Journal ArticleDOI
Relaxation-Based Electrical Simulation
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TLDR
The techniques used in relaxation-based electrical simulation are presented in a rigorous and unified framework, and the numerical properties of the various methods are explored.Abstract:
Circuit simulation programs have proven to be most important computer-aided design tools for the analysis of the electrical performance of integrated circuits. One of the most common analyses performed by circuit simulators and the most expensive in terms of computer time is nonlinear time-domain transient analysis. Conventional circuit simulators were designed initially for the cost-effective analysis of circuits containing a few hundred transistors or less. Because of the need to verify the performance of larger circuits, many users have successfully simulated circuits containing thousands of transistors despite the cost.Recently, a new class of algorithms has been applied to the electrical IC simulation problem. New simulators using these methods provide accurate waveform information with up to two orders of magnitude speed improvement for large circuits. These programs use relaxation methods for the solution of the set of ordinary differential equations, which describe the circuit under analysis, rather than the direct sparse-matrix methods on which standard circuit simulators are based.In this paper, the techniques used in relaxation-based electrical simulation are presented in a rigorous and unified framework, and the numerical properties of the various methods are explored. Both the advantages and the limitations of these techniques for the analysis of large IC's are described.read more
Citations
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Heterogeneous Concurrent Modeling and Design in Java (Volume 1: Introduction to Ptolemy II)
Christopher Brooks,Edward A. Lee,Xiaojun Liu,Stephen Neuendorffer,Yang Zhao,Haiyang Zheng,Shuvra S. Bhattacharyya,Elaine Cheong,John Davis,Mudit Goel,Bart Kienhuis,Man-Kit Leung,Jie Liu,Lukito Muliadi,John Reekie,Neil Smyth,Jeff Tsay,Brian Vogel,Winthrop Williams,Yuhong Xiong +19 more
TL;DR: This volume describes how to construct Ptolemy II models for web-based modeling or building applications with a brief description of each of the models of computation that have been implemented.
Journal ArticleDOI
Space-time domain decomposition for parabolic problems
Eldar Giladi,Herbert B. Keller +1 more
TL;DR: A space-time domain decomposition iteration is analyzed, for a model advection diffusion equation in one and two dimensions, the block red-black variant of the waveform relaxation method, and the analysis provides new convergence results for this scheme.
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Co-simulation: State of the art.
TL;DR: An overview of co-simulation approaches, research challenges, and research opportunities, together with a detailed taxonomy with different aspects of the state of the art of co -simulation and classification for the past five years are provided.
Heterogeneous Concurrent Modeling and Design in Java (Volume 2: Ptolemy II Software Architecture)
Christopher Brooks,Edward A. Lee,Xieojun Liu,Stephen Neuendorffer,Yang Zhao,Haiyang Zheng,Shuvra S. Bhattacharyya,Elaine Cheong,John Davis,Mudit Goel,Bart Kienhuis,Man-Kit Leung,Jie Liu,Lukito Muliadi,John Reekie,Neil Smyth,Jeff Tsay,Brian Vogel,Winthrop Williams,Yuhong Xiong +19 more
TL;DR: This volume describes the software architecture of Ptolemy II, which provides a set of Java classes supporting clustered graph topologies for models and provides a mechanism to systematically transform models by means of graph rewriting.
Journal ArticleDOI
Multigrid waveform relaxation on spatial finite element meshes: the continuous-time case
Jan Janssen,Stefan Vandewalle +1 more
TL;DR: The waveform relaxation method and its multigrid acceleration are studied as solution procedures for the system of ordinary differential equations obtained by finite element discretisation of a linear parabolic initial boundary value problem.
References
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Book
Iterative Solution of Nonlinear Equations in Several Variables
J.M. Ortega,Werner C. Rheinboldt +1 more
TL;DR: In this article, the authors present a list of basic reference books for convergence of Minimization Methods in linear algebra and linear algebra with a focus on convergence under partial ordering.
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Analysis of Numerical Methods
TL;DR: Reference Record created on 2005-11-18, modified on 2016-08-08 as discussed by the authors, created on 2011-11 -18, created on 2006-11 18 and modified on 2008-08 -08,08