Parallel Implementation of the Implicitly Restarted Arnoldi/Lanczos Method

G.O. Ainsworth Jr., F.L.B. Ribeiro, and C. Magluta (Brazil)


Applications, Arnoldi/Lanczos eigensolvers, finite elementanalysis, parallel computing


This work presents a parallel implementation of the implicitly restarted Arnoldi/Lanczos method for the solution of eigenproblems approximated by the finite element method. The implicitly restarted Arnoldi/Lanczos uses a restart scheme in order to improve the convergence of the desired portion of the spectrum, maintaining the orthogonality of the Krylov basis. The presented implementation is suitable for distributed memory architectures, specially PC clusters. In the parallel solution, a subdomain by sub domain approach was implemented and overlapping and non-overlapping mesh partitions were used. Compressed data structures in the formats CSRC and CSRC/CSR were used to store the global matrices coefficients. The parallelization of numerical linear algebra operations presented in both Krylov and implicitly restarted methods are discussed. In order to point out the efficiency and applicability of the proposed algorithms, a numerical example is shown.

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