Block sparse Cholesky algorithms on advanced uniprocessor computers
SIAM Journal on Scientific Computing
The symmetric eigenvalue problem
The symmetric eigenvalue problem
A Supernodal Approach to Sparse Partial Pivoting
SIAM Journal on Matrix Analysis and Applications
Large-Scale Normal Coordinate Analysis for Molecular Structures
SIAM Journal on Scientific Computing
An Automated Multilevel Substructuring Method for Eigenspace Computation in Linear Elastodynamics
SIAM Journal on Scientific Computing
Computation of Smallest Eigenvalues using Spectral Schur Complements
SIAM Journal on Scientific Computing
An Algebraic Substructuring Method for Large-Scale Eigenvalue Calculation
SIAM Journal on Scientific Computing
Finite Elements in Analysis and Design
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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.