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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…

Numerical Analysis · Mathematics 2023-10-04 Thomas Takacs

Based on spline manifolds we introduce and study a mathematical framework for analysis-suitable unstructured B-spline spaces. In this setting the parameter domain has a manifold structure, which allows for the definition of function spaces…

Numerical Analysis · Mathematics 2015-07-31 Giancarlo Sangalli , Thomas Takacs , Rafael Vázquez

B-spline modeling is fundamental to CAD systems, and its evaluation and manipulation algorithms currently in use were developed decades ago, specifically for CPU architectures. While remaining effective for many applications, these…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-04-17 Jiayu Wu , Qiang Zou

Isogeometric analysis has brought a paradigm shift in integrating computational simulations with geometric designs across engineering disciplines. This technique necessitates analysis-suitable parameterization of physical domains to fully…

Numerical Analysis · Mathematics 2024-03-18 Ye Ji , Matthias Möller , Yingying Yu , Chungang Zhu

This contribution explores the combined capabilities of reduced basis methods and IsoGeometric Analysis (IGA) in the context of parameterized partial differential equations. The introduction of IGA enables a unified simulation framework…

Numerical Analysis · Mathematics 2025-10-14 Margarita Chasapi , Pablo Antolin , Annalisa Buffa

We prove that a planar $C^2$-regular boundary $\Gamma$ can always be parameterized with its closest point projection $\pi$ over a certain collection of edges $\Gamma_h$ in an ambient triangulation, by making simple assumptions on the…

Numerical Analysis · Mathematics 2013-02-19 Ramsharan Rangarajan , Adrian J. Lew

The construction of volumetric parametrizations for computational domains is a key step in the pipeline of isogeometric analysis. Here, we investigate a solution to this problem based on the mesh deformation approach. The desired domain is…

Numerical Analysis · Mathematics 2019-03-25 Alexander Shamanskiy , Michael Helmut Gfrerer , Jochen Hinz , Bernd Simeon

We present an isogeometric framework based on collocation to construct a $C^2$-smooth approximation of the solution of the Poisson's equation over planar bilinearly parameterized multi-patch domains. The construction of the used globally…

Numerical Analysis · Mathematics 2020-02-19 Mario Kapl , Vito Vitrih

We present medial parametrization, a new approach to parameterizing any compact planar domain bounded by simple closed curves. The basic premise behind our proposed approach is to use two close Voronoi sites, which we call dipoles, to…

Graphics · Computer Science 2024-03-08 Vinayak Krishnamurthy , Ergun Akleman

We present a robust and efficient multigrid method for single-patch isogeometric discretizations using tensor product B-splines of maximum smoothness. Our method is based on a stable splitting of the spline space into a large subspace of…

Numerical Analysis · Mathematics 2017-08-22 Clemens Hofreither , Stefan Takacs

In the Isogeometric Analysis (IGA) framework, the computational domain has very often a multipatch representation. The multipatch domain can be obtained by a volume segmentation of a boundary represented domain, e.g., provided by a Computer…

Numerical Analysis · Mathematics 2018-03-28 Christoph Hofer , Ioannis Toulopoulos

Tube-like surfaces are widely encountered in geometry processing, engineering structures, and medical anatomy, yet their intrinsic longitudinal and circumferential topology is not well preserved by conventional planar annular or rectangular…

Graphics · Computer Science 2026-05-19 Shunyu Yao , Gary P. T. Choi

We study the dimension and construct a basis for $C^1$-smooth isogeometric function spaces over two-patch domains. In this context, an isogeometric function is a function defined on a B-spline domain, whose graph surface also has a B-spline…

Numerical Analysis · Mathematics 2017-01-24 Mario Kapl , Giancarlo Sangalli , Thomas Takacs

The paper is concerned with locally stabilized space-time IgA approximations to initial boundary value problems of the parabolic type. Originally, similar schemes (but weighted with a global mesh parameter) was presented and studied by U.…

Numerical Analysis · Mathematics 2018-07-17 Ulrich Langer , Svetlana Matculevich , Sergey Repin

Isogeometric analysis (IGA) represents a recently developed technology in computational mechanics that offers the possibility of integrating methods for analysis and Computer Aided Design (CAD) into a single, unified process. The…

Numerical Analysis · Computer Science 2016-02-01 Vinh Phu Nguyen , Stéphane P. A. Bordas , Timon Rabczuk

Computer-aided design (CAD) models play a crucial role in the design, manufacturing and maintenance of products. Therefore, the mesh-based finite element descriptions common in structural optimisation must be first translated into CAD…

Graphics · Computer Science 2020-07-15 Ge Yin , Xiao Xiao , Fehmi Cirak

We present an algorithm for fast generation of quasi-uniform and variable-spacing nodes on domains whose boundaries are represented as computer-aided design (CAD) models, more specifically non-uniform rational B-splines (NURBS). This new…

Numerical Analysis · Mathematics 2024-07-04 Urban Duh , Varun Shankar , Gregor Kosec

We present the first method to handle curvature regularity in region-based image segmentation and inpainting that is independent of initialization. To this end we start from a new formulation of length-based optimization schemes, based on…

Computer Vision and Pattern Recognition · Computer Science 2011-02-21 Thomas Schoenemann , Fredrik Kahl , Simon Masnou , Daniel Cremers

Contextual Partitioning introduces an innovative approach to enhancing the architectural design of large-scale computational models through the dynamic segmentation of parameters into context-aware regions. This methodology emphasizes the…

Computation and Language · Computer Science 2025-08-11 Offa Kingsleigh , Alfred Abercrombie , David Woolstencroft , Beorhtric Meadowcroft , Marcus Irvin

In this paper, we employ Bayesian optimization to concurrently explore the optimal values for both the shape parameter and the radius in the partition of unity interpolation using radial basis functions. Bayesian optimization is a…

Numerical Analysis · Mathematics 2023-11-09 Roberto Cavoretto , Alessandra De Rossi , Sandro Lancellotti , Federico Romaniello