Lawrence Berkeley National Laboratory

We describe an efficient implementation and present a performance study of an algebraic multilevel sub-structuring (AMLS) method for sparse eigenvalue problems. We assess the time and memory requirements associated with the key steps of the algorithm, and compare itwith the shift-and-invert Lanczos algorithm in computational cost. Our eigenvalue problems come from two very different application areas: the accelerator cavity design and the normal mode vibrational analysis of the polyethylene particles. We show that the AMLS method, when implemented carefully, is very competitive with the traditional method in broad application areas, especially when large numbers of eigenvalues are sought.