Paper Info
Title
Stability and Convergency Exploration of Matrix Exponential Integration on Power Delivery Network Transient Simulation
Abstract
We propose a stability preserved Arnoldi algorithm for matrix exponential in the time domain simulation of large-scale power delivery networks (PDNs), which are formulated as semi-explicit differential-algebraic equations (DAEs). The matrix exponential and vector products (MEVPs) compose the solution of DAEs in multistep integration methods and can be efficiently approximated with the rational Krylov subspace. To produce stable simulation results for the ill-conditioned system from semi-explicit DAEs, the revised Arnoldi algorithm introduces a new structured orthogonalization process to construct the Krylov subspace. We demonstrate the performance of the new algorithm with theoretical proof and experiments. In the computation of MEVPs, we utilize the exponential related <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varphi $ </tex-math></inline-formula> functions to improve the numerical accuracy. We further explore the optimal ratio to confine the spectrum in the rational Krylov subspace. Finally, the transient framework is tested on a group of system-level PDNs, showing that matrix exponential-based algorithms could achieve high efficiency and accuracy.
Year
DOI
Venue
2020
10.1109/TCAD.2019.2954473
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Keywords
DocType
Volume
Transient analysis,Integrated circuit modeling,Numerical stability,Computational modeling,Circuit stability,Stability analysis,Numerical models
Journal
39
Issue
ISSN
Citations 
10
0278-0070
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
Xinyuan Wang121.39
Peng-Wen Chen29011.56
Chung-Kuan Cheng32314285.85