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

Model reduction is an area of fundamental importance in many modeling and c ontrol applications. In this paper we analyze the use of parallel computing in model reduction methods based on balanced truncation of large-scale den se systems. The methods require the computation of the Gramians of a linear -time invariant system. Using a sign function-based solver for computing fa ll-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 effi cient implementations of basic linear algebra operations readily available, e.g., in the BLAS, LAPACK, and ScaLAPACK, good performance of the resultin g algorithms on parallel computers is to be expected. Our experimental resu lts on a PC cluster show the performance and scalability of the parallel im plementation.