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) 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:
https://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
- Dirichlet-Neumann Iteration, Fixed Point Iteration, Transmission Problem, Coupled Problems, Thermal Fluid Structure Interaction
- host publication
- 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)
- conference dates
- 2015-05-18 - 2015-05-20
- external identifiers
-
- scopus:84938703707
- ISBN
- 978-84-943928-3-2
- language
- English
- LU publication?
- yes
- additional info
- The complete proceedings of the conference may be found at: http://congress.cimne.com/coupled2015/frontal/doc/Ebook_COUPLED_15.pdf
- 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
- 2016-04-04 11:44:18
- date last changed
- 2024-04-13 17:56:55
@inproceedings{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}}, booktitle = {{VI International Conference on Computational Methods for Coupled Problems in Science and Engineering (COUPLED PROBLEMS 2015), Proceedings of the}}, editor = {{Schrefler, Bernhard A. and Oñate, Eugenio and Papadrakakis, Manolis}}, isbn = {{978-84-943928-3-2}}, keywords = {{Dirichlet-Neumann Iteration; Fixed Point Iteration; Transmission Problem; Coupled Problems; Thermal Fluid Structure Interaction}}, language = {{eng}}, pages = {{452--463}}, publisher = {{CIMNE}}, title = {{Convergence Speed of Coupling Iterations for the Unsteady Transmission Problem}}, url = {{http://www.maths.lu.se/fileadmin/maths/personal_staff/Philipp_Birken/coupled.pdf}}, year = {{2015}}, }