Speaker
Kshitij Patil, Simon Fraser University
Abstract
We discuss boundary and eigenvalue problems for the Laplace and Helmholtz equations in the plane using layer potentials for both interior and exterior domains. For the Steklov-Helmholtz operator, a new strategy is proposed to deal with Helmholtz wave numbers that correspond with Dirichlet-Laplace eigenvalues. We demonstrate the use of our method in numerical shape optimization and eigenvalue asymptotics. Applicability of the discretized layer potentials is shown to other eigenvalue and boundary value problems.