In this work, we focus on the Optimized Schwarz Method for circular flat interfaces and geometric heterogeneous coupling arising when cylindrical geometries are coupled along the axial direction. In the first case, we provide a convergence analysis for the diffusion-reaction problem and jumping coefficients and we apply the general optimization procedure developed in Gigante and Vergara (Numer. Math. 131 (2015) 369–404). In the numerical simulations, we discuss how to choose the range of frequencies in the optimization and the influence of the Finite Element and projection errors on the convergence. In the second case, we consider the coupling between a three-dimensional and a one-dimensional diffusion-reaction problem and we develop a new optimization procedure. The numerical results highlight the suitability of the theoretical findings.
Mots-clés : Optimized Schwarz Method, cylindrical domains, geometric multiscale, Bessel functions
@article{M2AN_2018__52_4_1597_0,
author = {Gigante, Giacomo and Vergara, Christian},
title = {Optimized {Schwarz} methods for the coupling of cylindrical geometries along the axial direction},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1597--1615},
publisher = {EDP-Sciences},
volume = {52},
number = {4},
year = {2018},
doi = {10.1051/m2an/2018039},
zbl = {1407.65260},
mrnumber = {3878606},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2018039/}
}
TY - JOUR AU - Gigante, Giacomo AU - Vergara, Christian TI - Optimized Schwarz methods for the coupling of cylindrical geometries along the axial direction JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2018 SP - 1597 EP - 1615 VL - 52 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2018039/ DO - 10.1051/m2an/2018039 LA - en ID - M2AN_2018__52_4_1597_0 ER -
%0 Journal Article %A Gigante, Giacomo %A Vergara, Christian %T Optimized Schwarz methods for the coupling of cylindrical geometries along the axial direction %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2018 %P 1597-1615 %V 52 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2018039/ %R 10.1051/m2an/2018039 %G en %F M2AN_2018__52_4_1597_0
Gigante, Giacomo; Vergara, Christian. Optimized Schwarz methods for the coupling of cylindrical geometries along the axial direction. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 4, pp. 1597-1615. doi : 10.1051/m2an/2018039. http://www.numdam.org/articles/10.1051/m2an/2018039/
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