Neumann–Neumann waveform relaxation algorithm in multiple subdomains for hyperbolic problems in 1D and 2D

We present a Waveform Relaxation (WR) version of the Neumann–Neumann algorithm for the wave equation in space‐time. The method is based on a nonoverlapping spatial domain decomposition, and the iteration involves subdomain solves in space‐time with corresponding interface conditions, followed by a c...

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Bibliographic Details
Published in:Numerical methods for partial differential equations Vol. 33; no. 2; pp. 514 - 530
Main Author: Mandal, Bankim C.
Format: Journal Article
Language:English
Published: New York Wiley Subscription Services, Inc 01.03.2017
Subjects:
Algorithms
Convergence
Domain decomposition
Mathematical analysis
Mathematical models
Neumann–Neumann
Transforms
wave equation
waveform relaxation
Waveforms
Windows (intervals)
ISSN:0749-159X, 1098-2426
Online Access:Get full text
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Summary:We present a Waveform Relaxation (WR) version of the Neumann–Neumann algorithm for the wave equation in space‐time. The method is based on a nonoverlapping spatial domain decomposition, and the iteration involves subdomain solves in space‐time with corresponding interface conditions, followed by a correction step. Using a Fourier‐Laplace transform argument, for a particular relaxation parameter, we prove convergence of the algorithm in a finite number of steps for the finite time intervals. The number of steps depends on the size of the subdomains and the time window length on which the algorithm is employed. We illustrate the performance of the algorithm with numerical results, followed by a comparison with classical and optimized Schwarz WR methods. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 514–530, 2017
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ISSN:0749-159X
1098-2426
DOI:10.1002/num.22112