# ON THE SOLUTION OF GENERALIZED EIGENVALUE PROBLEMS USING PROJECTED ARNOLDI AND DUAL DOMAIN DECOMPOSITION METHODS

## Palavras-chave:

FETI, Projected Arnoldi, Constrained Eigenmodes, Krylov Method## Resumo

Modal Analysis plays an important role in understanding the dynamics of structures. The

mode shapes and natural frequencies are crucial structural properties that must the known to avoid catas-

trophic failures due to resonances. Moreover, eigenmodes can be used to reduce the number of degrees

of freedom of a Dynamic System by using Reduced Order Models (ROM) such as Craig-Bampton, Dual-

Craig-Bampton, Rubin, among others. Despite its importance, full eigenanalysis is rarely required, and

in general, only the smallest eigenvalues are computed due to their relevance for practical problems.

Therefore, Lanczos and implicit restarted Arnoldi algorithms are often used as eigensolvers due to their

efficiency. The major cost of those algorithms lies in the multiple solutions of static-like problems, which

can produce prohibitive computational cost when the discretized dynamic model has more than millions

of unknowns. In this work, a nonoverlapping dual domain decomposition method, namely Finite El-

ement Tearing and Interconnection, is combined with a modified version of the Arnoldi Algorithm to

efficiently compute the eigenpairs of large scale structural problems.