Introduction to Shape Optimization: Theory, Approximation, and Computation
Introduction to Shape Optimization: Theory, Approximation, and Computation
Computational Optimization and Applications
Optimal Quadratic Programming Algorithms: With Applications to Variational Inequalities
Optimal Quadratic Programming Algorithms: With Applications to Variational Inequalities
Shape Optimization in Three-Dimensional Contact Problems with Coulomb Friction
SIAM Journal on Optimization
TFETI coarse space projectors parallelization strategies
PPAM'11 Proceedings of the 9th international conference on Parallel Processing and Applied Mathematics - Volume Part I
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An application of a variant of the parallel domain decomposition method that we call Total FETI or TFETI (Total Finite Element Tearing and Interconnecting) for the solution of contact problems of elasticity to the parallel solution of contact shape optimization problems is described. A unique feature of the TFETI algorithm is its capability to solve large contact problems with optimal, i.e., asymptotically linear complexity. We show that the algorithm is even more efficient for the solution of the contact shape optimization problems as it can exploit effectively a specific structure of the auxiliary problems arising in the semi-analytic sensitivity analysis. Thus the triangular factorizations of the stiffness matrices of the subdomains are carried out in parallel only once for each design step, the evaluation of the components of the gradient of the cost function can be carried out in parallel, and even the evaluation of each component of the gradient itself can be further parallelized using the standard TFETI scheme. Theoretical results which prove asymptotically linear complexity of the solution are reported and documented by numerical experiments. The results of numerical solution of a 3D contact shape optimization problem confirm the high degree of parallelism of the algorithm.