  Frictional contact is one of the most challenging problems in computational
mechanics. Typically, it is a tough nonlinear problem often requiring several
Newton iterations to converge and causing troubles also in the solution to the
related linear systems. When contact is modeled with the aid of Lagrange
multipliers, the impenetrability condition is enforced exactly, but the
associated Jacobian matrix is indefinite and needs a special treatment for a
fast numerical solution. In this work, a constraint preconditioner is proposed
where the primal Schur complement is computed after augmenting the zero block.
The name Reverse is used in contrast to the traditional approach where only the
structural block undergoes an augmentation. Besides being able to address
problems characterized by singular structural blocks, often arising in contact
mechanics, it is shown that the proposed approach is significantly cheaper than
traditional constraint preconditioning for this class of problems and it is
suitable for an efficient HPC implementation through the Chronos parallel
package. Our conclusions are supported by several numerical experiments on mid-
and large-size problems from various applications. The source files
implementing the proposed algorithm are freely available on GitHub.
