A matching of singularities in domain decomposition methods for reaction-diffusion problems with discontinuous coefficients
ESAIM: Mathematical Modelling and Numerical Analysis (2011)
- Volume: 45, Issue: 1, page 23-37
- ISSN: 0764-583X
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topChniti, Chokri. "A matching of singularities in domain decomposition methods for reaction-diffusion problems with discontinuous coefficients." ESAIM: Mathematical Modelling and Numerical Analysis 45.1 (2011): 23-37. <http://eudml.org/doc/197476>.
@article{Chniti2011,
abstract = {
In this paper we certify that the same approach proposed in previous works by Chniti et al. [C. R. Acad. Sci.342 (2006) 883–886; CALCOLO45 (2008) 111–147; J. Sci. Comput.38 (2009) 207–228] can be applied to more general operators with strong heterogeneity in the coefficients. We consider here the case of reaction-diffusion problems with piecewise constant coefficients. The problem reduces to determining the coefficients of some transmission conditions
to obtain fast convergence of domain decomposition methods.
After explaining the theoretical results, we explicitly compute the coefficients in the transmission boundary conditions. The numerical results presented in this paper confirm the optimality properties.
},
author = {Chniti, Chokri},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Corner singularity; domain decomposition method; Kondratiev theory; reaction-diffusion problems; heterogeneous coefficients; corner singularity; domain decomposition; transmission conditions; convergence; mixed boundary value problem; numerical experiments},
language = {eng},
month = {1},
number = {1},
pages = {23-37},
publisher = {EDP Sciences},
title = {A matching of singularities in domain decomposition methods for reaction-diffusion problems with discontinuous coefficients},
url = {http://eudml.org/doc/197476},
volume = {45},
year = {2011},
}
TY - JOUR
AU - Chniti, Chokri
TI - A matching of singularities in domain decomposition methods for reaction-diffusion problems with discontinuous coefficients
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2011/1//
PB - EDP Sciences
VL - 45
IS - 1
SP - 23
EP - 37
AB -
In this paper we certify that the same approach proposed in previous works by Chniti et al. [C. R. Acad. Sci.342 (2006) 883–886; CALCOLO45 (2008) 111–147; J. Sci. Comput.38 (2009) 207–228] can be applied to more general operators with strong heterogeneity in the coefficients. We consider here the case of reaction-diffusion problems with piecewise constant coefficients. The problem reduces to determining the coefficients of some transmission conditions
to obtain fast convergence of domain decomposition methods.
After explaining the theoretical results, we explicitly compute the coefficients in the transmission boundary conditions. The numerical results presented in this paper confirm the optimality properties.
LA - eng
KW - Corner singularity; domain decomposition method; Kondratiev theory; reaction-diffusion problems; heterogeneous coefficients; corner singularity; domain decomposition; transmission conditions; convergence; mixed boundary value problem; numerical experiments
UR - http://eudml.org/doc/197476
ER -
References
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- C. Chniti, F. Nataf and F. Nier, Improved interface conditions for 2D domain decomposition with corners: a theoretical determination. CALCOLO45 (2008) 111–147.
- C. Chniti, F. Nataf and F. Nier, Improved interface conditions for 2D domain decomposition with corners: Numerical applications. J. Sci. Comput.38 (2009) 207–228.
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