An additive Schwarz preconditioner for the FETI method

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 + In(H / h)] , 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.