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.