Nonlocal Advection-Driven Equations of Evolution on the Sphere (19rit260)


(University of Manitoba)

(Columbia University)


The Banff International Research Station will host the "Nonlocal advection-driven equations of evolution on the sphere" workshop in Banff from August 18, 2019 to August 25, 2019.

Nonlocal models are becoming more and more prevalent in new and classical disciplines, including microbiology, climate modeling, image processing, and fluid dynamics, among others. During this week at BIRS, Montanelli and Slevinsky are developing algorithms for nonlocal vector calculus on the sphere and investigating appropriate methods for the simulation of time-dependent phenomena.

Why do we care? It turns out that many real-world applications on the sphere (weather forecasting, analysis of the cosmic dawn, chemotaxis on the cellular level) are based on nonlocal phenomena. If one approximates nonlocal operators by local operators (the classical operators of vector calculus), then simulations can lead to completely erroneous and/or nonphysical results. Therefore, it is important for us as numerical analysts to provide optimal solutions to the problems as they are formulated, rather than working with approximations.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).