Deal.t: an implementation of multivariate analysis suitable T-splines within the deal.ii framework

IF 8.7 2区工程技术 Q1 Mathematics

Engineering with Computers Pub Date : 2024-07-02 DOI:10.1007/s00366-024-02002-1

Sven Beuchler, Robin Hiniborch, Philipp Morgenstern

引用次数: 0

Abstract

We present a numerical framework for solving partial differential equations within an isogeometric context using T-splines in two and three space dimensions. Within this paper, we explain the data structures used for the implementation of deal.t (deal.II with T-splines) and main differences when using deal.t in contrast to deal.II. The authors present numerical experiments with error-based refinement (2D) and a priori refinement (3D) for scalar-valued problems. A full tutorial is given in the appendix. Since the new framework is based on deal.II, T-splines may be applied to various different PDEs.

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Deal.t：在 deal.ii 框架内实现适合 T 样条的多元分析

我们提出了一个数值框架，用于在二维和三维空间中使用 Tplines 解决等几何背景下的偏微分方程。在本文中，我们解释了用于实现 deal.t（带 T 样条的 deal.II）的数据结构，以及使用 deal.t 与 deal.II 的主要区别。作者介绍了对标量值问题进行基于误差的细化（2D）和先验细化（3D）的数值实验。附录中提供了完整的教程。由于新框架基于 deal.II，T-样条曲线可应用于各种不同的 PDE。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Engineering with Computers 工程技术-工程：机械

CiteScore

16.50

自引率

2.30%

发文量

203

审稿时长

9 months

期刊介绍： Engineering with Computers is an international journal dedicated to simulation-based engineering. It features original papers and comprehensive reviews on technologies supporting simulation-based engineering, along with demonstrations of operational simulation-based engineering systems. The journal covers various technical areas such as adaptive simulation techniques, engineering databases, CAD geometry integration, mesh generation, parallel simulation methods, simulation frameworks, user interface technologies, and visualization techniques. It also encompasses a wide range of application areas where engineering technologies are applied, spanning from automotive industry applications to medical device design.