|Date: Friday, February 02, 2018
Location: 1084 East Hall (4:10 PM to 5:00 PM)
Title: Green's Functions, Boundary Integral Equations and Rotational Symmetry: Constructing a Fast Solver for Stokes' Equation
Abstract: Boundary integral equations (BIEs), and in particular, surface integral equations show up everywhere; any fluid-particle interaction model (eg. protein folding) gives rise to these kind of equations. However, despite their prevalence, constructing high order accurate numerical methods to solve these BIEs, especially when the kernel is singular, remains an active area of research even today.
Sometimes though, when we are lucky, we can take advantage of certain symmetries of the problem, and reduce it to simpler integral equations that we know how to solve. For example, a surface integral equation with rotational symmetry can be reduced to a sequence of integral equations on a curve. In this talk, I'll describe this dimensionality reduction for BIEs associated to Stokes' equation.
We will start with an informal (and I hope, intuitive) description of Green's functions and BIEs. Next, we will see how we can use Fourier series for reducing the dimension. Finally, we'll use these ideas to construct a fast numerical solver for Stokes' equation.
Speaker: Saibal De
Institution: University of Michigan
Event Organizer: Audra McMillan firstname.lastname@example.org