Convergence of dynamic iteration methods for initial value problems
SIAM Journal on Scientific and Statistical Computing
Waveform relaxation with overlapping splittings
SIAM Journal on Scientific Computing
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
Waveform relaxation as a dynamical system
Mathematics of Computation
Space-Time Continuous Analysis of Waveform Relaxation for the Heat Equation
SIAM Journal on Scientific Computing
Optimized Schwarz Waveform Relaxation Methods for Advection Reaction Diffusion Problems
SIAM Journal on Numerical Analysis
Optimized waveform relaxation methods for longitudinal partitioning of transmission lines
IEEE Transactions on Circuits and Systems Part I: Regular Papers - Special section on 2008 custom integrated circuits conference (CICC 2008)
The Waveform Relaxation Method for Time-Domain Analysis of Large Scale Integrated Circuits
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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Waveform relaxation techniques are an important tool for the simulation of very large scale circuits. They are based on a partition of the circuit into sub-circuits, and then use an iteration between sub-circuits to converge to the solution of the entire circuit. Their importance has increased with the wide availability of parallel computers with a large number of processors. Unfortunately classical waveform relaxation is hampered by slow convergence, but this can be addressed by better transmission conditions, which led to the new class of optimized waveform relaxation methods. In these methods, both voltage and current information is exchanged in a combination which can be optimized for the performance of the method. We prove in this paper a conjecture for the optimal combination for the particular case of a small RC circuit, and also present and analyze a transmission condition which includes a time derivative.