Convergence Analysis of the Dirichlet-Neumann Iteration for Finite Element Discretizations
(2016) Joint 87th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM) and Deutsche Mathematiker-Vereinigung (DMV), Braunschweig 2016 In PAMM - Proceedings in Applied Mathematics and Mechanics 16. p.733-734- Abstract
- We analyze the convergence rate of the Dirichlet-Neumann iteration for the fully discretized unsteady transmission problem. Specifically, we consider the coupling of two linear heat equations on two identical non overlapping domains with jumps in the material coefficients across these. In this context, we derive the iteration matrix of the coupled problem. In the 1D case, the spectral radius of the iteration matrix tends to the ratio of heat conductivities in the semidiscrete spatial limit, but to the ratio of the products of density and specific heat capacity in the semidiscrete temporal one. This explains the fast convergence previously observed for cases with strong jumps in the material coefficients.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/e7cc2b4d-bb6f-4675-8d9e-e9f4aeaae024
- author
- Monge, Azahar LU and Birken, Philipp LU
- organization
- publishing date
- 2016-10-25
- type
- Contribution to journal
- publication status
- published
- subject
- in
- PAMM - Proceedings in Applied Mathematics and Mechanics
- volume
- 16
- pages
- 2 pages
- publisher
- John Wiley & Sons Inc.
- conference name
- Joint 87th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM) and Deutsche Mathematiker-Vereinigung (DMV), Braunschweig 2016
- conference location
- Braunschweig, Germany
- conference dates
- 2016-03-07 - 2016-03-11
- ISSN
- 1617-7061
- DOI
- 10.1002/pamm.201610355
- language
- English
- LU publication?
- yes
- additional info
- Vol. 16 of PAMM is a special issue dedicated to the proceedings of the Joint 87th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM) and Deutsche Mathematiker-Vereinigung (DMV), Braunschweig 2016
- id
- e7cc2b4d-bb6f-4675-8d9e-e9f4aeaae024
- date added to LUP
- 2016-10-31 14:19:46
- date last changed
- 2018-11-21 21:29:34
@article{e7cc2b4d-bb6f-4675-8d9e-e9f4aeaae024, abstract = {{We analyze the convergence rate of the Dirichlet-Neumann iteration for the fully discretized unsteady transmission problem. Specifically, we consider the coupling of two linear heat equations on two identical non overlapping domains with jumps in the material coefficients across these. In this context, we derive the iteration matrix of the coupled problem. In the 1D case, the spectral radius of the iteration matrix tends to the ratio of heat conductivities in the semidiscrete spatial limit, but to the ratio of the products of density and specific heat capacity in the semidiscrete temporal one. This explains the fast convergence previously observed for cases with strong jumps in the material coefficients.}}, author = {{Monge, Azahar and Birken, Philipp}}, issn = {{1617-7061}}, language = {{eng}}, month = {{10}}, pages = {{733--734}}, publisher = {{John Wiley & Sons Inc.}}, series = {{PAMM - Proceedings in Applied Mathematics and Mechanics}}, title = {{Convergence Analysis of the Dirichlet-Neumann Iteration for Finite Element Discretizations}}, url = {{http://dx.doi.org/10.1002/pamm.201610355}}, doi = {{10.1002/pamm.201610355}}, volume = {{16}}, year = {{2016}}, }