Parallel solution of eigenproblems in structural dynamics using the implicitly restarted Lanczos method

Abstract

This paper presents a parallel implementation of the implicitly restarted Lanczos method for the solution of large and sparse eigenproblems that occur in modal analysis of complex structures using the finite element method. The implicitly restarted technique improves convergence of the desired eigenvalues without the penalty of lost of orthogonality keeping the number of factorization steps in a modest size. In the parallel solution, a subdomain by subdomain approach was implemented and overlapping and non-overlapping mesh partitions were used. Compressed data structures in the formats CSRC and CSRC/CSR were employed to store the global matrices coefficients. The parallelization of numerical linear algebra operations presented in both Krylov and implicitly restarted methods are discussed.

Keywords

• Generalized eigenvalue problem
• Lanczos method
• Finite elements