Parallel direct and iterative linear system solution methods: a comparison |
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| Both parallel direct and iterative methods for the solution of large sparse linear systems received much attention in recent years. Reduced communication overhead and dynamic load balancing have resulted from several algorithmic improvements in direct methods especially for nonsymmetric problems, whereas more efficient preconditioners capable of tackling increasingly difficult problems to be solved is the emphasis of the research in parallel iterative methods. Both classes of solution methods have undergone extensive testing on real-world applications as well as on model linear systems considered difficult in the respective classes. The aim of this talk is to describe an attempt in a uniform comparison of these two classes of solution methods. Our approach is to take a representative software package, a direct (MUMPS) and iterative (pARMS), as the main basis for comparison, design a set of criteria that is a synthesis of the ones used in both communities, and use the test cases considered challenging in either class. We experiment with different input and tuning parameters, such as orderings, scaling, fill-in and tolerances (for iterative methods), to achieve a solution for which the parallel solution time, including the factorization or preconditioner construction phase, is minimized. In addition, we give an overview on recent developments in the considered software packages. |
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algweb@cerfacs.fr Last Update: Apr 7, 2003 |