FETI based algorithms for contact problems: scalability, large displacements and 3D Coulomb friction

摘要

Theoretical and experimental results concerning FETI based algorithms for contact problems of elasticity are reviewed. 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 optionally modified by means of orthogonal projectors to the natural coarse space introduced by Farhat and Roux in the framework of their FETI method. The resulting problem is then solved either by special algorithms for bound constrained quadratic programming problems combined with penalty that imposes the equality constraints, or by an augmented Lagrangian type algorithm with the inner loop for the solution of bound constrained quadratic programming problems. Recent theoretical results are reported that guarantee certain optimality and scalability of both algorithms. The results are confirmed by numerical experiments. The performance of the algorithm in solution of more realistic engineering problems by basic algorithm is demonstrated on the solution of 3D problems with large displacements or Coulomb friction.