Localized Kernel-Based Meshless Methods for Partial Differential Equations
(August 7 - 11, 2017)
This workshop will provide a platform for researchers working on localized kernel-based methods to present and discuss their latest developments, as well as the current theoretical and practical challenges in the field. These methods, such as radial basis function-generated finite differences (RBF-FD) or RBF-generated partition of unity methods (RBF-PUM), promise to develop into general-purpose meshless techniques for the numerical solution of partial differential equations that inherit the ease of implementation of the finite difference method, and yet potentially possess a greater ability than the finite element method to fit any geometry or adapt to singularities or other features of the solution.
The numerical evidence collected in recent years by a rapidly growing community of researchers suggests that these methods combine numerical stability on irregular node layouts, high computational speed, high accuracy, easy local adaptive refinement, and excellent opportunities for large-scale parallel computing. Despite recent efforts to provide error bounds for local kernel-based methods, their theory is still in its infancy.
The key topics of the workshop will include the latest computational achievements for large-scale computing in the geosciences, the mathematical tools of analysis for providing a solid foundation for the development and exploitation of the methods, the applications that benefit the most from their meshless nature, and the ways for techniques developed within other numerical methods to be combined with localized kernel-based methods in order to optimize a model in terms of accuracy and computational cost.
The main aspects of localized kernel-based methods and their applications will be presented in a number of survey lectures and tutorials accessible to graduate students and other researchers with background in numerical analysis and scientific computation.
- Oleg Davydov
(University of Giessen, Germany)
- Greg Fasshauer
(Colorado School of Mines)
- Natasha Flyer
(National Center for Atmospheric Research (NCAR))
- Bengt Fornberg
(University of Colorado-Boulder)
- Elisabeth Larsson
(Uppsala University, Sweden)