A Kernel-free Boundary Integral Method for the Poisson-Boltzmann Equation
Professor Wenjun Ying
Department of Mathematics and Institute of Natural Sciences
Shanghai Jiao Tong University
In this talk, first I will present a kernel-free boundary integral (KFBI) method for the linearized Poisson-Boltzmann equation, which may have variable coefficients and is in general not applicable for the standard boundary integral method. Then I will present the KFBI method for the nonlinear Poisson-Boltzmann equation. The KFBI method is a Cartesian grid method. It uses Cartesian grid-based solutions to compute approximations to boundary and volume integrals involved in the solution of boundary integral equations for the Poisson-Boltzmann equation. I will also present numerical examples in both two and three space dimensions to demonstrate the efficiency and accuracy of the KFBI method.