Theoretically supported scalable feti for numerical solution of variational inequalities

The FETI method with a natural coarse grid is combined with recently proposed optimal algorithms for the solution of bound and/or equality constrained quadratic programming problems in order to develop a scalable solver for elliptic boundary variational inequalities such as those describing equilibrium of a system of bodies in mutual contact. A discretized model problem is first reduced by the duality theory of convex optimization to the quadratic programming problem with bound and equality constraints. The latter is then modified by means of orthogonal projectors to the natural coarse grid introduced by Farhat, Mandel, and Roux [Comput. Methods Appl. Mech. Engrg., 115 ( 1994), pp. 365-385]. Finally, the classical results on linear scalability for linear problems are extended to boundary variational inequalities. The results are validated by numerical experiments. The experiments also confirm that the algorithm enjoys the same parallel scalability as its linear counterpart.