用于固态机械学的开源器 (Hybrid high-order methods. A primer with application to solid mechanics)

from arxiv, This is a preprint of the following work: M. Cicuttin, A. Ern, N. Pignet, Hybrid high-order methods. A primer with applications to solid mechanics, Springer, (in press) 2021, reproduced with the permission of the publisher

This book is organized into eight chapters. The first three gently introduce the basic principles of hybrid high-order methods on a linear diffusion problem, the key ideas underlying the mathematical analysis, and some useful variants of the method as well as links to other methods from the literature. The following four present various challenging applications to solid mechanics, including linear elasticity and hyperelasticity, elastodynamics, contact/friction, and plasticity. The last chapter reviews implementation aspects. This book is primarily intended for graduate students, researchers (in applied mathematics, numerical analysis, and computational mechanics), and engineers working in related fields of application. Basic knowledge of the devising and analysis of finite element methods is assumed. Special effort was made to streamline the presentation so as to pinpoint the essential ideas, address key mathematical aspects, present examples, and provide bibliographic pointers.

翻译：该书分为八章。前三章轻轻地介绍了关于线性扩散问题的混合高阶方法的基本原则、数学分析所依据的关键思想、该方法的一些有用变式以及同文献中其他方法的链接。以下四章介绍了固体机械的各种具有挑战性的应用,包括线性弹性和超弹性、弹性动力学、接触/裂变和可塑性。最后一章审查了执行方面。这本书主要面向研究生、研究人员(应用数学、数字分析和计算力学)和从事相关应用领域的工程师。设想了设计和分析有限元素方法的基本知识。特别努力精简了介绍,以便确定基本思想、解决关键的数学方面、目前的例子和提供书目指针。