Preconditioning of the coarse problem in the method of balanced domain decomposition by constraints

The method of balanced domain decomposition by constraints is an iterative algorithm for numerical solution of partial differential equations which exploits a non‐overlapping partition of a domain. As an essential part of each step, restricted problems are solved on every subdomain and a certain coarse grid solution is found. In this paper we present a new strategy of preconditioning of the coarse problem. This is based on the algebraic multilevel preconditioning technique. We present numerical estimates of constants defining the condition numbers of the preconditioned coarse problems for several two‐ and three‐dimensional elliptic equations.