The INTERNODES method for applications in contact mechanics and dedicated preconditioning techniques

Abstract

• The INTERNODES method is applied to problems in contact mechanics. • We propose a highly efficient preconditioner to solve the sequence of linear systems. • An algorithm is suggested to cheaply solve linear systems with the preconditioning matrix. • The quality of the preconditioner is assessed on small to medium size 2D problems. The mortar finite element method is a well-established method for the numerical solution of partial differential equations on domains displaying non-conforming interfaces. The method is known for its application in computational contact mechanics. However, its implementation remains challenging as it relies on geometrical projections and unconventional quadrature rules. The INTERNODES (INTERpolation for NOn-conforming DEcompositionS) method, instead, could overcome the implementation difficulties thanks to flexible interpolation techniques. Moreover, it was shown to be at least as accurate as the mortar method making it a very promising alternative for solving problems in contact mechanics. Unfortunately, in such situations the method requires solving a sequence of ill-conditioned linear systems. In this paper, preconditioning techniques are designed and implemented for the efficient solution of those linear systems.