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ETNA - Electronic Transactions on Numerical Analysis
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
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DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
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ETNA - Electronic Transactions on Numerical Analysis, pp. 553-570, 2020/09/28
The BDDC (balancing domain decomposition by constraints) methods have been applied to solve the saddle point problem arising from a hybridizable discontinuous Galerkin (HDG) discretization of the incompressible Stokes problem. In the BDDC algorithms, the coarse problem is composed by the edge/face constraints across the subdomain interface for each velocity component. As for the standard approaches of the BDDC algorithms for saddle point problems, these constraints ensure that the BDDC preconditioned conjugate gradient (CG) iterations stay in a subspace where the preconditioned operator is positive definite. However, there are several popular choices of the local stabilization parameters used in the HDG discretizations. Different stabilization parameters change the properties of the resulting discretized operators, and some special observations and tools are needed in the analysis of the condition numbers of the BDDC preconditioned Stokes operators. In this paper, condition number estimates for different choices of stabilization parameters are provided. Numerical experiments confirm the theory.
Keywords: discontinuous Galerkin, HDG, domain decomposition, BDDC, Stokes problems, Saddle point problems, benign subspace