mathematics
and
computer
science

LANS

LANS Publications

"SIPs: Shift-and-Invert Parallel Spectral Transformations"

H. Zhang, B. Smith, M. Sternberg, and P. Zapol

ACM TOMS, vol. 33, no. 2, ACM, . Also Preprint ANL/MCS-P1263-0605

Preprint Version: [pdf]

SIPs is a new efficient and robust software package implementing multiple shift-and-invert spectral transformations on parallel computers. Built on top of SLEPc and PETSc, it can compute very large number of eigenpairs for sparse generalized Hermitian eigenvalue problems. The development of SIPs is motivated by applications in nanoscale materials modeling, in which the growing size of the matrices and the pathological eigenvalue distribution challenge the efficiency and robustness of the solver. In this paper, we develop a parallel eigevnalue algorithm that is based on the idea of distributed spectrum slicing. We describe SIPs' object-oriented software design and implementation techniques, and demonstrate its numerical performance on an advanced distributed computer.