Marzio Sala : January 12, 2006

Object-Oriented Programming Techniques for Sparse Linear System Solvers.

Abstract

In this talk we consider the usage of object-oriented programming techniques for the direct and iterative solution of sparse linear systems on distributed memory computers.

First, we focus on direct solvers, and we present an overview of the Amesos project of Trilinos. Amesos is based on an abstract matrix interface to access the matrix elements, and an abstract solver interface that controls the solution of the linear system. Amesos allows a high-level view and usage of severaldirect solver libraries. We comment on the advantages and limitations of the framework, and we report numerical results to show that the overhead required by the interface is negligible.

Then, we consider iterative solvers of Krylov type, and we focus on the definition of algebraic preconditioners. A class of preconditioners based on the concept of smoothed aggregation is introduced. The resulting procedure, that does not require geometric information, is completely algebraic and well-suited for parallel computations on unstructured grids in two and three dimensions. Convergence estimates and numerical results are reported.