The Waveform Relaxation Method for Time-Domain Analysis of Large Scale Integrated Circuits

Authors:
E. Lelarasmee;A. E. Ruehli;A. L. Sangiovanni-Vincentelli
Affiliations:
-;-;-
Venue:
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Year:
2006

Citing 0
Cited 24

Generalized coupling as a way to improve the convergence in relaxation-based solvers

EURO-DAC '96/EURO-VHDL '96 Proceedings of the conference on European design automation
A multiprocessor implementation of relaxation-based electrical circuit simulation

DAC '84 Proceedings of the 21st Design Automation Conference
NETHDL: abstraction of schematics to high-level HDL

EURO-DAC '90 Proceedings of the conference on European design automation
Evaluation of the asynchronous iterative algorithms in the context of distant heterogeneous clusters

Parallel Computing
Optimizing locality and scalability of embedded Runge--Kutta solvers using block-based pipelining

Journal of Parallel and Distributed Computing
Convergence analysis of waveform relaxation methods for neutral differential-functional systems

Journal of Computational and Applied Mathematics
An iterated pseudospectral method for delay partial differential equations

Applied Numerical Mathematics
Remarks on evaluation of spectral radius of operators arising in WR methods for linear systems of ODEs

Applied Numerical Mathematics
Spectral collocation and waveform relaxation methods for nonlinear delay partial differential equations

Applied Numerical Mathematics
Alternating splitting waveform relaxation method and its successive overrelaxation acceleration

Computers & Mathematics with Applications
Waveform relaxation method for stochastic differential equations with constant delay

Applied Numerical Mathematics
On convergence conditions of waveform relaxation methods for linear differential-algebraic equations

Journal of Computational and Applied Mathematics
JACEP2P-V2: A fully decentralized and fault tolerant environment for executing parallel iterative asynchronous applications on volatile distributed architectures

Future Generation Computer Systems
Hybrid dynamic iterations for the solution of initial value problems

Journal of Parallel and Distributed Computing
Two stage waveform relaxation method for the initial value problems of differential-algebraic equations

Journal of Computational and Applied Mathematics
The Waveform Relaxation method for systems of differential/algebraic equations

Mathematical and Computer Modelling: An International Journal
Monotone iterative method for numerical solution of nonlinear ODEs in MOSFET RF circuit simulation

Mathematical and Computer Modelling: An International Journal
A parareal waveform relaxation algorithm for semi-linear parabolic partial differential equations

Journal of Computational and Applied Mathematics
Original Articles: A parareal algorithm based on waveform relaxation

Mathematics and Computers in Simulation
Waveform relaxation methods for fractional differential equations with the Caputo derivatives

Journal of Computational and Applied Mathematics
Time-domain segmentation based massively parallel simulation for ADCs

Proceedings of the 50th Annual Design Automation Conference
Semi-convergence of parameterized Uzawa waveform relaxation method for a class of differential-algebraic equations

Journal of Computational and Applied Mathematics
Optimization of Schwarz waveform relaxation over short time windows

Numerical Algorithms
A mathematical analysis of optimized waveform relaxation for a small RC circuit

Applied Numerical Mathematics

Quantified Score

Hi-index	0.04

Visualization

Abstract

The Waveform Relaxation (WR) method is an iterative method for analyzing nonlinear dynamical systems in the time domain. The method, at each iteration, decomposes the system into several dynamical subsystems each of which is analyzed for the entire given time interval. Sufficient conditions for convergence of the WR method are proposed and examples in MOS digital integrated circuits are given to show that these conditions are very mild in practice. Theoretical and computational studies show the method to be efficient and reliable.