TBETI and TFETI Algorithms for Contact Shape Optimization Problems

The paper shows how to accelerate solution of contact shape optimization problems on massively parallel computers. We proposed two efficient algorithms for solution such problems. The first one is called Finite Element Tearing and Interconnecting (FETI) domain decomposition method, which is based on finite element approximation of the state problem. The second one is based on the boundary element approximation and we call it Boundary Element Tearing and Interconnecting (BETI) method. In this paper we shall apply those methods to the efficient parallel solution of sensitivity analysis which shows to be the most expensive part of the shape optimization process. The performance comparison of proposed methods will be demonstrated on the Hertz type problem.