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Scalable Domain Decomposition Algorithms for Contact Problems: Theory, Numerical Experiments, and Realworld Problems

Thursday, April 12, 3:30PM – 5PM
POB 6.304

Z. Dostal

Results related to the development of theoretically supported scalable algorithms for the solution of large scale contact problems of elasticity will be reviewed. The algorithms combine the Total FETI/BETI based domain decomposition methods adapted to the solution of 2D and 3D multibody contact problems of elasticity, both frictionless and with friction, with our (in a sense) optimal algorithms for the solution of resulting quadratic programming and QPQC problems. Solutions of transient contact problems will be also reported. Rather surprisingly, the theoretical results are qualitatively the same as the classical results on scalability of FETI/BETI for linear elliptic problems, i.e., the inequality constraints are treated in a sense for free. The numerical and parallel scalability of the method is demonstrated with numerical experiments on parallel solution of 2D and 3D contact problems of elasticity discretized with more than forty million nodal variables. A number of solutions to industrial problems will be also presented.

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