Journal ArticleDOI
Quasi-Optimized Overlapping Schwarz Waveform Relaxation Algorithm for PDEs with Time-Delay
Shu-Lin Wu,Ting-Zhu Huang +1 more
TLDR
This paper investigates the convergence behavior of the overlapping SWR algorithm with Robin transmission condition by using the reaction diffusion equations with a constant discrete delay as the underlying model problem and proposes new notion to solve the min-max problem and obtains a quasi-optimized choice of the parameter.Abstract:
Schwarz waveform relaxation (SWR) algorithm has been investigated deeply and widely for regular time dependent problems. But for time delay problems, complete analysis of the algorithm is rare. In this paper, by using the reaction diffusion equations with a constant discrete delay as the underlying model problem, we investigate the convergence behavior of the overlapping SWR algorithm with Robin transmission condition. The key point of using this transmission condition is to determine a free parameter as better as possible and it is shown that the best choice of the parameter is determined by the solution of a min-max problem, which is more complex than the one arising for regular problems without delay. We propose new notion to solve the min-max problem and obtain a quasi-optimized choice of the parameter, which is shown efficient to accelerate the convergence of the SWR algorithm. Numerical results are provided to validate the theoretical conclusions.read more
Citations
More filters
Journal ArticleDOI
Quasi-overlapping Semi-discrete Schwarz Waveform Relaxation Algorithms: The Hyperbolic Problem
Mohammad Al-Khaleel,Shu-Lin Wu +1 more
TL;DR: A semi-discrete level analysis is considered and it is demonstrated that as the ratio between the overlap size and the spatial discretization size gets bigger, the convergence factor gets smaller which results in a better convergence.
Journal ArticleDOI
A Meshless and Parallelizable Method for Differential Equations with Time-Delay
TL;DR: This talk proposes a method for a class of time-delay problems, which is completely meshless, representing the solution by its Laplace inverse transform along a carefully designed contour in the complex plane and then approximating the contour integral by the Filon-Clenshaw-Curits (FCC) quadrature in a few fast growing subintervals.
References
More filters
Book
Theory and Applications of Partial Functional Differential Equations
TL;DR: In this paper, the existence and compactness of solution semiflows of linear systems are investigated. But the authors focus on the nonhomogeneous systems and do not consider the linearized stability of non-homogeneous solutions.
Journal ArticleDOI
The Waveform Relaxation Method for Time-Domain Analysis of Large Scale Integrated Circuits
TL;DR: Sufficient conditions for convergence of the WR method are proposed and examples in MOS digital integrated circuits are given to show that these conditions are very mild in practice.
Journal ArticleDOI
Optimized Schwarz Methods without Overlap for the Helmholtz Equation
TL;DR: A variant of the Schwarz method which converges without overlap for the Helmholtz equation is studied, and it is shown that the key ingredients for such an algorithm are the transmission conditions, which lead to convergence of the algorithm in a finite number of steps.
Journal Article
Schwarz Methods over the Course of Time
TL;DR: The motivations that led to the newest class called optimized Schwarz methods are traced, how they can greatly enhance the performance of the solver, and why one has to be cautious when testing them numerically are traced.
Journal ArticleDOI
Optimal Schwarz Waveform Relaxation for the One Dimensional Wave Equation
TL;DR: A nonoverlapping variant of the Schwarz waveform relaxation algorithm for wave propagation problems with variable coefficients in one spatial dimension is introduced, and convergence in two iterations can be achieved independently of the number of subdomains in that case.
Related Papers (5)
A successive approximation method for non-linear distributed-parameter control systems†
G. Zone,K. S. Chang +1 more
An optimal time-stepping algorithm for unsteady advection-diffusion problems
Naresh M. Chadha,Niall Madden +1 more