Timon Rabczuk - Böcker

Extended Finite Element and Meshfree Methods provides an overview of, and investigates, recent developments in extended finite elements with a focus on applications to material failure in statics and dynamics. This class of methods is ideally suited for applications, such as crack propagation, two-phase flow, fluid-structure-interaction, optimization and inverse analysis because they do not require any remeshing. These methods include the original extended finite element method, smoothed extended finite element method (XFEM), phantom node method, extended meshfree methods, numerical manifold method and extended isogeometric analysis.

This book also addresses their implementation and provides small MATLAB codes on each sub-topic. Also discussed are the challenges and efficient algorithms for tracking the crack path which plays an important role for complex engineering applications.

Explains all the important theory behind XFEM and meshfree methods Provides advice on how to implement XFEM for a range of practical purposes, along with helpful MATLAB codes Draws on the latest research to explore new topics, such as the applications of XFEM to shell formulations, and extended meshfree and extended isogeometric methods Introduces alternative modeling methods to help readers decide what is most appropriate for their work

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.

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.

Machine learning (ML) approaches have been extensively and successfully employed in various areas, like in economics, medical predictions, face recognition, credit card fraud detection, and spam filtering.

Machine learning (ML) approaches have been extensively and successfully employed in various areas, like in economics, medical predictions, face recognition, credit card fraud detection, and spam filtering.

This book equips readers with a rigorous and practical framework for solving complex engineering problems directly from governing equations using modern machine learning techniques. It bridges established principles from mechanics, numerical analysis, and scientific computing with emerging physics-based learning approaches, enabling reliable modeling, simulation, optimization, and inverse analysis beyond purely data-driven methods. A distinctive feature is its critical comparison of machine learning-based solvers with classical techniques such as the finite element method, isogeometric analysis, and meshfree methods, highlighting strengths, limitations, and domains of applicability. The scope ranges from foundational concepts to advanced engineering applications, supported by worked examples, reproducible code, and extensive references. The book is intended for graduate students, researchers, and practitioners in engineering, applied mathematics, and computational sciences who seek a principled entry point and a state-of-the-art reference for physics-based machine learning in modeling and simulation.

This book provides an overview of state-of-the-art methods in computational engineering for modeling and simulation.This proceedings volume includes a selection of refereed papers presented at the International Conference on Advances in Computational Mechanics (ACOME) 2017, which took place on Phu Quoc Island, Vietnam on August 2-4, 2017.The contributions highlight recent advances in and innovative applications of computational mechanics. Subjects covered include: biological systems; damage, fracture and failure; flow problems; multiscale multiphysics problems; composites and hybrid structures; optimization and inverse problems; lightweight structures; computational mechatronics; computational dynamics; numerical methods; and high-performance computing.The book is intended for academics, including graduate students and experienced researchers interested in state-of-the-art computational methods for solving challenging problems in engineering.