Relaxation techniques for the simulation of VLSI circuits
Relaxation techniques for the simulation of VLSI circuits
Circuit analysis, simulation, and design: general aspects of circuit analysis and design
Circuit analysis, simulation, and design: general aspects of circuit analysis and design
Rapid convergence of waveform relaxation
Applied Numerical Mathematics - Special issue: parallel methods for ordinary differential equations
An improved relaxation approach for mixed system analysis with several simulation tools
EURO-DAC '95/EURO-VHDL '95 Proceedings of the conference on European design automation
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
Space-Time Continuous Analysis of Waveform Relaxation for the Heat Equation
SIAM Journal on Scientific Computing
Optimal Schwarz Waveform Relaxation for the One Dimensional Wave Equation
SIAM Journal on Numerical Analysis
Optimized Schwarz Waveform Relaxation Methods for Advection Reaction Diffusion Problems
SIAM Journal on Numerical Analysis
Analysis of Multiconductor Transmission Lines
Analysis of Multiconductor Transmission Lines
IEEE Transactions on Circuits and Systems Part I: Regular Papers
Time-domain segmentation based massively parallel simulation for ADCs
Proceedings of the 50th Annual Design Automation Conference
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
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Waveform relaxation (WR) is a technique that can be used to solve large systems of ordinary differential equations (ODEs). It is particularly suitable for the parallel solution of ODEs with multiple time scales and has successfully been used for the solution of electronic circuits and for solving partial differential equations. The main issue limiting the utility of WR is the class of problems with strong subsystem-to-subsystem couplings and long analysis time intervals resulting in nonuniform slow convergence. Here, we consider transmission-line (TL) circuits since they represent an important part of a Spice-type circuit solver. For TLs, the coupling between different lines is relatively weak, and thus, partitioning in the transverse direction leads to very fast WR algorithms. However, longitudinal partitioning of TLs is very challenging due to the strong coupling that results. In this paper, we propose an approach with improved convergence properties for strongly coupled longitudinal partitioning of TLs and other similarly strongly coupled circuits.