A second-order discretization of the nonlinear PoissonBoltzmann equation over irregular geometries using non-graded adaptive Cartesian grids
In this paper we present a finite difference scheme for the discretization of the nonlinear PoissonBoltzmann (PB) equation over irregular domains that is second-order accurate. The interface is represented by a zero level set of a signed distance function using Octree data structure, allowing a natural and systematic approach to generate non-graded adaptive grids. Such a method guaranties computational efficiency by ensuring that the finest level of grid is located near the interface. The nonlinear PB equation is discretized using finite difference method and several numerical experiments are carried which indicate the second-order accuracy of method. Finally the method is used to study the supercapacitor behaviour of porous electrodes.
second-order discretization nonlinear poissonboltzmann equation octree data structure non-graded adaptive grid supercapacitors arbitrary geometries