  In this paper we propose a variant of the substructuring preconditioner for
solving three-dimensional elliptic-type equations with strongly discontinuous
coefficients. In the proposed preconditioner, we use the simplest coarse solver
associated with the finite element space induced by the coarse partition, and
construct vertex-related inexact interface solvers based on overlapping domain
decomposition with small overlaps. This new preconditioner has an important
merit: its construction and efficiency do not depend on the concrete form of
the considered elliptic-type equations. % in the sense that they not only are
cheap but also are easy to implement. We apply the proposed preconditioner to
solve the linear elasticity problems and Maxwell's equations in three
dimensions. Numerical results show that the convergence rate of PCG method with
the preconditioner is nearly optimal, and also robust with respect to the
(possibly large) jumps of the coefficients in the considered equations.
