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Keywords: domain decomposition, natural coarse grid, multibody contact problem, friction, scalability.

Summary

In Reference [1], a total FETI (TFETI) based domain decomposition algorithm with preconditioning by a natural coarse grid defined by the rigid body motions of the subdomains is adapted to the solution of multibody contact problems with friction in three dimensions and proved to be scalable for Tresca friction. The analysis admits "floating" bodies. The algorithm finds an approximate solution at a cost asymptotically proportional to the number of variables provided the ratio of the decomposition and the discretization parameters is bounded. The analysis is based on the classical results by Farhat, Mandel, and Roux [2] on the scalability of the FETI algorithm for linear problems and on our development of optimal quadratic programming algorithms. The algorithm preserves the parallel scalability of the classical FETI method. Both theoretical results and numerical experiments indicate that our algorithm is effective. The effectiveness of the method in the inner loop of the fixed point iterations for the solution of the contact problems with Coulomb's friction is illustrated with the analysis of a mine support. Other engineering benchmarks solved can be found in [3,4].

References

1: Z. Dostál, T. Kozubek, A. Markopoulos, T. Brzobohatý, V. Vondrák, P. Horyl, "Scalable TFETI algorithm for the solution of multibody contact problems of elasticity", submitted to Comp. Methods Appl. Mech. Engrg., 2010.
2: C. Farhat, J. Mandel, F.-X. Roux "Optimal convergence properties of the FETI domain decomposition method", Comput. Methods Appl. Mech. Eng., 115, 365-385, 1994. doi:10.1016/0045-7825(94)90068-X
3: Z. Dostál, T. Kozubek, V. Vondrák, T. Brzobohatý, A. Markopoulos, "Theoretically supported scalable TFETI algorithm for the solution of multibody 3D contact problems with friction", International Journal for Numerical Methods in Engineering, 2009. doi:10.1002/nme.2807
4: Z. Dostál, T. Kozubek, P. Horyl, T. Brzobohatý, A. Markopoulos, "Scalable TFETI algorithm for two dimensional multibody contact problems with friction", Journal of Computational and Applied Mathematics, 235(2), 403-418, 2010. doi:10.1016/j.cam.2010.05.042

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 94 PROCEEDINGS OF THE SEVENTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: Paper 7 Numerically and Parallel Scalable TFETI based Algorithms for Contact Problems T. Kozubek, A. Markopoulos and T. Brzobohatý VŠB, Technical University of Ostrava, Czech Republic doi:10.4203/ccp.94.7 purchase the full-text of this paper Full Bibliographic Reference for this paper , "Numerically and Parallel Scalable TFETI based Algorithms for Contact Problems", in , (Editors), "Proceedings of the Seventh International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 7, 2010. doi:10.4203/ccp.94.7 Keywords: domain decomposition, natural coarse grid, multibody contact problem, friction, scalability. Summary In Reference [1], a total FETI (TFETI) based domain decomposition algorithm with preconditioning by a natural coarse grid defined by the rigid body motions of the subdomains is adapted to the solution of multibody contact problems with friction in three dimensions and proved to be scalable for Tresca friction. The analysis admits "floating" bodies. The algorithm finds an approximate solution at a cost asymptotically proportional to the number of variables provided the ratio of the decomposition and the discretization parameters is bounded. The analysis is based on the classical results by Farhat, Mandel, and Roux [2] on the scalability of the FETI algorithm for linear problems and on our development of optimal quadratic programming algorithms. The algorithm preserves the parallel scalability of the classical FETI method. Both theoretical results and numerical experiments indicate that our algorithm is effective. The effectiveness of the method in the inner loop of the fixed point iterations for the solution of the contact problems with Coulomb's friction is illustrated with the analysis of a mine support. Other engineering benchmarks solved can be found in [3,4]. References 1 Z. Dostál, T. Kozubek, A. Markopoulos, T. Brzobohatý, V. Vondrák, P. Horyl, "Scalable TFETI algorithm for the solution of multibody contact problems of elasticity", submitted to Comp. Methods Appl. Mech. Engrg., 2010. 2 C. Farhat, J. Mandel, F.-X. Roux "Optimal convergence properties of the FETI domain decomposition method", Comput. Methods Appl. Mech. Eng., 115, 365-385, 1994. doi:10.1016/0045-7825(94)90068-X 3 Z. Dostál, T. Kozubek, V. Vondrák, T. Brzobohatý, A. Markopoulos, "Theoretically supported scalable TFETI algorithm for the solution of multibody 3D contact problems with friction", International Journal for Numerical Methods in Engineering, 2009. doi:10.1002/nme.2807 4 Z. Dostál, T. Kozubek, P. Horyl, T. Brzobohatý, A. Markopoulos, "Scalable TFETI algorithm for two dimensional multibody contact problems with friction", Journal of Computational and Applied Mathematics, 235(2), 403-418, 2010. doi:10.1016/j.cam.2010.05.042 purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £125 +P&P)
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