A parallel multifrontal algorithm and its implementation

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.