERS IN COMPUTATIONAL ASTROPHYSICS

Particle and Flames in Radiative and Magnetic Flows

October 11-15, 2010
Lyon, France

Contribution of Jean-Yves L'Excellent

Title

Parallel sparse direct methods and the MUMPS package

Topics

"Explosive fate of stars"

Keywords

sparse matrices, systems of linear equations, direct methods, parallel solvers

Abstract

Direct methods for the solution of sparse systems of linear equations are extensively used in the context of numerical simulation. Such methods are based on a matrix decomposition of the form A = LU, LL^t or LDL^t, followed by triangular solves. In comparison to iterative methods, they are known for their numerical robustness. However, they are also characterized by a high memory consumption (especially for 3D problems) and a large amount of computations. In this talk, we will present some of the characteristics of direct methods, and some of the challenges that need to be tackled to solve larger and larger problems on emerging computing platforms. We will also present the MUMPS package (see http://graal.ens-lyon.fr/MUMPS or http://mumps.enseeiht.fr), a parallel sparse direct solver developed in France in Lyon, Toulouse and Bordeaux, available free of charge. MUMPS is based on a so-called multifrontal approach, and uses message passing for parallelism. We will discuss its features compared to other parallel sparse direct solvers, and present some of the current research we are involved in.

Talk