Efficient and Accurate Higher-order Fast Multipole Boundary Element Method for Poisson Boltzmann Electrostatics

The Poisson-Boltzmann equation is a partial differential equation that describes the electrostatic behavior of molecules in ionic solutions. Significant efforts have been devoted to accurate and efficient computation for solving this equation. In this paper, we developed a boundary element framework based on the linear time fast multipole method for solving the linearized PoissonBoltzmann equation. A higher-order parametric formulation called algebraic spline model is used for accurately approximation of the unknown solution of the linearized Poisson-Boltzmann equation. The numerical test and experimental results show that these techniques offer an efficient and accurate solution for solving the electrostatic problem of molecules.