Parallel Algorithms for Balanced Truncation Model Reduction of Sparse Systems

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Abstract

We describe the parallelization of an efficient algorithm for balanced truncation that allows to reduce models with state-space dimension up to \(\mathcal{O}(10^5)\) . The major computational task in this approach is the solution of two large-scale sparse Lyapunov equations, performed via a coupled LR-ADI iteration with (super-)linear convergence. Experimental results on a cluster of Intel Xeon processors illustrate the efficacy of our parallel model reduction algorithm.

José M. Badía, Rafael Mayo, and E.S. Quintana-Ortí were supported by the CICYT project No. TIC2002-004400-C03-01 and FEDER, and project No. P1B-2004-6 of the Fundación Caixa-Castelló n/Bancaixa and UJI. P. Benner was supported by the DFG Research Center “Mathematics for key technologies” (FZT 86) in Berlin.