On favorable bounds on the spectrum of discretized Steklov-Poincaré operator and applications to domain decomposition methods in 2D

The efficiency of numerical solvers of PDEs depends on the approximation properties of the discretization methods and the conditioning of the resulting linear systems. If applicable, the boundary element methods typically provide better approximation with unknowns limited to the boundary than the Sc...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2024-08, Vol.167, p.12-20
Main Authors: Vodstrčil, Petr, Lukáš, Dalibor, Dostál, Zdeněk, Sadowská, Marie, Horák, David, Vlach, Oldřich, Bouchala, Jiří, Kružík, Jakub
Format: Article
Language:English
Subjects:
BETI
Boundary element method
Domain decomposition
FETI
Schur complement conditioning
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Summary:The efficiency of numerical solvers of PDEs depends on the approximation properties of the discretization methods and the conditioning of the resulting linear systems. If applicable, the boundary element methods typically provide better approximation with unknowns limited to the boundary than the Schur complement of the finite element stiffness matrix with respect to the interior variables. Since both matrices correctly approximate the same object, the Steklov-Poincaré operator, it is natural to assume that the matrices corresponding to the same fine boundary discretization are similar. However, this note shows that the distribution of the spectrum of the boundary element stiffness matrix is significantly better conditioned than the finite element Schur complement. The effect of the favorable conditioning of BETI clusters is demonstrated by solving huge problems by H-TBETI-DP and H-TFETI-DP.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2024.04.033