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Geometric Challenges in Isogeometric Analysis

  • Conference proceedings
  • © 2022

Overview

Editors:
  1. Carla Manni

    1. Department of Mathematics, University of Rome Tor Vergata, Rome, Italy

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    You can also search for this editor in PubMed   Google Scholar

  2. Hendrik Speleers

    1. Department of Mathematics, University of Rome Tor Vergata, Rome, Italy

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    You can also search for this editor in PubMed   Google Scholar

  • Covers topics related to spline theory, computer aided geometric design and isogeometric analysis
  • Presents theoretical and computational aspects of advanced geometric and numerical methods
  • Contains contributions from internationally renowned experts

Part of the book series: Springer INdAM Series (SINDAMS, volume 49)

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Table of contents (15 papers)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Quadrilateral Orbifold Splines

    • Carolina Vittoria Beccari, Hartmut Prautzsch
    Pages 1-18

  3. B-Symmetric Univariate Splines and Euler Numbers

    • Timothy Boafo-Adade, Daniel Larison, Irwin Paredes Escobar, Tatyana Sorokina
    Pages 19-29

  4. A Collocation IGA-BEM for 3D Potential Problems on Unbounded Domains

    • Antonella Falini, Carlotta Giannelli, Tadej Kanduč, M. Lucia Sampoli, Alessandra Sestini
    Pages 31-47

  5. DPB-Splines: The Decoupled Basis of Patchwork Splines

    • Nora Hemelmayr, Bert Jüttler
    Pages 49-83

  6. Simplex-Splines on the Clough-Tocher Split with Arbitrary Smoothness

    • Tom Lyche, Jean-Louis Merrien, Tomas Sauer
    Pages 85-121

  7. Trimmed Spline Surfaces with Accurate Boundary Control

    • Florian Martin, Ulrich Reif
    Pages 123-148

  8. Fast Formation and Assembly of Isogeometric Galerkin Matrices for Trimmed Patches

    • Benjamin Marussig
    Pages 149-169

  9. Subdivision and G-Spline Hybrid Constructions for High-Quality Geometric and Analysis-Suitable Surfaces

    • Jörg Peters, Kȩstutis Karčiauskas
    Pages 171-189

  10. Meshing as the Choice of Basis Functions for Finite Element Analysis

    • Malcolm A. Sabin
    Pages 191-215

  11. Scattered Data Approximation by LR B-Spline Surfaces: A Study on Refinement Strategies for Efficient Approximation

    • Vibeke Skytt, Tor Dokken
    Pages 217-258Open Access

  12. A Block ILUT Smoother for Multipatch Geometries in Isogeometric Analysis

    • Roel Tielen, Matthias Möller, Kees Vuik
    Pages 259-278

  13. Completeness Characterization of Type-I Box Splines

    • Nelly Villamizar, Angelos Mantzaflaris, Bert Jüttler
    Pages 279-304

  14. THU-Splines: Highly Localized Refinement on Smooth Unstructured Splines

    • Xiaodong Wei
    Pages 305-332

  15. HexGen and Hex2Spline: Polycube-Based Hexahedral Mesh Generation and Spline Modeling for Isogeometric Analysis Applications in LS-DYNA

    • Yuxuan Yu, Xiaodong Wei, Angran Li, Jialei Ginny Liu, Jeffrey He, Yongjie Jessica Zhang
    Pages 333-363

  16. \(C^{1}\) Triangular Isogeometric Analysis of the von Karman Equations

    • Mehrdad Zareh, Xiaoping Qian
    Pages 365-384
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Keywords

About this book

This book collects selected contributions presented at the INdAM Workshop "Geometric Challenges in Isogeometric Analysis", held in Rome, Italy on January 27-31, 2020. It gives an overview of the forefront research on splines and their efficient use in isogeometric methods for the discretization of differential problems over complex and trimmed geometries. A variety of research topics in this context are covered, including (i) high-quality spline surfaces on complex and trimmed geometries, (ii) construction and analysis of smooth spline spaces on unstructured meshes, (iii) numerical aspects and benchmarking of isogeometric discretizations on unstructured meshes, meshing strategies and software. Given its scope, the book will be of interest to both researchers and graduate students working in the areas of approximation theory, geometric design and numerical simulation.

Chapter 10 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.





Editors and Affiliations

  • Department of Mathematics, University of Rome Tor Vergata, Rome, Italy

    Carla Manni, Hendrik Speleers

About the editors

Carla Manni is a Full Professor of Numerical Analysis at the Department of Mathematics, University of Rome Tor Vergata, Italy. She received her Ph.D. in Mathematics from the University of Florence in 1990. Her research interest is primarily in spline functions and their applications, constrained interpolation and approximation, computer aided geometric design and isogeometric analysis. She is the author of more than 100 peer-reviewed research publications.

Hendrik Speleers received his Ph.D. in Engineering (Numerical Analysis and Applied Mathematics) from the University of Leuven, Belgium in 2008. He is currently an Associate Professor of Numerical Analysis at the Department of Mathematics, University of Rome Tor Vergata, Italy. His main research interest is in the construction, analysis, and application of multivariate splines. He is the author of more than 70 peer-reviewed scientific papers.



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