353PARALLEL DISTRIBUTED SOLVER A PARALLEL DISTRIBUTED SOLVER FOR LARGE DENSE SYMMETRIC SYSTEMS: APPLICATIONS TO GEODESY AND ELECTROMAGNETISM PROBLEMS

In this paper we describe the parallel distributed imple-mentation of a linear solver for large-scale applications involving real symmetric positive definite or complex sym-metric 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 J-variant Cholesky algorithm and a one-dimensional block-cyclic column data distribution but gives similar Gigaflops performance when applied to problems that can be solved on moderately parallel computers with up to 32 proces-sors. Experiments and performance comparisons with ScaLAPACK and PLAPACK on our target applications are presented. These applications arise from the Earth’s grav-ity field recovery and computational electromagnetics. Key words: Scientific computing, parallel distributed algo-rithms, symmetric dense linear systems, packed storage format, Cholesky factorization, ScaLAPACK, PLAPACK