Title: Extended Finite Element Method (X-FEM) Short Course

Speaker: Professor John E. Dolbow, Department of Civil and Environmental Engineering, Duke University

Location: All sessions will be held in Bldg 980, Room 95 from 10:00-11:30 am

Brief Abstract: The eXtended Finite Element Method (X-FEM) is a generalized approach for treating evolving boundary value problems within the finite-element framework. It emphasizes the use of enrichment functions (a particular form of adaptivity) to capture sharp gradients, singularities, and discontinuities in the solution.  For example, it has been used to simulate three-dimensional crack growth, multi-phase flow, and fluid-structure interaction.  The method provides a means to represent sharp features such as crack fronts and phase interfaces independently of the mesh. In conjunction with level-set methods, the X-FEM represents both the local solution and geometric evolution of evolving (sharp) features with evolving functions.

This short course will provide four ninety-minute lectures on the X-FEM and its coupling with level sets. The first lecture will cover the background for the method, current state of the art, and highlight some existing applications. The partition-of-unity framework that provides much of the structure for the enrichment will also be discussed. The second lecture will cover the basics of the method in detail, with emphasis on enrichment for linear elastic crack growth, material interfaces, and free surfaces/voids. The third lecture will cover advanced topics such as enforcing constraints, robustly evaluating conservation-based quantities, and time-dependent enrichment. Finally, the last lecture will cover basic level set concepts and algorithms that have been specifically designed for use with unstructured finite-element meshes. 

Course materials will include copies of the lecture slides and accompanying notes, along with preprints from Professor Dolbow and his colleagues.

CSRI POC: Tom Voth, (505) 844-6004, Josh Robbins, (505) 284-5653