Robust treatment of cross-points in optimized Schwarz methods
نویسندگان
چکیده
In the field of domain decomposition, optimized Schwarz method (OSM) appears to be one prominent techniques solve large scale time-harmonic wave propagation problems. It is based on appropriate transmission conditions using carefully designed impedance operators exchange information between subdomains. The efficiency such methods however hindered by presence cross-points, where more than two subdomains abut, if no treatment provided. this work, we propose a new cross-point issue for Helmholtz equation that remains valid in any geometrical interface configuration. We exploit multi-trace formalism define operator with suitable continuity and isometry properties. then develop complete theoretical framework generalizes classical OSM partitions cross-points contains rigorous proof geometric convergence, uniform respect mesh discretization, positive operators. Extensive numerical results 2D 3D are provided as an illustration proposed method.
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ژورنال
عنوان ژورنال: Numerische Mathematik
سال: 2022
ISSN: ['0945-3245', '0029-599X']
DOI: https://doi.org/10.1007/s00211-022-01288-x