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Convergence Analysis of the Dirichlet-Neumann Iteration for Finite Element Discretizations

Monge, Azahar LU and Birken, Philipp LU (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.
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organization
publishing date
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
conference name
Joint 87th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM) and Deutsche Mathematiker-Vereinigung (DMV), Braunschweig 2016
ISSN
1617-7061
DOI
10.1002/pamm.201610355
language
English
LU publication?
yes
id
e7cc2b4d-bb6f-4675-8d9e-e9f4aeaae024
date added to LUP
2016-10-31 14:19:46
date last changed
2017-02-16 12:55:20
@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},
  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},
  volume       = {16},
  year         = {2016},
}