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

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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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Introduction: People, Place, Cancerant 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 subdomains) and have limited memory requirements.
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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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