THE MULTIFRONTAL METHOD FOR SPARSE-MATRIX SOLUTION - THEORY AND PRACTICE

This paper presents an overview of the multifrontal method for the solution of large sparse symmetric positive definite linear systems. The method is formulated in terms of frontal matrices, update matrices, and an assembly tree. Formal definitions of these notions are given based on the sparse matrix structure. Various advances to the basic method are surveyed. They include the role of matrix reorderings, the use of supernodes, and other implementation techniques. The use of the method in different computational environments is also described.