Domain decomposition methods for Laplace's equation are investigated in the present paper. An optimization approach is adopted to satisfy the Dirichlet and/or Neumann interface conditions. The adjoint variable method is used to find the sensitivity of the objective function of optimization. The boundary element method is utilized for the discretization of the primary and adjoint problems. Two example problems are studied with the proposed solution method. Comparisons are also provided by using two other techniques, namely the Uzawa and Schwarz methods, already available in the literature. It is also suggested that a parallel implementation of the method could be performed leading to computational efficiency. Copyright (C) 2000 John Wiley bt Sons, Ltd.