Close Evaluation of Layer Potentials for Stokes Equations

To understand the fluid dynamics of complex biological phenomena, fluid-structure interaction problems must be solved. Challenges exist in developing numerical techniques to solve these flow problems with boundary conditions at fluid-structure interfaces. I will present details of a novel method that is being developed to address these challenges for the Stokes equations. We are looking at accurate evaluation of layer potentials near interfaces and boundaries. I will present how classical numerical methods are problematic for evaluations close to boundaries and how newly developed numerical methods based on asymptotics can be used to improve accuracy.