We consider elliptic problems with discontinuous coefficients discretized by FEM on non-matching triangulations across the interface using the mortar technique. The resulting discrete problem is solved by a FETI–DP method using a preconditioner with special scaling described in Dokeva, Dryja and Proskurowski [to appear]. Experiments performed on hundreds of processors show that this FETI–DP mor...

A scalable FETI–DP (Dual-Primal Finite Element Tearing and Interconnecting) algorithm for the Stokes problem is developed and analyzed. Advantages of this approach are a coarse problem without primal pressure unknowns and the use of a relatively cheap lumped preconditioner. Especially in three dimensions, these advantages provide a more robust and faster FETI-DP algorithm. In three dimensions, ...

We investigate whether different choices of nonmortar sides for the geometrically conforming partitions inherent to FETI–DP influence the convergence of the algorithms for four different preconditioners. We conclude experimentally that they do not, although better condition number estimates exist for a Neumann-Dirichlet choice of nonmortars.

A Scalable FETI–DP Algorithm with Non–penetration Mortar Conditions on Contact Interface Zdeněk Dostál∗, David Horák†and Dan Stefanica‡§

The main purpose of this paper is to introduce novel two-level overlapping 15 Schwarz methods for solving the Helmholtz equation. Among the most effective par16 allel two-level domain decomposition solvers for the Helmholtz equation on general 17 unstructured meshes, we mention the FETI-H method introduced by Farhat et al. [5], 18 and the WRAS-H-RC method introduced by Kimn and Sarkis [10]. FET...

The FETI algorithms are numerically scalable iterative domain decomposition methods. These methods are well documented for solving equations arising from the Finite Element discretization of second or fourth order elasticity problems. The one level FETI method equipped with the Dirichlet preconditioner was shown to be numerically scalable for second order elasticity problems while the two level...

Finite element tearing and interconnecting (FETI) methods are efficient parallel domain decomposition solvers for large-scale finite element equations. In this work we investigate the robustness of FETI methods in case of highly heterogeneous (multiscale) coefficients. Our main application are magnetic field computations where both large jumps and large variation in the reluctivity coefficient ...

The dual-primal finite element tearing and interconnecting (FETI-DPEM) method, as an application of a nonoverlapping domain decomposition method to the finite element analysis of electromagnetic problems, is applied to the three-dimensional (3D) full-wave simulation of a high quality (Q) factor photonic crystal (PhC) nanocavity in an optically thin dielectric slab. Curvilinear tetrahedral eleme...

The Finite Element Tearing and Interconnecting (FETI) methods were first introduced by Farhat and Roux [FMR94]. An important advance, making the rate of convergence of the iteration less sensitive to the number of unknowns of the local problems, was made by Farhat, Mandel, and Roux a few years later [FMR94]. For a detailed introduction, see [FR94] and we also refer to our own papers for many ad...