Isogeometric Analysis and Applications 2014 by Bert Jüttler, Bernd Simeon

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By Bert Jüttler, Bernd Simeon

Isogeometric research is a groundbreaking computational process that supplies the potential of integrating the finite aspect process into traditional spline-based CAD layout instruments. It hence bridges the space among numerical research and geometry, and furthermore it permits to take on new leading edge purposes on the frontiers of study in technological know-how and engineering. This lawsuits quantity incorporates a collection of amazing study papers offered on the moment overseas Workshop on Isogeometric research and functions, held at Annweiler, Germany, in April 2014.

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Moore, Discontinuous Galerkin Isogeometric Analysis of elliptic PDEs on surfaces. NFN Technical Report 12, Johannes Kepler University Linz, NFN Geometry and Simulation, Linz, 2014. 1185 and accepted for publication in the DD22 proceedings 30. U. Langer, I. Toulopoulos, Analysis of multipatch discontinuous Galerkin IgA approximations to elliptic boundary value problems. RICAM Reports 2014-08, Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Linz, 2014.

D spanfBO i . /; i D 1; : : : ; ng the corresponding spline space. The smoothness of B-splines is defined by the breakpoint multiplicity. More precisely, each basis function is Cp mj at each j 2 Z. To define multivariate spline spaces, we introduce the multivariate knot vector D . 1 ::: 2 d /, and for simplicity of notations assume in the following that the degree is the same in all parametric directions and denote it by p. p Multivariate B-splines BO i . i1 ; : : : ; id / W 1 Ä iı Ä nı g. We denote by Sp .

16 U. Langer et al. 1 Regularity Properties of the Solution Around the Boundary Singular Points Let us assume a domain ˝ R2 and let Ps 2 @˝ be a boundary point with internal angle ! 2 . ; 2 /. r; Â/ with pole Ps , and define the cone, see Fig. r/ r sin. ˝/ and where is the stress intensity factor (is a real number depending only on f ), and D =! 0; 1/ is an exponent which determines the strength of the singularity. ˝/ with p D 2=2 . The representation (30) of us helps us to reduce our study to the examination of the behavior of u in the vicinity of the singular point, since the regularity properties of u are determined by the regularity of us .

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