Parallel implementations of the trace minimization scheme TraceMIN for the sparse symmetric eigenvalue problem

Eigenvalue problems arise in many computational science and engineering applications: in structural mechanics, nanoelectronics, and Google’s PageRank link analysis, for example. Often, the large size of these eigenvalue problems requires the development of eigensolvers that scale well on parallel computing platforms. In this paper, we compare the effectiveness and robustness of our eigensolver for the symmetric generalized eigenvalue problem, the trace minimization scheme TraceMIN–developed in the early 1980s–against today’s well-known sparse eigensolvers including: the LOBPCG and block Krylov–Schur implementations in Trilinos; ARPACK; and several methods in the PRIMME package such as the Jacobi–Davidson one. In addition, we demonstrate the parallel scalability of two variants of TraceMIN on multicore nodes as well as on large clusters of such nodes. Our results show that TraceMIN is more robust and has higher parallel scalability than the above-mentioned competing eigensolvers.