Jacko Koster

A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling

In this paper, we analyze the main features and discuss the tuning of the algorithms for the direct solution of sparse linear systems on distributed memory computers developed in the context of a long term European research project. The algorithms use a multifrontal approach and are especially designed to cover a large class of problems. The problems can be symmetric positive definite, general symmetric, or unsymmetric matrices, both possibly rank deficient, and they can be provided by the user in several formats. The algorithms achieve high performance by exploiting parallelism coming from the sparsity in the problem and that available for dense matrices. The algorithms use a dynamic distributed task scheduling technique to accommodate numerical pivoting and to allow the migration of computational tasks to lightly loaded processors. Large computational tasks are divided into subtasks to enhance parallelism. Asynchronous communication is used throughout the solution process to efficiently overlap communication with computation. We illustrate our design choices by experimental results obtained on an SGI Origin 2000 and an IBM SP2 for test matrices provided by industrial partners in the PARASOL project.

On Algorithms For Permuting Large Entries to the Diagonal of a Sparse Matrix

We consider bipartite matching algorithms for computing permutations of a sparse matrix so that the diagonal of the permuted matrix has entries of large absolute value. We discuss various strategies for this and consider their implementation as computer codes. We also consider scaling techniques to further increase the relative values of the diagonal entries. Numerical experiments show the effect of the reorderings and the scaling on the solution of sparse equations by a direct method and by preconditioned iterative techniques.

The Design and Use of Algorithms for Permuting Large Entries to the Diagonal of Sparse Matrices

We consider techniques for permuting a sparse matrix so that the diagonal of the permuted matrix has entries of large absolute value. We discuss various criteria for this and consider their implementation as computer codes. We then indicate several cases where such a permutation can be useful. These include the solution of sparse equations by a direct method and by an iterative technique. We also consider its use in generating a preconditioner for an iterative method. We see that the effect of these reorderings can be dramatic although the best a priori strategy is by no means clear.

MUMPS: A General Purpose Distributed Memory Sparse Solver

MUMPS is a public domain software package for the multifrontal solution of large sparse linear systems on distributed memory computers. The matrices can be symmetric positive definite, general symmetric, or unsymmetric, and possibly rank deficient. MUMPS exploits parallelism coming from the sparsity in the matrix and parallelism available for dense matrices. Additionally, large computational tasks are divided into smaller subtasks to enhance parallelism. MUMPS uses a distributed dynamic scheduling technique that allows numerical pivoting and the migration of computational tasks to lightly loaded processors. Asynchronous communication is used to overlap communication with computation. In this paper, we report on recently integrated features and illustrate the present performance of the solver on an SGI Origin 2000 and a CRAY T3E.

Domain Decomposition Solvers for Large Scale Industrial Finite Element Problems

The European research project PARASOL aimed to design and develop a public domain library of scalable sparse matrix solvers for distributed memory computers. Parallab was a partner in the project and developed a domain decomposition code for solving large scale finite element problems in a robust, yet efficient way. Although the PARASOL project finished in June 1999, Parallab has continued the development of the solver. In this paper, we report on the present status of the solver and show its performance on some challenging industrial problems.

Balancing domain decomposition applied to structural analysis problems

Publisher Summary This chapter discusses the present status of a library of iterative sub-structuring solvers for the parallel solution of large sparse linear systems of equations that arise from large scale industrial finite-element applications. The iterative solution schemes have been applied to a series of model problems but also to real-life test cases that include structural analysis problems from the automobile industry and ship structure analysis. The library provides a single framework that includes Schur complement techniques and Schwarz procedures. The pre-conditioners include well-known incomplete factorization variants, as well as more advanced techniques, (such as for example balancing domain decomposition). The chapter shows some of the performance of the software on a real-life industrial problem. The SALSA software package features state-of-the-art domain decomposition techniques. These include iterative sub-structuring techniques with l-level and 2-level Neumann-Neumann pre-conditioners. The 2-level method features a variety of coarse spaces. Some of these coarse spaces are designed for specific classes of problems, but others are computed algebraically and no additional problem information is required. The software contains other domain decomposition techniques as well, but this chapter restricts the discussion to iterative sub-structuring and the Neumann-Neumann pre-conditioners.