Inexact FETI-DP methods

Inexact FETI-DP domain decomposition methods are considered. Preconditioners based on formulations of FETI-DP as a saddle point problem are used which allow for an inexact solution of the coarse problem. A positive definite reformulation of the preconditioned saddle point problem, which also allows for approximate solvers, is considered as well. In the formulation that iterates on the original FETI-DP saddle point system, it is also possible to solve the local Neumann subdomain problems inexactly. Given good approximate solvers for the local and coarse problems, convergence bounds of the same quality as for the standard FETI-DP methods are obtained. Numerical experiments which compare the convergence of the inexact methods with that of standard FETI-DP are shown for 2D and 3D elasticity using GMRES and CG as Krylov space methods. Based on parallel computations, a comparison of one variant of the inexact FETI-DP algorithms and the standard FETI-DP method is carried out and similar parallel performance is achieved. Parallel scalability of the inexact variant is also demonstrated. It is shown that for a very large number of subdomains and a very large coarse problem, the inexact method can be superior. Copyright 2006 John Wiley & Sons, Ltd