389 research outputs found

    On Triangular Splines:CAD and Quadrature

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    The standard representation of CAD (computer aided design) models is based on the boundary representation (B-reps) with trimmed and (topologically) stitched tensor-product NURBS patches. Due to trimming, this leads to gaps and overlaps in the models. While these can be made arbitrarily small for visualisation and manufacturing purposes, they still pose problems in downstream applications such as (isogeometric) analysis and 3D printing. It is therefore worthwhile to investigate conversion methods which (necessarily approximately) convert these models into water-tight or even smooth representations. After briefly surveying existing conversion methods, we will focus on techniques that convert CAD models into triangular spline surfaces of various levels of continuity. In the second part, we will investigate efficient quadrature rules for triangular spline space

    On Triangular Splines:CAD and Quadrature

    Get PDF

    On Triangular Splines:CAD and Quadrature

    Get PDF

    International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

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    The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

    Numerical predictions of the hydrodynamic drag of the plat-o tidal energy converter and comparison with measurements in a water channel

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    Tidal energy industry is currently involved in a strong growth phase and it is expected to play an important role as far as meeting the renewable energy targets is concerned. The product development strategy adopted by tidal energy companies is nowadays broadly based on a gradual increase of the prototypes scaling factor. Thus, the prediction of important engineering quantities such as drag at intermediate stages becomes of vital importance for developers. The diversity and complexity of the geometries adopted by second-generation tidal energy converters preclude the use of already existing drag scaling methods conceived for specific applications such as ship design. In this context, numerical simulations are regarded as a suitable alternative. This study addresses the use of Computational Fluid Dynamics (CFD) to determine the drag of the unique tidal energy converter developed by Sustainable Marine Energy (SME) called PLAT-O. Several preliminary simulations were performed on the isolated PLAT-O components. The results were compared with previous CFD studies devoted to similar form bodies and good agreement was found. Following this stage, the drag predictions on the whole PLAT-O device were undertaken and compared to existing experimental data. Significant differences between them were observed. This work has demonstrated that a RANS flow solver is not an efficient tool to predict the resistance of a small-scale PLAT-O device. In addition, this study has predicted that CFD will be suitable to assess the design of larger-scale prototypes.Outgoin

    Geometric deep learning: going beyond Euclidean data

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    Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field
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