An optimized Schwarz method with relaxation for the Helmholtz equation: the negative impact of overlap
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 53 (2019) no. 1, pp. 249-268.

In this paper we study how the overlapping size influences the convergence rate of an optimized Schwarz domain decomposition (DD) method with relaxation in the two subdomain case for the Helmholtz equation. Through choosing suitable parameters, we find that the convergence rate is independent of the wave number k and mesh size h, but sensitively depends on the overlapping size. Furthermore, by careful analysis, we obtain that the convergence behavior deteriorates with the increase of the overlapping size. Numerical results which confirm our theory are given.

DOI : 10.1051/m2an/2018061
Classification : 65N55
Mots-clés : optimized Schwarz method, the Helmholtz equation, overlapping size
Liu, Yongxiang 1 ; Xu, Xuejun 1

1 
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     title = {An optimized {Schwarz} method with relaxation for the {Helmholtz} equation: the negative impact of overlap},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {249--268},
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Liu, Yongxiang; Xu, Xuejun. An optimized Schwarz method with relaxation for the Helmholtz equation: the negative impact of overlap. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 53 (2019) no. 1, pp. 249-268. doi : 10.1051/m2an/2018061. http://www.numdam.org/articles/10.1051/m2an/2018061/

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