Investigating the performance of parallel eigensolvers for large processor counts

Abstract

Eigensolving (diagonalizing) small dense matrices threatens to become a bottleneck in the application of massively parallel computers to electronic structure methods. Because the computational cost of electronic structure methods typically scales asO(N3) or worse, even teraflop computer systems with thousands of processors will often confront problems withN 10,000. At present, diagonalizing anN×N matrix onP processors is not efficient whenP is large compared toN. The loss of efficiency can make diagonalization a bottleneck on a massively parallel computer, even though it is typically a minor operation on conventional serial machines. This situation motivates a search for both improved methods and identification of the computer characteristics that would be most productive to improve.