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A deluxe FETI-DP preconditioner for a composite finite element and DG method. (English) Zbl 1321.65047

Summary: In this paper, we present and analyze a FETI-DP solver with deluxe scaling for a Nitsche-type discretization [the first author, ibid. 3, No. 1, 76–85 (2003; Zbl 1039.65079); Z. Cai et al., SIAM J. Numer. Anal. 49, No. 5, 1761–1787 (2011; Zbl 1232.65142)] based on a discontinuous Galerkin (DG) method for elliptic two-dimensional problems with discontinuous coefficients and non-matching meshes only across subdomains. We establish a condition number estimate for the preconditioned linear system which is scalable with respect to the number of subdomains, is quasi-optimal polylogarithmic with respect to subdomain mesh size, and is independent of coefficient discontinuities and ratio of mesh sizes across subdomain interfaces. Numerical experiments support the theory and show that the deluxe scaling improves significantly the performance over classical scaling.

MSC:

65F10 Iterative numerical methods for linear systems
65F08 Preconditioners for iterative methods
65N20 Numerical methods for ill-posed problems for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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