Parallel Algorithms for Balanced Truncation Model Reduction of Sparse Systems

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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.