Pascal Hénon

PASTIX: a high-performance parallel direct solver for sparse symmetric positive definite systems

Solving large sparse symmetric positive definite systems of linear equations is a crucial and time-consuming step, arising in many scientific and engineering applications. The block partitioning and scheduling problem for sparse parallel factorization without pivoting is considered. There are two major aims to this study: the scalability of the parallel solver, and the compromise between memory overhead and efficiency. Parallel experiments on a large collection of irregular industrial problems validate our approach.

PaStiX: A Parallel Sparse Direct Solver Based on a Static Scheduling for Mixed 1D/2D Block Distributions

We presen t and analyze a general algorithm which computes an efficient static scheduling of block computations for a parallel L:D:Lt factorization of sparse symmetric positive definite systems based on a combination of 1D and 2D block distributions. Our solver uses a supernodal fan-in approach and is fully driven by this scheduling. We give an overview of the algorithm and present performance results and comparisons with PSPASES on an IBM-SP2 with 120 MHz Pow er2SC nodes for a collection of irregular problems.

On finding approximate supernodes for an efficient block-ILU(k) factorization

Among existing preconditioners, the level-of-fill ILU has been quite popular as a general-purpose technique. Experimental observations have shown that, when coupled with block techniques, these methods can be quite effective in solving realistic problems arising from various applications. In this work, we consider an extension of this kind of method which is suitable for parallel environments. Our method is developed from the framework of high performance sparse direct solvers. The main idea we propose is to define an adaptive blockwise incomplete factorization that is much more accurate (and numerically more robust) than the scalar incomplete factorizations commonly used to precondition iterative solvers. These requirements lead to a robust class of parallel preconditioners based on generalized versions of block ILU techniques.

A Mapping and Scheduling Algorithm for Parallel Sparse Fan-In Numerical Factorization

We present and analyze a general algorithm which computes efficient static schedulings of block computations for parallel sparse linear factorization. Our solver, based on a supernodal fan-in approach, is fully driven by this scheduling. We give an overview of the algorithms and present performance results on a 16-node IBM-SP2 with 66 MHz Power2 thin nodes for a collection of grid and irregular problems.

Parallel Sparse Linear Algebra and Application to Structural Mechanics

The framework of this paper is the parallelization of a plasticity algorithm that uses an implicit method and an incremental approach. More precisely, we will focus on some specific parallel sparse linear algebra algorithms which are the most time-consuming steps to solve efficiently such an engineering application. First, we present a general algorithm which computes an efficient static scheduling of block computations for parallel sparse linear factorization. The associated solver, based on a supernodal fan-in approach, is fully driven by this scheduling. Second, we describe a scalable parallel assembly algorithm based on a distribution of elements induced by the previous distribution for the blocks of the sparse matrix. We give an overview of these algorithms and present performance results on an IBM SP2 for a collection of grid and irregular problems.

Applying parallel direct solver techniques to build robust high performance preconditioners

The purpose of our work is to provide a method which exploits the parallel blockwise algorithmic approach used in the framework of high performance sparse direct solvers in order to develop robust preconditioners based on a parallel incomplete factorization. The idea is then to define an adaptive blockwise incomplete factorization that is much more accurate (and numerically more robust) than the scalar incomplete factorizations commonly used to precondition iterative solvers.

Partitioning and blocking issues for a parallel incomplete factorization

The purpose of this work is to provide a method which exploits the parallel blockwise algorithmic approach used in the framework of high performance sparse direct solvers in order to develop robust and efficient preconditioners based on a parallel incomplete factorization.