A reverse augmented constraint preconditioner for Lagrange multiplier methods in contact mechanics

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