Title: HIPS : a parallel hybrid direct/iterative solver based on a Schur complement approach

Speaker: Jérémie Gaidamour, University of Bordeaux, France

Date/Time:  Thursday, October 1, 2009, 9:00 am        

Location: CSRI Building, Room 90 (Sandia NM)

Brief Abstract: Nowadays, three dimensional numerical simulations often require a
tremendous amount of resources. On one hand, direct methods can be mandatory to solve very ill-conditioned systems. But for large 3D simulations, they are constrained by prohibitive memory requirements and they also need a high amount of floating point
operations. Iterative methods on the other hand require much less memory and are more scalable in general.

Hybrid methods based on a Schur complement approach try to combine the assets of the two class of methods. An usual method is to use a decomposition of the matrix graph into sub-domains. The matrix part corresponding to the interior unknowns is treated using a direct method and the resolution of the global system is then reduced to the
resolution of the Schur complement system. The Schur complement can then be solved using an iterative method.

In the HIPS library (http://hips.gforge.inria.fr/), we have developed such an approach. The corner stone of our method is to use a special decomposition and ordering of the matrix that allows to construct a reduced system and a robust preconditioner at low memory cost. In this talk, I will present the hybrid method and compare two ways to compute the incomplete factorization of the Schur complement. I will also present a parallelization scheme based on using several domain per processor. I will also give some results for large difficult test cases on a large number of processors.

CSRI POC: Mike Heroux, (320) 845-7695