Relevant bibliographies by topics / Waveform Relaxation (WR)

Academic literature on the topic 'Waveform Relaxation (WR)'

Author: Grafiati
Published: 14 March 2023

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Journal articles on the topic "Waveform Relaxation (WR)"

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Habib, S. E. D., and G. J. Al-Karim. "An Initialization Technique for the Waveform-Relaxation Circuit Simulation." VLSI Design 9, no. 2 (January 1, 1999): 213–18. http://dx.doi.org/10.1155/1999/10238.

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This paper reports the development of the Cairo University Waveform Relaxation (CUWORX) simulator. In order to accelerate the convergence of the waveform relaxation (WR) in the presence of logic feedback, CUWORK is initialized via a logic simulator. This logic initialization scheme is shown to be highly effective for digital synchronous circuits. Additionally, this logic initialization scheme preserves fully the multi-rate properties of the WR algorithm.
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Fan, Zhencheng. "Zero-stability of waveform relaxation methods for ordinary differential equations." Electronic Research Archive 30, no. 3 (2022): 1126–41. http://dx.doi.org/10.3934/era.2022060.

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<abstract><p>Zero-stability is the basic property of numerical methods of ordinary differential equations (ODEs). Little work on zero-stability is obtained for the waveform relaxation (WR) methods, although it is an important numerical method of ODEs. In this paper we present a definition of zero-stability of WR methods and prove that several classes of WR methods are zero-stable under the Lipschitz conditions. Also, some numerical examples are given to outline the effectiveness of the developed results.</p></abstract>
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Kumar, Umesh. "Organization of a Circuit Simulator Based on Waveform-Relaxation Method." Active and Passive Electronic Components 26, no. 3 (2003): 137–39. http://dx.doi.org/10.1080/08827510310001603429.

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Geiser, Jürgen, Eulalia Martínez, and Jose L. Hueso. "Serial and Parallel Iterative Splitting Methods: Algorithms and Applications to Fractional Convection-Diffusion Equations." Mathematics 8, no. 11 (November 4, 2020): 1950. http://dx.doi.org/10.3390/math8111950.

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The benefits and properties of iterative splitting methods, which are based on serial versions, have been studied in recent years, this work, we extend the iterative splitting methods to novel classes of parallel versions to solve nonlinear fractional convection-diffusion equations. For such interesting partial differential examples with higher dimensional, fractional, and nonlinear terms, we could apply the parallel iterative splitting methods, which allow for accelerating the solver methods and reduce the computational time. Here, we could apply the benefits of the higher accuracy of the iterative splitting methods. We present a novel parallel iterative splitting method, which is based on the multi-splitting methods, The flexibilisation with multisplitting methods allows for decomposing large scale operator equations. In combination with iterative splitting methods, which use characteristics of waveform-relaxation (WR) methods, we could embed the relaxation behavior and deal better with the nonlinearities of the operators. We consider the convergence results of the parallel iterative splitting methods, reformulating the underlying methods with a summation of the individual convergence results of the WR methods. We discuss the numerical convergence of the serial and parallel iterative splitting methods with respect to the synchronous and asynchronous treatments. Furthermore, we present different numerical applications of fluid and phase field problems in order to validate the benefit of the parallel versions.
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Balti, Moez. "Noise Bus Modeling in Network on Chip." Journal of Circuits, Systems and Computers 27, no. 09 (April 26, 2018): 1850149. http://dx.doi.org/10.1142/s0218126618501499.

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This paper considers the noise modeling of interconnections in on-chip communication. We present an approach to illustrate modeling and simulation of interconnections on chip microsystems that consist of electrical circuits connected to subsystems described by partial differential equations, which are solved independently. A model for energy dissipation in RLC mode is proposed for the switching current/voltage of such on-chip interconnections. The Waveform Relaxation (WR) algorithm is presented in this paper to address limiting in simulating NoCs due to the large number of coupled lines. We describe our approach to the modeling of on-chip interconnections. We present an applicative example of our approach with VHDL-AMS implementations and simulation results. This article analyzes the coupling noise, the bit error rate (BER) as well as the noise as a function of the rise/fall time of the signal source which can significantly limit the scalability of the NoCs.
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Meisrimel, Peter, and Philipp Birken. "Waveform Relaxation with asynchronous time-integration." ACM Transactions on Mathematical Software, November 2, 2022. http://dx.doi.org/10.1145/3569578.

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We consider Waveform Relaxation (WR) methods for parallel and partitioned time-integration of surface-coupled multiphysics problems. WR allows independent time-discretizations on independent and adaptive time-grids, while maintaining high time-integration orders. Classical WR methods such as Jacobi or Gauss-Seidel WR are typically either parallel or converge quickly. We present a novel parallel WR method utilizing asynchronous communication techniques to get both properties. Classical WR methods exchange discrete functions after time-integration of a subproblem. We instead asynchronously exchange time-point solutions during time-integration and directly incorporate all new information in the interpolants. We show both continuous and time-discrete convergence in a framework that generalizes existing linear WR convergence theory. An algorithm for choosing optimal relaxation in our new WR method is presented. Convergence is demonstrated in two conjugate heat transfer examples. Our new method shows an improved performance over classical WR methods. In one example we show a partitioned coupling of the compressible Euler equations with a nonlinear heat equation, with subproblems implemented using the open source libraries DUNE and FEniCS .
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Ding, Xiao-Li, and Juan J. Nieto. "Numerical Analysis of Fractional Neutral Functional Differential Equations Based on Generalized Volterra-Integral Operators." Journal of Computational and Nonlinear Dynamics 12, no. 3 (January 11, 2017). http://dx.doi.org/10.1115/1.4035267.

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We use waveform relaxation (WR) method to solve numerically fractional neutral functional differential equations and mainly consider the convergence of the numerical method with the help of a generalized Volterra-integral operator associated with the Mittag–Leffler function. We first give some properties of the integral operator. Using the proposed properties, we establish the convergence condition of the numerical method. Finally, we provide a new way to prove the convergence of waveform relaxation method for integer-order neutral functional differential equation, which is a special case of fractional neutral functional differential equation. Compared to the existing proof in the literature, our proof is concise and original.
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Dissertations / Theses on the topic "Waveform Relaxation (WR)"

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Pon, Carlos (Carlos Roberto) Carleton University Dissertation Engineering Electronics. "Time warping - waveform relaxation (TW - WR) in a distributed simulation environment." Ottawa, 1995.

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