Optimal complexity Navier-Stokes simulations in the ball

In the first part of this talk, I will present an extension of Chebfun, called Ballfun, for computing with functions and vectors in the unit ball. I will then describe an algorithm for solving the incompressible Navier-Stokes equations in the ball. Contrary to projection methods, we use the poloidal-toroidal decomposition to decouple the PDEs and solve scalars equations. The solver has an optimal complexity (up to polylogarithmic terms) in terms of the degrees of freedom required to represent the solution.