Partition of Unity Methods

A revolution similar to that initiated by the FEM is taking place through the XFEM, which is already implemented in leading commercial packages (ABAQUS, ANSYS, etc.) that are taught at undergraduate and post-graduate levels and to industrial end-users.

XFEM provides a detailed overview of the basics around the newly introduced extended finite element method for applications in solving moving boundary problems. XFEM is introduced naturally as an extension of FEM, through simple one dimensional examples which then allow the introduction of higher-dimensional problems. Throughout the book, each key concept is highlighted by the corresponding piece of MATLAB code which is provided via an accompanying web portal. Uniquely, this portal allows readers to obtain real-time feedback and help from an existing community of more than 130 researchers and industrialists.

• Demystifies the theory behind XFEM and makes it accessible to all with previous knowledge of the FEM
• Provides a simple introduction to XFEM but also provides a range of tools which the reader can build upon to take on a large breadth of more complex problems.
• Presents each key theoretical concept in parallel with its implementational aspects in the form of simple MATLAB routines provided along with the book via an interactive companion website and portal
• Provides a detailed account of applications of XFEM to fracture mechanics, including techniques absent from current literature

首本提供XFEM基礎指南及其實施的書籍

XFEM正在引發類似有限元法（FEM）所引發的革命，已經在領先的商業軟體（如ABAQUS、ANSYS等）中實施，並在本科和研究生課程以及工業用戶中教授。

《XFEM》詳細介紹了新引入的擴展有限元法在解決移動邊界問題中的應用基礎。XFEM自然地作為FEM的擴展引入，通過簡單的一維示例，然後引入更高維度的問題。在整本書中，每個關鍵概念都通過相應的MATLAB代碼突出顯示，這些代碼可以通過附帶的網站獲取。獨特的是，這個網站允許讀者從超過130名研究人員和工業界人士的現有社區中獲得即時反饋和幫助。

本書的特點包括：
- 將XFEM的理論解密，使其對所有具有FEM先備知識的人士易於理解
- 提供對XFEM的簡單介紹，同時提供一系列工具，讓讀者能夠應對更複雜的問題
- 通過簡單的MATLAB例程以及與書籍附帶的互動伴侶網站和門戶一起，將每個關鍵理論概念與其實施方面呈現
- 詳細介紹了XFEM在斷裂力學中的應用，包括目前文獻中缺乏的技術