A parallel subdomain by subdomain implementation of the implicitly restarted Arnoldi/Lanczos method

摘要

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, addressing issues such as memory requirements and computational costs related to the generation and storage of the Krylov basis. The presented implementation is suitable for distributed memory architectures, especially PC clusters. In the parallel solution, a subdomain by subdomain approach was implemented and overlapping and non-overlapping mesh partitions were tested. Compressed data structures in the formats CSRC and CSRC/CSR were used to store the coefficient matrices. The parallelization of numerical linear algebra operations present in both Krylov and implicitly restarted methods are discussed. Numerical examples are shown, in order to point out the efficiency and applicability of the proposed method.