**Date & Time:** Monday, December 15, 2014, 11:30-12:30.

**Venue:** Ramanujan Hall

**Title:** Integral equation methods for elastance and mobility problems in two dimensions

**Speaker:** Manas Rachh, Courant Institute of Mathematical Sciences

**Abstract:** The capacitance matrix in electrostatics relates the potentials of a given configuration of perfect
conductors to the charges induced on them. The inverse of this matrix is called the elastance matrix.
Existing integral equation formulations for the elastance problem involve solving a modified Dirichlet
problem. This results in solving a bordered linear system with N + M unknowns where N is the number of
discretization points and M is the number of boundary components (which can be ill-conditioned for large
M). Integral equation methods for computing grand mobility tensors for rigid bodies in a Stokesian fluid
encounter similar issues. In this talk, we will describe a second kind integral formulation for applying the
elastance matrix which involves a Neumann problem, eliminating the requirement for auxilliary unknowns.
We extend this idea to the computation of the grand mobility tensor.