The FETI Based Domain Decomposition Method for Solving 3D-Multibody Contact Problems with Coulomb Friction

The FETI method was proposed by Farhat and Roux [1992] for parallel solution of problems described by elliptic partial differential equations. The key idea is elimination of the primal variables so that the original problem is reduced to a small, relatively well conditioned quadratic programming problem in terms of the Lagrange multipliers. Then the iterative solver is used to compute the solution. Our recent papers (see Dostál et al. [2002] or Haslinger et al. [2002]) apply the FETI procedure to the contact problems with Coulomb friction in 2D. It leads to the sequence of quadratic programming problems with simple inequality bounds so that the fast algorithm based on an active set strategy and an adaptive precision control (see Dostál and Schöberl [2003]) can be used directly. The situation is not so easy in 3D. The reason is that the tangential contact stress has two components in each contact node which are subject to quadratic inequality constraints. Fortunately the structure of this constraints is relatively simple: the vector whose components are the tangential contact stresses belongs to a circle in IR with the center at the origin and a given radius. A convenient piecewise linear approximation of the circle can be defined by the intersection of squares rotated of a constant angle α. Doing this approximation at all the contact nodes, we obtain a new quadratic