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...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:Numerical methods for partial differential equations Ročník 33; číslo 2; s. 514 - 530
Hlavný autor: Mandal, Bankim C.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Wiley Subscription Services, Inc 01.03.2017
Predmet:
Algorithms
Convergence
Domain decomposition
Mathematical analysis
Mathematical models
Neumann–Neumann
Transforms
wave equation
waveform relaxation
Waveforms
Windows (intervals)
ISSN:0749-159X, 1098-2426
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Popis
Shrnutí: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
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
content type line 23
ISSN:0749-159X
1098-2426
DOI:10.1002/num.22112