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A FETI-DP TYPE DOMAIN DECOMPOSITION ALGORITHM FOR THREE-DIMENSIONAL INCOMPRESSIBLE STOKES EQUATIONS
Tu, Xuemin Li, Jing
Tu, Xuemin
Li, Jing
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Abstract
The FETI-DP (dual-primal finite element tearing and interconnecting) algorithms,
proposed by the authors in [SIAM J. Numer. Anal., 51 (2013), pp. 1235–1253] and [Internat. J.
Numer. Methods Engrg., 94 (2013), pp. 128–149] for solving incompressible Stokes equations, are
extended to three-dimensional problems. A new analysis of the condition number bound for using
the Dirichlet preconditioner is given. The algorithm and analysis are valid for mixed finite
elements with both continuous and discontinuous pressures. An advantage of this new analysis is
that the numerous coarse level velocity components, required in the previous analysis to enforce the
divergence-free subdomain boundary velocity conditions, are no longer needed. This greatly reduces
the size of the coarse level problem in the algorithm, especially for three-dimensional problems. The
coarse level velocity space can be chosen as simple as those coarse spaces for solving scalar elliptic
problems corresponding to each velocity component. Both the Dirichlet and lumped preconditioners
are analyzed using the same framework in this new analysis. Their condition number bounds are
proved to be independent of the number of subdomains for fixed subdomain problem size. Numerical
experiments in both two and three dimensions, using mixed finite elements with both continuous
and discontinuous pressures, demonstrate the convergence rate of the algorithms.
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Date
2015-03-03
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Society for Industrial and Applied Mathematics
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Keywords
Domain Decomposition, Incompressible Strokes, FETI-DP, BDDC, Divergence-Free
Citation
Tu, X., & Li, J. (2015). A FETI-DP Type Domain Decomposition Algorithm for Three-Dimensional Incompressible Stokes Equations. SIAM Journal on Numerical Analysis, 53(2), 720-742. doi:10.1137/13094997x