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

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Lecture Notes in Computer Scienceitions with Cahn-Hilliard type. We show that the condition number of the preconditioned system is bounded by .(1 + (.. ∕ ..)), where . is the typical diameter of a subdomain, . measures the overlap among the subdomains, and the positive constant . is independent of the mesh sizes and the number of subdomains.

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Danielle S. Rudes,Jason R. Ingramension. 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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Danielle S. Rudes,Jason R. Ingramition 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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Nathalie Saint-Jacques,Trevor Dummerasticity. 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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Research, Education, and Practice of the grand challenges of applied mathematics. High-dimensional problems arise in many fields of application such as data analysis and statistics, but first of all in the sciences. One of the most notorious and complicated problems of this type is the Schrödinger equation.

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