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Название: Computational Methods Based on Peridynamics and Nonlocal Operators: Theory and ApplicationsАвтор: Timon Rabczuk, Huilong Ren, Xiaoying Zhuang
Издательство: Springer
Год: 2023
Страниц: 327
Язык: английский
Формат: pdf (true)
Размер: 10.29 MB
This book provides an overview of computational methods based on peridynamics and nonlocal operators and their application to challenging numerical problems which are difficult to deal with traditional methods such as the finite element method, material failure being “only” one of them. The authors have also developed a higher-order nonlocal operator approaches capable of solving higher-order partial differential equations on arbitrary domains in higher-dimensional space with ease. This book is of interest to those in academia and industry. Feynman once said, calculus is the language of God. Calculus uses the partial differential derivatives (PDE) and integrals to account for various physical phenomena. On one hand, it is well known that many physical problems or physical theories are formulated concisely by partial differential equations. No matter how complicated the physical phenomena appear, the PDEs to describe the mechanism are just one/several lines of equations. Mathematically, PDEs are a combinational result of partial differential derivatives of different orders. Partial differential derivatives are defined at a point without size, in this sense, the PDEs model can be viewed as a local model. On the other hand, integral expression is defined in a finite domain, which consists of infinite points. In this sense, the integral can be viewed as a nonlocal model.
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