Hadrien Montanelli (Columbia University)

Title:Fast algorithms for solving local and nonlocal differential equations with periodicity

Abstract:

A large number of phenomena in natural and social sciences exhibit periodicity. Examples include day and night cycles, seasons, ocean waves, heartbeat and breathing, economic and political cycles, and many others. These phenomena vary in time but recur at intervals: these are examples of temporal periodicity. Another type of periodicity is spatial periodicity: even if the phenomenon we are looking at is not periodic in time, it might occur in a periodic domain, such as rows of turbine blades or Earth's surface. In both cases, periodicity is a special feature that we can take advantage of when solving differential equations that model such phenomena. We present in this talk a collection of algorithms for solving local and nonlocal differential equations with periodicity in time or in space.