Improving convergence performance of relaxation-based transient analysis by matrix splitting in circuit simulation

We study the convergence performance of relaxation-based algorithms for circuit simulation in the time domain. The circuits are modeled by linear integral-differential-algebraic equations. We show that in theory, convergence depends only on the spectral properties of certain matrices when splitting is applied to the circuit matrices to set up the waveform relaxation solution of a circuit. A new decoupling technique is derived, which speeds up the convergence of relaxation-based algorithms. In function spaces a Krylov´s subspace method, namely the waveform generalized minimal residual algorithm, is also presented in the paper. Numerical examples are given to illustrate how judicious splitting and how Krylov´s method can help improve convergence in some situations