The authors propose a substructuring preconditioner for solving three-dimensional elliptic equations with strongly discontinuous coefficients. The new preconditioner can be viewed as a variant of the classical substructuring preconditioner proposed by J. H. Bramble, J. E. Pasciak
and A. H. Schatz
[Math. Comput. 53, No. 187, 1–24 (1989; Zbl 0668.65082
)], but with much simpler coarse solvers. It is shown that the preconditioned conjugate gradient method with such substructuring preconditioner has a nearly optimal convergence rate, although the condition numbers of the preconditioned systems are not quasi-optimal yet.