Parallel Schwarz Waveform Relaxation Algorithm for an N-Dimensional Semilinear Heat Equation
Analysis of PDEs
2010-08-03 v2 Numerical Analysis
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.
Cite
@article{arxiv.1006.1323,
title = {Parallel Schwarz Waveform Relaxation Algorithm for an N-Dimensional Semilinear Heat Equation},
author = {Minh-Binh Tran},
journal= {arXiv preprint arXiv:1006.1323},
year = {2010}
}