Meshfree Methods: Progress Made After 20 Years and Future Directions
Jiun-Shyan (JS) Chen
Structural Engineering & Center for Extreme Events Research, University of California, San Diego
ABSTRACT: In the past two decades, meshfree methods have emerged into a new class of computational methods with considerable success. In addition, a significant amount of progress has been made in addressing the major shortcomings that were present in these methods at the early stages of their development. For instance, essential boundary conditions are almost trivial to enforce by employing the techniques now available, and the need for high order quadrature has been circumvented with the development of advanced techniques, essentially eliminating the previously existing bottleneck of computational expense in meshfree methods. Given the proper treatment, nodal integration can be made accurate and free of spatial instability, making it possible to eliminate the need for a mesh entirely. Meshfree collocation methods have also undergone significant development, which also offer a truly meshfree solution. This presentation will give an overview of major progresses made in the field, the application to many challenging engineering mechanics problems, and the future directions of this research area.
