Titlebook: Domain Decomposition Methods in Science and Engineering XX; Randolph Bank,Michael Holst,Jinchao Xu Conference proceedings 2013 Springer-Ve

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Equidistribution and Optimal Approximation Classension. In recent years, mathematicians start to prove the convergence and optimal complexity of the adaptive procedure in multi-dimensions. Dörfler [11] first proved an error reduction in the energy norm for the Poisson equation provided the initial mesh is fine enough.

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Some Recent Tools and a BDDC Algorithm for 3D Problems in H(curl)ition lemma which allows us to obtain improved estimates for a BDDC algorithm under less restrictive assumptions than have appeared previously in the literature. Numerical results are also presented to confirm the theory and to provide additional insights.

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Symbolic Techniques for Domain Decomposition Methodsant since numerical simulations heavily rely on solving systems of PDEs. For the large-scale problems we deal with in today’s standard applications, it is necessary to rely on iterative Krylov methods that are scalable (i.e., weakly dependent on the number of degrees on freedom and number of subdoma

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Scalable Domain Decomposition Algorithms for Contact Problems: Theory, Numerical Experiments, and Reasticity. The algorithms combine the Total FETI/BETI based domain decomposition method 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 QP

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A Two-Level Schwarz Preconditioner for Heterogeneous Problemsce for Schwarz– type preconditioners for elliptic problems with highly heterogeneous coefficients when the discontinuities are not just across but also along subdomain interfaces, where classical results break down [3, 6, 9, 15].

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Heterogeneous Domain Decomposition Methods for Eddy Current Problemsor the numerical approximation of this heterogeneous problem it is very natural to use iterative substructuring methods based on transmission conditions at the interface. We analyze the convergence of the Dirichlet-Neumann iterative method for two different formulations of the eddy current problem: