WS, Connor Greene: A High-order Boundary Integral and Function Extension Method for the Poisson-Nernst-Planck Equations

Speaker
Connor Greene,New Jersey Institute of Technology

Abstract
We present a method using boundary integral equation methods and function extension along normals to model a cellular vesicle in an electrolyte solution with an applied electromagnetic field. We present an overview of the model, which includes a moving boundary with a stiff forcing term and piecewise smooth body forces. Function extension allows us to solve for the body forcing with high-order spatial accuracy. We also describe a novel analytic preconditioner for achieving a well-conditioned system matrix for evolving an inextensible boundary under Stokes flow.