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Convergence Speed of Coupling Iterations for the Unsteady Transmission Problem

Monge, Azahar LU and Birken, Philipp LU (2015) VI International Conference on Computational Methods for Coupled Problems in Science and Engineering (COUPLED PROBLEMS 2015) In VI International Conference on Computational Methods for Coupled Problems in Science and Engineering (COUPLED PROBLEMS 2015), Proceedings of the p.452-463
Abstract
We present an estimate for the convergence rate of the Dirichlet-Neumann

iteration for the discretized unsteady transmission problem. Specifically, we consider the coupling of two heat equations on two identical squared domains. The Laplacian is discretized by second order central finite differences and the implicit Euler method is used for the time discretization. For the semidiscrete case, Henshaw and Chad provided in

2009 a method to analyse stability and convergence speed based on applying the continuous Fourier transform to the semi-discretized equations. Numerical results for the fully discrete case show differences, which is why we propose a complementary analysis based on approximating the spectral radius of the... (More)
We present an estimate for the convergence rate of the Dirichlet-Neumann

iteration for the discretized unsteady transmission problem. Specifically, we consider the coupling of two heat equations on two identical squared domains. The Laplacian is discretized by second order central finite differences and the implicit Euler method is used for the time discretization. For the semidiscrete case, Henshaw and Chad provided in

2009 a method to analyse stability and convergence speed based on applying the continuous Fourier transform to the semi-discretized equations. Numerical results for the fully discrete case show differences, which is why we propose a complementary analysis based on approximating the spectral radius of the iteration matrix. Numerical results are presented to illustrate the analysis. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
Dirichlet-Neumann Iteration, Fixed Point Iteration, Transmission Problem, Coupled Problems, Thermal Fluid Structure Interaction
in
VI International Conference on Computational Methods for Coupled Problems in Science and Engineering (COUPLED PROBLEMS 2015), Proceedings of the
editor
Schrefler, Bernhard A.; Oñate, Eugenio and Papadrakakis, Manolis
pages
12 pages
publisher
CIMNE
conference name
VI International Conference on Computational Methods for Coupled Problems in Science and Engineering (COUPLED PROBLEMS 2015)
external identifiers
  • Scopus:84938703707
ISBN
978-84-943928-3-2
language
English
LU publication?
yes
id
3cf01601-7778-4587-bf2f-c86aca05c45d (old id 8230695)
alternative location
http://www.maths.lu.se/fileadmin/maths/personal_staff/Philipp_Birken/coupled.pdf
date added to LUP
2016-02-19 22:15:29
date last changed
2016-10-13 04:47:32
@misc{3cf01601-7778-4587-bf2f-c86aca05c45d,
  abstract     = {We present an estimate for the convergence rate of the Dirichlet-Neumann<br/><br>
iteration for the discretized unsteady transmission problem. Specifically, we consider the coupling of two heat equations on two identical squared domains. The Laplacian is discretized by second order central finite differences and the implicit Euler method is used for the time discretization. For the semidiscrete case, Henshaw and Chad provided in<br/><br>
2009 a method to analyse stability and convergence speed based on applying the continuous Fourier transform to the semi-discretized equations. Numerical results for the fully discrete case show differences, which is why we propose a complementary analysis based on approximating the spectral radius of the iteration matrix. Numerical results are presented to illustrate the analysis.},
  author       = {Monge, Azahar and Birken, Philipp},
  editor       = {Schrefler, Bernhard A. and Oñate, Eugenio and Papadrakakis, Manolis},
  isbn         = {978-84-943928-3-2},
  keyword      = {Dirichlet-Neumann Iteration,Fixed Point Iteration,Transmission Problem,Coupled Problems,Thermal Fluid Structure Interaction},
  language     = {eng},
  pages        = {452--463},
  publisher    = {ARRAY(0x925cb50)},
  series       = {VI International Conference on Computational Methods for Coupled Problems in Science and Engineering (COUPLED PROBLEMS 2015), Proceedings of the},
  title        = {Convergence Speed of Coupling Iterations for the Unsteady Transmission Problem},
  year         = {2015},
}