Measuring error propagation in waveform relaxation algorithms

A new analysis tool is introduced that characterizes and measures subcircuit coupling and error attenuation in waveform relaxation (WR) circuit simulation algorithms with full dimensionality. Unlike current methods that use heuristics to calculate scalar "coupling," this method captures al...

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Published inIEEE transactions on circuits and systems. 1, Fundamental theory and applications Vol. 46; no. 3; pp. 337 - 348
Main Authors Gristede, G.D., Zukowski, C.A., Ruehli, A.E.
Format Journal Article
LanguageEnglish
Published New York, NY IEEE 01.03.1999
Institute of Electrical and Electronics Engineers
Subjects
Algorithm design and analysis
Applied sciences
Attenuation measurement
Circuit simulation
Convergence
Coupling circuits
Design. Technologies. Operation analysis. Testing
Electronics
Exact sciences and technology
Frequency estimation
Integrated circuits
Jacobian matrices
Nonlinear circuits
Partitioning algorithms
Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices
Time varying systems
BiCMOS technology
Non linear circuit
Error analysis
Integrated circuit
Digital circuit
Verification
Mapping
Waveform relaxation
Growth of error
Computer aided design
Measurement error
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Summary:A new analysis tool is introduced that characterizes and measures subcircuit coupling and error attenuation in waveform relaxation (WR) circuit simulation algorithms with full dimensionality. Unlike current methods that use heuristics to calculate scalar "coupling," this method captures all of the effects of error attenuation over time and space. The new method characterizes the propagation of errors in the solution iterates by a linear time-varying (LTV) system model. It is shown that the LTV system model can be simplified by a careful discretization into an error propagation matrix which provides a simple and very complete characterization of the so-called "gains" in a circuit as errors propagate from one subcircuit to another. The concept of error propagation matrices and the LTV system model are applied experimentally and analytically to linear and nonlinear circuits to illustrate the usefulness of these tools in understanding the convergence properties of WR methods.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:1057-7122
1558-1268
DOI:10.1109/81.751307