Download Advanced finite element methods and applications by Thomas Apel, Olaf Steinbach PDF

By Thomas Apel, Olaf Steinbach

This quantity on a few fresh facets of finite aspect equipment and their functions is devoted to Ulrich Langer and Arnd Meyer at the social gathering in their sixtieth birthdays in 2012. Their paintings combines the numerical research of finite point algorithms, their effective implementation on state-of-the-art architectures, and the collaboration with engineers and practitioners. during this spirit, this quantity comprises contributions of former scholars and collaborators indicating the huge diversity in their pursuits within the thought and alertness of finite aspect methods.

Topics conceal the research of area decomposition and multilevel tools, together with hp finite components, hybrid discontinuous Galerkin tools, and the coupling of finite and boundary aspect tools; the effective answer of eigenvalue difficulties relating to partial differential  equations with functions in electric engineering and optics; and the answer of direct and inverse box difficulties in strong mechanics.

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We declare some notation. With a b we mean the existence of a generic constant c such that a ≤ cb, where c is independent of parameters h and p. Otherwise, we denote the dependence as c(p). The space of univariate polynomials of order p is P p , and P p (T ) is the space of multivariate polynomials of total order p on a simplex T . To simplify notation we redefine log p := 1 for p ∈ {0, 1}. In Sect. 2 we give the hybrid DG formulation, in Sect. 3 we prove the main result, Theorem 3, and show how to apply it to analyze domain decomposition algorithms for HDG.

By the way, nearly all PhD students from that group in Heidelberg occupy full professorships now. 18 G. Haase and M. Pester Fig. 8 Numerical analysis group in Chemnitz with the MultiCluster 2, from left to right: Beate Jung, Arnd Meyer, Stefan Meinel, Torsten Steidten, Thomas Hommel, Thomas Apel, Bernd Heinrich, Michael Jung, Ulrich Langer, Matthias Pester, Bodo Heise [Gundolf Haase visited the IWR Heidelberg when the photograph had been taken]. 5 FEM Symposia In 1992 the research group SPC (“Scientific Parallel Computing”, long title “Algorithmische Grundlagen der Simulation von ausgew¨ahlten Problemen der Kontinuumsmechanik auf massiv parallelen Rechnern”) was established in Chemnitz as a package of single projects in cooperation between mathematicians and mechanical engineers (Fig.

Multigrid-Newton-methods for the calculation of electromagnetic fields. In: [50], pp. : Nichtlineare Berechnung station¨arer Magnetfelder einer Gleichstrommaschine mittels Full-Multigrid-Newton-Techniken. In: [51], pp. 135–146 (1990) [35] Hengst, S. ): Proceedings of the ”5-th Multigrid Seminar” held at Eberswalde, May 14-18. R-MATH-09/90. , Meyer, A. ): Parallel Algorithms and Cluster Computing. : On the parallelization of multi-grid methods using a non-overlapping domain decomposition data structure.

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