Non-Overlapping Domain Decomposition via BURA Preconditioning of the Schur Complement
نویسندگان
چکیده
A new class of high-performance preconditioned iterative solution methods for large-scale finite element method (FEM) elliptic systems is proposed and analyzed. The non-overlapping domain decomposition (DD) naturally introduces coupling operator at the interface γ. In general, γ a manifold lower dimensions. At level, key property that energy norm associated with Steklov-Poincaré spectrally equivalent to Sobolev index 1/2. We define multiplicative DD preconditioner by approximating Schur complement using best uniform rational approximation (BURA) Lγ1/2. Here, Lγ1/2 denotes discrete Laplacian over goal paper develop unified framework analysis methods. As final result, we prove BURA-based has optimal computational complexity O(n), where n number unknowns (degrees freedom) FEM linear system. All theoretical estimates are robust, respect geometry Results systematic numerical experiments given end illustrate convergence properties method, as well choice involved parameters.
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ژورنال
عنوان ژورنال: Mathematics
سال: 2022
ISSN: ['2227-7390']
DOI: https://doi.org/10.3390/math10132327