Construction of a Preconditioner for Domain Decomposition Methods with Polynomial Lagrangian Multipliers

Abstract

In this paper we consider domain decomposition methods with polynomial Lagrangian multipliers to two-dimensional elliptic problems, and construct a kind of simple preconditioners for the corresponding interface equation. It will be shown that condition number of the resulting preconditioned interface matrix is almost optimal (namely, it has only logarithmic growth with dimension of the local interface space).