NSF/CBMS Regional Conference on Radial Basis Functions: Mathematical Developments and Applications June 20 - 24, 2011 University of Massachusetts Dartmouth
RBF methods for the solution of partial differential equations have generated enthusiasm among researchers and made RBF methods an emerging topic. RBF methods have become popular for their mesh-tolerance, simplicity of implementation, and dimension-independence. The impact of RBF methods is evident by the large number of publications on RBF methods, which have appeared in the past decade in mathematics, physics, and engineering journals. It is a field, which has grown through significant collaborations across disciplines, and the open and free exchange of ideas and MATLAB research codes. RBF methods have also been successfully applied to large-scale geophysical computations, which demonstrate their great potential in simulation of physical problems.
Despite their growing popularity, there have been few, if any, conferences dedicated to RBF methods. We propose to host the regional conference entitled *Radial Basis Functions: Mathematical Developments and Applications *. The mission of our RBF conference is to educate and motivate researchers (at all levels) and students in RBF methods, and to stimulate and inspire research in this field.
The conference will feature ten talks by two leading researchers in this field, Bengt Fornberg at the Applied Mathematics Department of the University of Colorado at Boulder and Natasha Flyer at the Institute for Mathematics Applied to Geosciences of National Center for Atmospheric Research (NCAR). In addition, supplementary forty-minute talks will be given by attendees who are emerging leaders in this field, who will focus on topics ranging from the numerical analysis of RBF methods to their applications to large-scale physical problems. Additionally, an expository monograph based on ten lectures will be prepared and made available for non-participants, and a web site devoted to the conference will make it accessible to those who could not attend. The talks will be designed to appeal to both experts and novices, and to stimulate discussion and collaboration between the speakers and attendees about recent advances and open problems in RBF. This conference will provide an environment to communicate the latest research and development of RBF methods in recent years, and will attract a wider and more diverse group of researchers to undertake research in RBF methods and build a supportive community of RBF researchers.
The NSF-CBMS conference on "Radial Basis Function" was successfully held at the UMass Dartmouth Advanced Technology Manufacturing Center (ATMC) for five days starting from 9 am on Monday June 20 and ending at 12:00 noon on Friday, June 24, 2011. The two principal lecturers were Professor Bengt Fornberg from Applied Mathematics at the University of Colorado at Boulder and Dr. Natasha Flyer from the Institute for Mathematics Applied to Geosciences and Computational Mathematics Group of National Center for Atmospheric Research (NCAR). Intellectual Merit: This conference has provided an environment to communicate the latest research and developments in Radial Basis Function (RBF) methods, which are of relevance in simulations of a wide variety of physical problems. The principal lecturers delivered outstanding ten lecture series regarding the evolution of accurate solution methods for numerically solving partial differential equations. The methods discusses were Finite Differences, Pseudospectral methods, RBF, and RBF-generated Finite Differences. Supplementing these methods with simulation results from large-scale calculations in the geosciences, the speakers illustrated with examples how the latter two methods have come to revolutionize the computational approaches, particularly in geoscience and related areas. Lecture topics spanned from the numerical analysis of RBF methods to cutting-edge implementation techniques. The approach provided a broad and deep understanding of the methods from a theoretical and practical perspective. Moreover, the talks facilitated the involvement and collaboration of participants on RBF methods, thus stimulating new research in the field. Broader Impact: This conference attracted a wide and diverse group of researchers from many backgrounds and fields. The lectures served to introduce RBF methods and their implementation to researchers who were not yet familiar with them, and to discuss the many challenging issues in this field, both on a theoretical and practical level. This conference encouraged the growing community of mathematicians studying RBF to study and overcome these issues, which will result in the wider applicability of RBF methods that will significantly impact the simulation of complex physical problems using high order numerical methods. Currently the principal lecturers are preparing an expository monograph based on ten lectures, which will be published by SIAM as an NSF-CBMS Regional Research Conference Series. Slides from some portions of the ten lectures along with abstracts of supplementary talks are available online at: www.umassdcomputing.org/conference/rbfcbms2011/.
