Speaker
Travis Askham, New Jersey Institute of Technology
Abstract
A number of multi-scale phenomena are modeled by
coupled bulk-surface partial differential equation systems. For example,
flexural-gravity models for ice floes couple bending forces in the ice to
fluid flow in the sea, resulting in a Laplace equation in the half-space
with a fourth order surface differential equation as a boundary condition on
$z=0$. A collection of similar problems can be found in the literature, where
the boundary effects include flexural, elastic, viscous, thermal, or surface
tension effects, and the bulk equations include potential flow and acoustic
wave equations. In the case of the half space, there is a particularly effective
numerical approach for this class of problems characterized by the use of a
nested integral representation for the solution. We will present the main ideas
behind the representations and an acceleration scheme for the associated
Green’s functions, which do not satisfy a PDE on surface. This is joint work
with Peter Nekrasov, Tristan Goodwill, Jeremy Hoskins (U. Chicago), and
Manas Rachh (IIT Bombay).