An Adaptive, Finite Difference Solver for the Nonlinear Poisson-Boltzmann Equation with Applications to Biomolecular Computations (Communications in Computational Physics, 2013)
We present a solver for the Poisson-Boltzmann equation and demonstrateits applicability for biomolecular electrostatics computation. The solver uses a levelset framework to represent sharp, complex interfaces in a simple and robust manner.It also uses non-graded, adaptive octree grids which, in comparison to uniform grids,drastically decrease memory usage and runtime without sacrificing accuracy. The basic solver was introduced in earlier works [16, 27], and here is extended to addressbiomolecular systems. First, a novel approach of calculating the solvent excluded andthe solvent accessible surfaces is explained; this allows to accurately represent the location of the molecule's surface. Next, a hybrid finite difference/finite volume approachis presented for discretizing the nonlinear Poisson-Boltzmann equation and enforcingthe jump boundary conditions at the interface. Since the interface is implicitly represented by a level set function, imposing the jump boundary conditions is straightforward and efficient.