Convergence Speed of Coupling Iterations for the Unsteady Transmission Problem
(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.452463 Abstract
 We present an estimate for the convergence rate of the DirichletNeumann
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 semidiscretized 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 DirichletNeumann
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 semidiscretized 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:
http://lup.lub.lu.se/record/8230695
 author
 Monge, Azahar ^{LU} and Birken, Philipp ^{LU}
 organization
 publishing date
 2015
 type
 Chapter in Book/Report/Conference proceeding
 publication status
 published
 subject
 keywords
 DirichletNeumann 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
 International Center for Numerical Methods in Engineering (CIMNE)
 conference name
 VI International Conference on Computational Methods for Coupled Problems in Science and Engineering (COUPLED PROBLEMS 2015)
 external identifiers

 Scopus:84938703707
 ISBN
 9788494392832
 language
 English
 LU publication?
 yes
 id
 3cf0160177784587bf2fc86aca05c45d (old id 8230695)
 alternative location
 http://www.maths.lu.se/fileadmin/maths/personal_staff/Philipp_Birken/coupled.pdf
 date added to LUP
 20160219 22:15:29
 date last changed
 20161013 04:47:32
@misc{3cf0160177784587bf2fc86aca05c45d, abstract = {We present an estimate for the convergence rate of the DirichletNeumann<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 semidiscretized 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 = {9788494392832}, keyword = {DirichletNeumann Iteration,Fixed Point Iteration,Transmission Problem,Coupled Problems,Thermal Fluid Structure Interaction}, language = {eng}, pages = {452463}, publisher = {ARRAY(0x8d8d100)}, 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}, }