A Deluxe FETI-DP Preconditioner for a Composite Finite Element and DG Method

作者：Dryja Maksymilian; Galvis Juan; Sarkis Marcus^*

来源：Computational Methods in Applied Mathematics, 2015, 15(4): 465-482.

DOI：10.1515/cmam-2015-0025

• Interior Penalty Discretization
• Discontinuous Galerkin
• Elliptic Problems with Discontinuous Coefficients
• Finite Element Method
• FETI-DP Algorithms
• Preconditioners
• Deluxe

In this paper, we present and analyze a FETI-DP solver with deluxe scaling for a Nitsche-type discretization [11, 16] 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.

• 出版日期2015-10