Static mapping of the multifrontal method applied to the modified cholesky factorization for sparse matrices

Abstract

Publisher Summary This chapter describes a heuristic static mapping of the computational load in the execution of the modified Cholesky factorization using a multifrontal strategy on distributed memory systems. The multifrontal method reorganizes the overall factorization of a sparse matrix into a sequence of partial factorizations of smaller dense submatrices. The key concepts in the multifrontal method are frontal and update matrices. Finally, the chapter discusses the execution times of the corresponding parallel code on the Fujitsu AP-1000 and Cray T3E. The elimination tree of a given matrix A represents the order in which the multifrontal method computes their columns. Their leaf nodes are initially processed, continuing up to the root. Therefore, a column cannot be computed until the processor containing the corresponding node has the update matrices of their children in the elimination tree. A compressed elimination tree in which each node corresponds to a sequence of nodes without any ramification in the elimination tree is introduced in the chapter.