Numerical computations with functions defined on the sphere and disk

Abstract: 

A classical technique for computing with functions on the sphere and disk is to "double wrap" the domain. We synthesize this with new techniques for constructing low rank function approximations to develop a whole collection of fast, adaptive, and regularity preserving algorithms based on the FFT for sphere and disk computations that are accurate to machine precision. Applications include vector calculus, the solution of PDEs, and the long-time simulation of active biological fluids. 

This is joint work with Heather Wilber and Grady Wright from Boise State University.