Convergence Speed of Coupling Iterations for the Unsteady Transmission Problem

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceeding

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 iteration matrix. Numerical results are presented to illustrate the analysis.

Details

Authors
Organisations
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Computational Mathematics

Keywords

  • Dirichlet-Neumann Iteration, Fixed Point Iteration, Transmission Problem, Coupled Problems, Thermal Fluid Structure Interaction
Original languageEnglish
Title of host publicationVI International Conference on Computational Methods for Coupled Problems in Science and Engineering (COUPLED PROBLEMS 2015), Proceedings of the
EditorsBernhard A. Schrefler, Eugenio Oñate, Manolis Papadrakakis
PublisherCIMNE
Pages452-463
Number of pages12
ISBN (Print)978-84-943928-3-2
Publication statusPublished - 2015
Publication categoryResearch
Peer-reviewedYes
EventVI International Conference on Computational Methods for Coupled Problems in Science and Engineering (COUPLED PROBLEMS 2015) - Venice (Italy)
Duration: 2015 May 182015 May 20

Conference

ConferenceVI International Conference on Computational Methods for Coupled Problems in Science and Engineering (COUPLED PROBLEMS 2015)
Period2015/05/182015/05/20

Bibliographic note

The complete proceedings of the conference may be found at: http://congress.cimne.com/coupled2015/frontal/doc/Ebook_COUPLED_15.pdf