A survey of RLCK reduction and simulation methods by fast truncated balanced realization

Model order reduction by truncated balanced realization (TBR) is better than Krylov subspace methods to achieve smaller models with global error control. TBR projects a system onto the dominant invariant subspace in terms of both controllability and observability measured by their gramians. However, to obtain two gramians, two Lyapunov equations have to be solved and its high computation costs involved limit its application to only small circuits. To mitigate this problem, several methods are proposed to obtain the approximated dominant subspace of the gramian (or gramian product). In this paper, we survey several recently proposed fast TBR methods by gramian approximation techniques for the model order reduction and simulation of RLCK circuits. We present the pros and cons of each method and compare them on some large RLCK circuits.