Parallel Schwarz Waveform Relaxation Algorithm for an N-dimensional semilinear heat equation

Minh-Binh Tran

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2014)

  • Volume: 48, Issue: 3, page 795-813
  • ISSN: 0764-583X

Abstract

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We present in this paper a proof of well-posedness and convergence for the parallel Schwarz Waveform Relaxation Algorithm adapted to an N-dimensional semilinear heat equation. Since the equation we study is an evolution one, each subproblem at each step has its own local existence time, we then determine a common existence time for every problem in any subdomain at any step. We also introduce a new technique: Exponential Decay Error Estimates, to prove the convergence of the Schwarz Methods, with multisubdomains, and then apply it to our problem.

How to cite

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Tran, Minh-Binh. "Parallel Schwarz Waveform Relaxation Algorithm for an N-dimensional semilinear heat equation." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 48.3 (2014): 795-813. <http://eudml.org/doc/273155>.

@article{Tran2014,
abstract = {We present in this paper a proof of well-posedness and convergence for the parallel Schwarz Waveform Relaxation Algorithm adapted to an N-dimensional semilinear heat equation. Since the equation we study is an evolution one, each subproblem at each step has its own local existence time, we then determine a common existence time for every problem in any subdomain at any step. We also introduce a new technique: Exponential Decay Error Estimates, to prove the convergence of the Schwarz Methods, with multisubdomains, and then apply it to our problem.},
author = {Tran, Minh-Binh},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {domain decomposition; waveform relaxation; Schwarz methods; semilinear heat equation; parallel computation; error estimate; convergence},
language = {eng},
number = {3},
pages = {795-813},
publisher = {EDP-Sciences},
title = {Parallel Schwarz Waveform Relaxation Algorithm for an N-dimensional semilinear heat equation},
url = {http://eudml.org/doc/273155},
volume = {48},
year = {2014},
}

TY - JOUR
AU - Tran, Minh-Binh
TI - Parallel Schwarz Waveform Relaxation Algorithm for an N-dimensional semilinear heat equation
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2014
PB - EDP-Sciences
VL - 48
IS - 3
SP - 795
EP - 813
AB - We present in this paper a proof of well-posedness and convergence for the parallel Schwarz Waveform Relaxation Algorithm adapted to an N-dimensional semilinear heat equation. Since the equation we study is an evolution one, each subproblem at each step has its own local existence time, we then determine a common existence time for every problem in any subdomain at any step. We also introduce a new technique: Exponential Decay Error Estimates, to prove the convergence of the Schwarz Methods, with multisubdomains, and then apply it to our problem.
LA - eng
KW - domain decomposition; waveform relaxation; Schwarz methods; semilinear heat equation; parallel computation; error estimate; convergence
UR - http://eudml.org/doc/273155
ER -

References

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