In this paper, we present and analyze a FETI-DP
solver with deluxe scaling for a Nitsche-type discretization
[Comput. Methods Appl. Math. 3 (2003), 76–85],
[SIAM J. Numer. Anal. 49 (2011), 1761–1787] 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.
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