Title: Towards automatically adaptive solvers for particulate Stokes flows in three dimensions
The simulation of particulate flows plays a critical role in the design of microfluidic devices, the study of colloidal suspensions, rheological studies, Brownian dynamics, and biophysical modeling to name a few. In order to enable design by simulation for problems arising in these applications, automatically adaptive solvers which resolve the complexity of the geometry and the input data play a critical role. In two dimensions, this has been made possible through the development of high-order integral equation based solvers which rely on well-conditioned integral representations, efficient quadrature formulas, and coupling to fast multipole methods. However, much is still to desired of these solvers in three dimensions (both in terms of their efficiency and accuracy), particularly in the context of enabling automatic adaptivity in complex geometries. In this talk, I will present an efficient high-order solver for solving Stokes equations in complex three-dimensional geometries with focus on the following two issues—development of high-order surface descriptions, and efficient quadrature methods for computing singularintegrals on these surfaces.
