IGA2025

GoTools - a Tool for Locally Refined Splines in IGA

  • Skytt, Vibeke (SINTEF)

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Tensor-product spline surfaces and volumes possess many desirable properties for IGA, including local support, non-negativity, partition of unity and linear independence of basis functions. However, their inherent tensor-product structure does not support local refinement, which is a significant limitation in IGA. Locally refined splines, including LR B-splines, address this issue. LR B-splines has got a strong theoretical foundation [1] and offer a flexible representation format, allowing the refinement strategy to be adapted to specific problems. Although they have historically faced challenges related to potential linear dependence, recent advancements provide tools to mitigate this issue. GoTools [2] is a suite of C++ software modules developed at SINTEF. Originally designed for spline curves and tensor-product spline surfaces, it has been extended to include topological structures, more surface types and volumetric entities. GoTools provides a set of spline-related tools for IGA and supports both 2-variate and 3-variate LR B-splines. The GoTools libraries are available from [3]. This talk will focus on the application of LR B-splines in IGA using GoTools. It will showcase the available tools and explore how they can be incorporated into an analysis framework. REFERENCES [1] T. Dokken, K. F. Pettersen, T. Lyche, Polynomial splines over locally refined box- partitions, Computer Aided Geometric Design, 30, 2013, 331–356 [2] https://www.sintef.no/projectweb/geometry-toolkits/gotools [3] https://github.com/SINTEF-Geometry/GoTools