July 27, 1998 | P. R. Amestoy, I. S. Duff and J.-Y. L'Excellent
This paper presents a new parallel distributed memory multifrontal approach for solving both symmetric and unsymmetric systems of sparse linear equations. The authors develop a parallel asynchronous algorithm with dynamic scheduling to efficiently handle numerical pivoting. The main algorithmic choices and implementation issues are discussed, including mapping, sources of parallelism, and the performance of $LDL^T$ and $LU$ factorizations. Performance analysis on an IBM SP2 demonstrates the efficiency and potential of the method. The test problems used are from the Rutherford-Boeing collection and from the PARASOL end users. The paper also includes a detailed description of the multifrontal method, the implementation issues, and the performance results, highlighting the benefits of the proposed approach in terms of speed-up and parallelism.This paper presents a new parallel distributed memory multifrontal approach for solving both symmetric and unsymmetric systems of sparse linear equations. The authors develop a parallel asynchronous algorithm with dynamic scheduling to efficiently handle numerical pivoting. The main algorithmic choices and implementation issues are discussed, including mapping, sources of parallelism, and the performance of $LDL^T$ and $LU$ factorizations. Performance analysis on an IBM SP2 demonstrates the efficiency and potential of the method. The test problems used are from the Rutherford-Boeing collection and from the PARASOL end users. The paper also includes a detailed description of the multifrontal method, the implementation issues, and the performance results, highlighting the benefits of the proposed approach in terms of speed-up and parallelism.