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自适应等几何分析的数学基础

Mathematical Foundations of Adaptive Isogeometric Analysis.

作者信息

Buffa Annalisa, Gantner Gregor, Giannelli Carlotta, Praetorius Dirk, Vázquez Rafael

机构信息

École polytechnique fédérale de Lausanne, Institute of Mathematics, 1015 Lausanne, Switzerland.

Istituto di Matematica Applicata e Tecnologie Informatiche "E. Magenes" del CNR, Pavia, Italy.

出版信息

Arch Comput Methods Eng. 2022;29(7):4479-4555. doi: 10.1007/s11831-022-09752-5. Epub 2022 Sep 30.

DOI:10.1007/s11831-022-09752-5
PMID:36397952
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC9646785/
Abstract

This paper reviews the state of the art and discusses recent developments in the field of adaptive isogeometric analysis, with special focus on the mathematical theory. This includes an overview of available spline technologies for the local resolution of possible singularities as well as the state-of-the-art formulation of convergence and quasi-optimality of adaptive algorithms for both the finite element method and the boundary element method in the frame of isogeometric analysis.

摘要

本文回顾了自适应等几何分析领域的技术现状，并讨论了该领域的最新进展，特别关注数学理论。这包括对用于局部解决可能奇点的可用样条技术的概述，以及在等几何分析框架下有限元法和边界元法自适应算法收敛性和拟最优性的最新表述。

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