An additive Schwarz preconditioner for the FETI method

Summary.  A new additive Schwarz preconditioner for the Finite Element Tearing and Interconnecting (FETI) method is analyzed in this paper. This preconditioner has the unique feature that the coefficient matrix of its ``coarse grid' problem is mesh independent. For a model second order heterogeneous elliptic boundary value problem in two dimensions, the condition number of the preconditioned system is shown to be bounded by C[1+ln(H/h)]², where h is the mesh size, H is the typical diameter of the subdomains, and the constant C is independent of h, H, the number of subdomains and the coefficients of the boundary value problem. Received May 8, 2000 / Revised version received January 2, 2002 / Published online July 18, 2002 Mathematics Subject Classification (1991): 65N55, 65N30