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A domain decomposition method for elliptic boundary value problems: Application to unsteady incompressible fluid flow. (English) Zbl 0767.76056
Domain decomposition methods for partial differential equations, Proc. 5th Int. SIAM Symp., Norfolk/VA (USA) 1991, 545-557 (1992).
[For the entire collection see Zbl 0758.00015.]
We propose a new pressure solver with the following key ingredients: domain decomposition; a global coarse system to take care of long-range interactions (solved directly); a global fine system to solve for the difference between the final solution and the coarse “skeleton” solution (solved iteratively); a local decoupled preconditioning system (solved directly for each subdomain). Numerical results suggest that the number of iterations is independent of the number of subdomains.

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76D05 Navier-Stokes equations for incompressible viscous fluids
76D07 Stokes and related (Oseen, etc.) flows
65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs