Geometric Challenges in Isogeometric Analysis

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.

本書收集了在2020年1月27日至31日於義大利羅馬舉行的INdAM Workshop「等幾何分析中的幾何挑戰」中所呈現的精選論文。它概述了關於樣條曲線及其在等幾何方法中對複雜和修剪幾何問題進行離散化的有效使用的前沿研究。本書涵蓋了該領域中的多個研究主題，包括：(i) 在複雜和修剪幾何上的高質量樣條曲面，(ii) 在非結構化網格上構建和分析平滑樣條空間，(iii) 非結構化網格上等幾何離散化的數值方面和基準測試，網格生成策略和軟件。鑑於其範圍，本書將對從事逼近理論、幾何設計和數值模擬領域的研究人員和研究生感興趣。
第10章可通過link.springer.com以創用CC Attribution 4.0國際許可證進行開放存取。