Exponential Time Integration for Transient Analysis of Large-Scale Circuits
Transient analysis of large-scale circuits relies on efficient numerical time integration algorithms. In this thesis, we focus on the high-order exponential integration and the explicit formulation for solving large-scale dynamical systems of VLSI designs. First, we demonstrate the advantages of exponential integration for the application to linear systems. To accelerate the computation of matrix exponential and vector product, Krylov subspace method and Arnoldi algorithm with different preconditioned matrices are explored. Second, we integrate the exponential integration based algorithms into a simulator for power network analysis, which is a challenging task for modern VLSI signoff. We verify the capability of adaptive stepping with high accuracy and the model of distributed computation. Comparing with the traditional approach, we observe the speedups up to 14X and 98X without the loss of accuracy by single-core and distributed computation models, respectively. Third, we devise a novel integration framework with the explicit formulation for nonlinear dynamical systems. This framework reduces the number of computationally expensive matrix factorizations required by traditional integration approaches. Furthermore, we demonstrate that the Krylov subspace methods can reduce the complexity of strongly coupled dynamical problems such as post layout analysis.