Bordas Stéphane P.A., Menk A., Natarajan M. Partition of Unity Methods: The Extended Finite Element Method

John Wiley & Sons, 2024. — 367 p. — ISBN: 9780470667088.While it is the number one tool for computer aided design and engineering, the finite element method (FEM) has difficulties with discontinuities, singularities, and moving boundaries. Partition of unity methods addresses these challenges and is now increasingly implemented in commercially available software. Partition of Unity Methods delivers a detailed overview of its fundamentals, in particular the extended finite element method for applications in solving moving boundary problems. The distinguished academics and authors introduce the XFEM as a natural extension of the traditional finite element method (FEM), through straightforward one-dimensional examples which form the basis for the subsequent introduction of higher dimensional problems. This book allows readers to fully understand and utilize XFEM just as it becomes ever more crucial to industry practice.Perfect for researchers and postdoctoral candidates working in the field of computational mechanics, Partition of Unity Methods also has a place in the libraries of senior undergraduate and graduate students working in the field. Finite element and CFD analysts and developers in private industry will also greatly benefit from this book.Introduction
A Step-by-Step Introduction to Enrichment
Partition of Unity Revisited
Advanced Topics
Applications
Recovery-Based Error Estimation and Bounding in XFEM
𝝓-FEM: An Efficient Simulation Tool Using Simple Meshes for Problems in Structure Mechanics and Heat Transfer
eXtended Boundary Element Method (XBEM) for Fracture Mechanics and Wave Problems
Combined Extended Finite Element and Level Set Method (XFE-LSM) for Free Boundary Problems
XFEM for 3D Fracture Simulation
XFEM Modeling of Cracked Elastic-Plastic Solids
An Introduction to Multiscale analysis with XFEM