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

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

Mohammad Mirzadeh 1*, Maxime Theillard 1, Asdis Helgadottir 1, David Boy 1, Frederic Gibou 2

1 Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA.
2 Department of Mechanical Engineering and Department of Computer Science, University of California, Santa Barbara, CA 93106, USA.

Received 29 July 2011; Accepted (in revised version) 18 October 2011
Available online 12 June 2012


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 surfaces is explained; this allows to accurately represent the 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.

AMS subject classifications: 92-08, 65N06, 65N08, 65N50, 92C05, 35F21

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Key words: Poisson-Boltzmann, non-graded adaptive grid, octree data structure, level set, irregular domain, hybrid finite volume/finite difference.

*Corresponding author.
Email: (M. Mirzadeh), (M. Theillard), (A. Helgadottir), (D. Boy), (F. Gibou)

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