A PARALLEL MULTIFRONTAL ALGORITHM AND ITS IMPLEMENTATION

In this paper, we describe a multifrontal method for solving sparse sy stems of linear equations arising in finite element and finite differe nce methods. The method proposed in this study is a combination of the nested dissection ordering and the frontal method. It can significant ly reduce the storage and computational time required by the conventio nal direct methods and is also a natural parallel algorithm. In additi on, 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 matri ces. The numerical implementation targets both distributed-memory mach ines as well as conventional sequential machines. Its performance is t ested through a series of examples.