On hierarchical CAD processing and simulation with Isogeometric Analysis
Decanato - Facoltà di scienze informatiche
Data d'inizio: 20 Aprile 2010
Data di fine: 21 Aprile 2010
The Faculty of Informatics is pleased to announce a seminar given by Maharavo Randrianarivony
DATE: Tuesday, April 20th 2010
PLACE: USI Università della Svizzera italiana, room SI-008, Informatics building (Via G. Buffi 13)
This talk is divided into two parts. In the first one, we show methods for processing CAD data so that they can be applied to hierarchical methods. Thinking of the standard IGES format, often trimmed surfaces appear. We present an algorithm to treat them to form a structure required for subsequent simulations. On the other hand, we describe the decomposition of solid models into curved tetrahedra. Practical results are reported to illustrate the approach. In particular, the decomposition techniques are applied to real CAD data which come from IGES files.
As for the second part, we treat locally adaptive Isogeometric Analysis which uses B-Spline and NURBS techniques. Our purpose is to improve existing techniques to enhance the efficiency. We use local B-Spline subdivisions and knot insertions for the goal of achieving better accuracy in simulations where we concentrate on two and three dimensions. Our main emphasis is to keep the curved geometry describing the physical CAD domain intact during the whole simulation process. In order to avoid unnecessary global refinements, grids are allowed to be non-conforming. The treatment of nonmatching grids is done with the help of the interior penalty methods. Only local refinements are required during the adaptivity. To achieve that, an a-posteriori error indicator is introduced in order to dynamically evaluate the errors. That is, we use spline error gauge with the help of the de Boor-Fix functional. On the other hand, we allow mesh coarsenings at regions where a sparse mesh density is sufficient to achieve a prescribed accuracy. To obtain an optimal mesh, some method is described to choose the types of refinement which are likely to reduce the error most. That is done by accurately determining the bases of the enrichment spaces using non-uniform B-splines enhanced with discrete B-splines. That is, the space of approximation is hierarchically decomposed into a coarse space and an enrichment space. Finally, we report on some practical results from our implementations. Some adaptive grid refinements in 2D and 3D from problems such as internal layers are reported.
Bachelor in Math from university of Antananarivo, Madagascar Master in Math and Computer Science from university of Chemnitz, Germany PhD. in Computer Science from university of Chemnitz, Germany
HOST: Prof. Rolf Krause