A parallel multifrontal algorithm and its implementation

• Published in: Computer methods in applied mechanics and engineering Vol. 149; no. 1; pp. 289 - 301
• Main Authors: Geng, P., Oden, J.T., van de Geijn, R.A.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Amsterdam Elsevier B.V 01.10.1997; Elsevier
• Subjects: Exact sciences and technology; Mathematical methods in physics; Numerical approximation and analysis; Numerical linear algebra; Physics; Direct method; Finite element method; Equation system solving; Positive definite matrix; Parallel processing; Numerical method; Matrix decomposition; Sparse matrices; Domain decomposition; Finite difference method
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/S0045-7825(97)00052-2

In this paper, we describe a multifrontal method for solving sparse systems of linear equations arising in finite element and finite difference methods. The method proposed in this study is a combination of the nested dissection ordering and the frontal method. It can significantly reduce the storage and computational time required by the conventional direct methods and is also a natural parallel algorithm. In addition, the method inherits major advantages of the frontal method, which include a simple interface with finite element codes and an effective data structure so that the entire computation is performed element by element on a series of small linear systems with dense stiffness matrices. The numerical implementation targets both distributed-memory machines as well as conventional sequential machines. Its performance is tested through a series of examples.