Thomas Takacs

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Isogeometric analysis (IGA) is a numerical simulation method which is directly based on the NURBS-based representation of CAD models. It exploits the tensor-product structure of 2or 3-dimensional NURBS objects to parameterize the physical domain. Hence the physical domain is parameterized with respect to a rectangle or to a cube. Consequently, singularly(More)
We consider isogeometric functions and their derivatives. Given a geometry mapping, which is defined by an n-dimensional NURBS patch in R, an isogeometric function is obtained by composing the inverse of the geometry mapping with a NURBS function in the parameter domain. Hence an isogeometric function can be represented by a NURBS parametrization of its(More)
This paper is motivated by the representation of the test functions in Isogeometric Analysis (IgA). IgA is a numerical method that uses the NURBS-based representation of a CAD model to generate the finite-dimensional space of test functions which is used for the simulation. More precisely, the test functions are obtained by composing the inverse of the(More)
We aim at constructing a smooth basis for isogeometric function spaces on domains of reduced geometric regularity. In this context an isogeometric function is the composition of a piecewise rational function with the inverse of a piecewise rational geometry parameterization. We consider two types of singular parameterizations, domains where a part of the(More)
In this paper, we will give approximation error estimates as well as corresponding inverse inequalities for B-splines of maximum smoothness, where both the function to be approximated and the approximation error are measured in standard Sobolev norms and semi-norms. The presented approximation error estimates do not depend on the polynomial degree of the(More)
The bacteriological status of the uteri of 150 cows was examined on 14 large-scale dairy farms 10 to 20 d after parturition and then twice again in 2-wk intervals during uterine involution. The degree of bacterial contamination and the proportion of the infected uterus as well as the composition of the isolated flora were determined. The antibiotic(More)
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