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.
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Badía, J.M., Benner, P., Mayo, R., Quintana-Ortí, E.S. (2006). Parallel Algorithms for Balanced Truncation Model Reduction of Sparse Systems. In: Dongarra, J., Madsen, K., Waśniewski, J. (eds) Applied Parallel Computing. State of the Art in Scientific Computing. PARA 2004. Lecture Notes in Computer Science, vol 3732. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11558958_32
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DOI: https://doi.org/10.1007/11558958_32
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