Balanced truncation model reduction of large-scale dense systems on parallel computers

Model reduction is an area of fundamental importance in many modeling and control applications. In this paper we analyze the use of parallel computing in model reduction methods based on balanced truncation of large-scale dense systems. The methods require the computation of the Gramians of a linear-time invariant system. Using a sign function-based solver for computing fall-rank factors of the Gramians yields some favorable computational aspects in the subsequent computation of the reduced-order model, particularly for non-minimal systems. As sign function-based computations only require efficient implementations of basic linear algebra operations readily available, e.g., in the BLAS, LAPACK, and ScaLAPACK, good performance of the resulting algorithms on parallel computers is to be expected. Our experimental results on a PC cluster show the performance and scalability of the parallel implementation.