An Implementation and Evaluation of the AMLS Method for Sparse Eigenvalue Problems

Abstract

We describe an efficient implementation and present a performance study of an automated multi-level substructuring (AMLS) method for sparse eigenvalue problems. We assess the time and memory requirements associated with the key steps of the algorithm, and compare it with the shift-and-invert Lanczos algorithm. Our eigenvalue problems come from two very different application areas: accelerator cavity design and normal-mode vibrational analysis of polyethylene particles. We show that the AMLS method, when implemented carefully, outperforms the traditional method in broad application areas when large numbers of eigenvalues are sought, with relatively low accuracy.