Volume 13, Issue 1
An Adaptive, Finite Difference Solver for the Nonlinear Poisson-Boltzmann Equation with Applications to Biomolecular Computations

Mohammad Mirzadeh ,  Maxime Theillard ,  Asdís Helgadóttir ,  David Boy and Frédéric Gibou

10.4208/cicp.290711.181011s

Commun. Comput. Phys., 13 (2013), pp. 150-173.

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  • Abstract

We present a solver for the Poisson-Boltzmann equation and demonstrate its applicability for biomolecular electrostatics computation. The solver uses a level set 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 address biomolecular systems. First, a novel approach of calculating the solvent excluded and the solvent accessible surfacesis explained; this allows to accuratelyrepresentthe location of the molecule’s surface. Next, a hybrid finite difference/finite volume approach is presented for discretizing the nonlinear Poisson-Boltzmann equation and enforcing the 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. 

  • History

Published online: 2013-01

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