Abstract
Parallel preconditioned solvers are presented to compute a few extreme eigenvalues and -vectors of large sparse Hermitian matrices based on the Jacobi-Davidson (JD) method by G.L.G. Sleijpen and H.A. van der Vorst. For preconditioning, an adaptive approach is applied using the QMR (Quasi-Minimal Residual) iteration. Special QMR versions have been developed for the real symmetric and the complex Hermitian case. To parallelise the solvers, matrix and vector partitioning is investigated with a data distribution and a communication scheme exploiting the sparsity of the matrix. Synchronization overhead is reduced by grouping inner products and norm computations within the QMR and the JD iteration. The efficiency of these strategies is demonstrated on the massively parallel systems NEC Cenju-3 and Cray T3E.
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Basermann, A. (1999). Parallel Preconditioned Solvers for Large Sparse Hermitian Eigenproblems. In: Hernández, V., Palma, J.M.L.M., Dongarra, J.J. (eds) Vector and Parallel Processing – VECPAR’98. VECPAR 1998. Lecture Notes in Computer Science, vol 1573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10703040_7
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DOI: https://doi.org/10.1007/10703040_7
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