Description
Speaker: Manas Rachh, Yale University
Title: Integral equation formulation of the biharmonic problem with Dirichlet boundary conditions
Abstract: In this talk, we present a novel integral representation for the Dirichlet problem of the biharmonic equation. To obtain the representation, the Dirichlet problem is first converted into a related Stokes problem for which the Sherman-Lauricella integral representation can be used. However, not all potentials for the Dirichlet problem correspond to a potential for Stokes flow, and vice-versa, but we show that the integral representation can be augmented and modified accordingly, with careful attention paid to the case of multiply connected domains. The resulting integral representation has a kernel with a lower order singularity (as a function of the ambient space) than classical representations. We illustrate the accuracy, and conditioning of our method with several numerical examples.