A General Compound Multirate Method for Circuit Simulation Problems

Abstract

Summary. The" General Compound" multirate methods are attractive integration methods for the transient analysis of mixed analog-digital circuits. From a stability analysis, it follows that they have good stability properties.

Comparison of the asymptotic stability properties for two multirate strategies

“…These strategies integrate the slow components with large time steps and the fast components with small time steps. In this paper we will focus on two strategies: the recursive refinement strategy proposed in [4,7] and the compound step strategy used in [1,3,9,10]. We will analyze these multirate approaches for solving systems of ODEs…”

Stability analysis of the BDF Slowest-first multirate methods

“…The approach used in this paper can be extended to find also stability conditions for the multidimensional test equation x= Ax in (17) or for the DAE test equations (16) and (18).…”

“…For a stability analysis of the Generalized Compound-Fast version of the Euler Backward scheme one may consult [17]. Although also other implicit methods can be used, like Runge Kutta methods, we use BDF integration methods because they use less function evaluations and they are very well suited for interpolation.…”

Terminal Current Interpolation for Multirate Time Integration of Hierarchical IC Models

“…Especially when the fast subcircuits are small in size, the additional costs for synchronisation and partitioning can be overcome and the overall multirate procedure becomes much more efficient than the single-rate time integration. An attractive multirate method is the Compound-Fast version [5,6,8], which first integrates the whole system at the new coarse time gridpoint and after that re-integrates only the active part at the fine time-grid. We will denote the coarse and fine time gridpoints by {T n , 0 ≤ n ≤ N } and {t n−1,m , 1 ≤ n ≤ N, 0 ≤ m ≤ q n } with macro-steps H n := T n −T n−1 , and micro-steps h n,m := t n,m −t n,m−1 and multirate factors q n such that t n−1,0 = T n−1 , t n−1,qn = T n .…”