A preconditioner for the FETI-DP formulation with mortar methods in two dimensions. (English) Zbl 1080.65117

Kim, Hyea Hyun; Lee, Chang-Ock

SIAM J. Numer. Anal. 42, No. 5, 2159-2175 (2005).

The authors are concerned with the construction and analysis of some preconditioners. They consider some iterative methods for the parallel solution of symmetric, positive definite systems of linear equations that arise from elliptic boundary value problems discretized by finite elements on nonconforming meshes. Thus, they introduce a Neumann-Dirichlet preconditioner and provide the respective condition number bound. This preconditioner is fairly easy to implement and two time cheaper as compared with the preconditioners developed elsewhere. In some numerical tests solving elliptic problems with highly discontinuous coefficients the respective preconditioner is related to that of M. Dryja and O. B. Widlund [Lect. Notes Comput. Sci. Eng. 23, 41–52 (2002; Zbl 1007.65094)].

Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca)

MSC:

65N55	Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65F10	Iterative numerical methods for linear systems
65F35	Numerical computation of matrix norms, conditioning, scaling
35J25	Boundary value problems for second-order elliptic equations
35R05	PDEs with low regular coefficients and/or low regular data
65Y05	Parallel numerical computation

Keywords:

nonmatching grids; mortar methods; preconditioning; condition number; numerical examples; parallel computation; finite element tearing and interconnecting; dual-primal method; elliptic boundary value problems; finite elements; discontinuous coefficients

Citations:

Zbl 1007.65094