ABSTRACT
This paper presents a new, meshless and inherently parallelizable floating random-walk (FRW) algorithm for the solution of the two-dimensional nonlinear Poisson-Boltzmann (NPB) equation. Historically, the FRW method has not been applied to nonlinear problems of significance, which can be attributed to the absence of Green's functions. This problem has been remedied in our work by a novel use of iterative perturbation theory. Our past work involved the FRW solution of the NPB equation in one dimension. In this work, we extend the algorithm to two dimensions and excellent agreement has been obtained with a finite-difference based solution. The application area of interest is the modeling of plasma sheaths.