Distributed solution of sparse symmetric positive definite systems

Abstract

We consider the solution of a linear system Ax=b on a distributed memory machine when the matrix A is large, sparse and symmetric positive definite. In a previous paper we developed an algorithm to compute a fill-reducing nested dissection ordering of A on a distributed memory machine. We now develop algorithms for the remaining steps of the solution process. The large-grain task parallelism resulting from sparsity is identified by a tree of separators available from nested dissection. Our parallel algorithms use this separator tree to estimate the structure of the Cholesky factor L and to organize numeric computations as a sequence of dense matrix operations. We present results of an implementation on an Intel iPSC/860 parallel computer.<>