  In this paper we propose two variants of the substructuring preconditioner
for solving three-dimensional elliptic-type equations with strongly
discontinuous coefficients. In the new preconditioners, we use the simplest
coarse solver associated with the finite element space induced by the coarse
partition, and construct novel interface solvers based on some new
observations. The resulting preconditioners share the merits of the
non-overlapping domain decomposition method (DDM) and the overlapping DDM in
the sense that they not only are cheap but also are easy to implement. We apply
the proposed preconditioners 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 preconditioners are nearly optimal, and
also robust with respect to the (possibly large) jumps of the coefficients in
the considered equations.
