Balancing domain decomposition by constraints and perturbation
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Cita com:
hdl:2117/99502
Tipus de documentArticle
Data publicació2016-11
Condicions d'accésAccés obert
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ProjecteNUMEXAS - NUMERICAL METHODS AND TOOLS FOR KEY EXASCALE COMPUTING CHALLENGES IN ENGINEERING AND APPLIED SCIENCES (EC-FP7-611636)
COMFUS - Computational Methods for Fusion Technology (EC-FP7-258443)
COMFUS - Computational Methods for Fusion Technology (EC-FP7-258443)
Abstract
In this paper, we formulate and analyze a perturbed formulation of the balancing domain decomposition by constraints (BDDC) method. We prove that the perturbed BDDC has the same polylogarithmic bound for the condition number as the standard formulation. Two types of properly scaled zero-order perturbations are considered: one uses a mass matrix, and the other uses a Robin-type boundary condition, i.e, a mass matrix on the interface. With perturbation, the wellposedness of the local Neumann problems and the global coarse problem is automatically guaranteed, and coarse degrees of freedom can be defined only for convergence purposes but not well-posedness. This allows a much simpler implementation as no complicated corner selection algorithm is needed. Minimal coarse spaces using only face or edge constraints can also be considered. They are very useful in extreme scale calculations where the coarse problem is usually the bottleneck that can jeopardize scalability. The perturbation also adds extra robustness as the perturbed formulation works even when the constraints fail to eliminate a small number of subdomain rigid body modes from the standard BDDC space. This is extremely important when solving problems on unstructured meshes partitioned by automatic graph partitioners since arbitrary disconnected subdomains are possible. Numerical results are provided to support the theoretical findings.
CitacióBadia, S., Nguyen, H. Balancing domain decomposition by constraints and perturbation. "SIAM journal on numerical analysis", Novembre 2016, vol. 54, núm. 6, p. 3436.
ISSN0036-1429
Versió de l'editorhttp://epubs.siam.org/doi/10.1137/15M1045648
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