A Robust Chunked Block Lanczos Method with Adaptive Shift Selection for Large-Scale Generalized Eigenvalue Problems in Structural Dynamics

We present a robust implementation of the shift-invert block Lanczos method for computing hundreds of eigenpairs in large-scale generalized eigenvalue problems arising from finite element analysis of structural dynamics. The proposed algorithm introduces four key innovations: a chunked computation strategy enabling reliable extraction of arbitrarily many eigenpairs without memory overflow, an adaptive shift selection mechanism guaranteeing non-singularity of the shifted operator while optimizing convergence, a dual residual monitoring scheme combining Ritz and true residuals for robust convergence detection, and partial reorthogonalization based on the Simon criterion that reduces computational cost by 33-50%. We demonstrate effectiveness on industrial-scale problems with up to 5 million degrees of freedom. Comprehensive numerical experiments on 18 representative matrix pairs across 45 test configurations demonstrate 100% reliability across problems with rigid body modes, clustered eigenvalues, and high multiplicity. The full validation suite of 58 tests and 1160 robustness runs confirm complete reliability without parameter tuning. Moderate chunking not only bounds memory but dramatically improves performance by up to 89% compared to monolithic computation, enabling large-scale computations that are otherwise infeasible due to memory constraints.