Summary
Domain decomposition methods are used to find the numerical solution of large boundary value problems in parallel. In optimized domain decomposition methods, one solves a Robin subproblem on each subdomain, where the Robin parameter a must be tuned (or optimized) for good performance. We show that the 2-Lagrange multiplier method can be analyzed using matrix analytical techniques and we produce sharp condition number estimates.
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Bibliography
Chandler Davis and W. M. Kahan. Some new bounds on perturbation of subspaces. Bulletin of the American Mathematical Society, pages 863–868, 1969.
Tobin A. Driscoll, Kim-Chuan Toh, and Lloyd N. Trefethen. From potential theory to matrix iterations in six steps. SIAM Review, pages 547–578, 1998.
Stephen W. Drury and Sébastien Loisel. The performance of optimized Schwarz and 2-Lagrange multiplier preconditioners for GMRES. Manuscript, 2011.
Charbel Farhat, Antonini Macedo, Michel Lesoinne, Francois-Xavier Roux, Frédéric Magoulès, and Armel de La Bourdonnaie. Two-level domain decomposition methods with lagrange multipliers for the fast iterative solution of acoustic scattering problems. Computer Methods in Applied Mechanics and Engineering, 184:213–239, 2000.
Roger A. Horn and Charles R. Johnson. Matrix Analysis. Cambridge University Press, 1990.
S. Loisel, J. Côté, M. J. Gander, L. Laayouni, and A. Qaddouri. Optimized domain decomposition methods for the spherical Laplacian. SIAM Journal on Numerical Analysis, 48:524–551, 2010.
Sébastien Loisel. Condition number estimates for the nonoverlapping optimized Schwarz method and the 2-Lagrange multiplier method for general domains and cross points. Submitted to SIAM Journal on Numerical Analysis, 2011.
Sébastien Loisel. Condition number estimates and weak scaling for 2-level 2-Lagrange multiplier methods for general domains and cross points. Submitted, 2011.
Andrea Toselli and Olof B. Widlund. Domain Decomposition Methods – Algorithms and Theory, volume 34 of Springer Series in Computational Mathematics. Springer Berlin Heidelberg, 2005.
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Drury, S.W., Loisel, S. (2013). Sharp Condition Number Estimates for the Symmetric 2-Lagrange Multiplier Method. In: Bank, R., Holst, M., Widlund, O., Xu, J. (eds) Domain Decomposition Methods in Science and Engineering XX. Lecture Notes in Computational Science and Engineering, vol 91. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35275-1_29
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DOI: https://doi.org/10.1007/978-3-642-35275-1_29
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