Wawrzinek, Anna
[Verfasser:in]
;
w
[Mitwirkende:r];
Konrad Polthier
[Mitwirkende:r];
David Levin
[Mitwirkende:r]
On Isoparametric Catmull-Clark Finite Elements for Mean Curvature Flow ; Über isoparametrische Catmull-Clark finite Elemente für den mittleren Krümmungsfluss
Titel:
On Isoparametric Catmull-Clark Finite Elements for Mean Curvature Flow ; Über isoparametrische Catmull-Clark finite Elemente für den mittleren Krümmungsfluss
Beteiligte:
Wawrzinek, Anna
[Verfasser:in]
Erschienen:
Freie Universität Berlin: Refubium (FU Berlin), 2016
Anmerkungen:
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Beschreibung:
Subdivision surfaces are widely used in the area of geometric modeling and computer animation. They represent a computer-aided tool for the construction of smooth surfaces based on the repeated refinement of coarse control grids. For some of these constructions, the limit surface, which is defined as the limit of such a refinement, can be described by means of a parameterization. As a result of the parameterization a new class of finite element methods has been introduced in recent years. The high regularity properties, that the so- called subdivision finite elements imply, are of particular interest in solving higher order partial differential equations. The finite elements satisfy the continuity conditions of the solution in respect thereof. Although this concept is based on a basically simple subdivision procedure, it has not yet been fully analyzed. Compared to the classical finite element methods, there is a significant problem with regard to the rather complex underlying structure of the included irregular elements. The development of integrated finite element methods evolved into a new, fast-growing area of the so-called isogeometric analysis. A major advantage of these methods against the previously known finite elements lies in the interoperability between systems of computer-aided design and manufacturing (CAD and CAM), and the finite element simulation. Using unified basis functions the gap between the representation of geometric shapes and finite element approaches can be bridged. Therefore, the expensive and error-prone data conversion between design and analysis systems can be ignored. In this thesis, we deal with the study of subdivision finite element methods for the solution of differential equations on curved surfaces based on the Catmull-Clark subdivisions. The focus is on quadrangular control grids and the characteristic parameterization of the limit surfaces. These are descried using the generalized B-spline basis functions of the Catmull-Clark type. In particular, we present a new finite ...