A Parallel Distributed Solver for Large Dense Symmetric Systems: Applications to Geodesy and Electromagnetism Problems

Abstract

In this paper we describe the parallel distributed implementation of a linear solver for large-scale applications involving real symmetric positive definite or complex symmetric non-Hermitian dense systems. The advantage of this routine is that it performs a Cholesky factorization by requiring half the storage needed by the standard parallel libraries ScaLAPACK and PLAPACK. Our solver uses a Jvariant Cholesky algorithm and a one-dimensional blockcyclic column data distribution but gives similar Gigaflops performance when applied to problems that can be solved on moderately parallel computers with up to 32 processors. Experiments and performance comparisons with ScaLAPACK and PLAPACK on our target applications are presented. These applications arise from the Earth's gravity field recovery and computational electromagnetics.