Xie, Dexuan
New solution decomposition and minimization schemes for Poisson-Boltzmann equation in calculation of biomolecular electrostatics
JOURNAL OF COMPUTATIONAL PHYSICS, 275:294-309, OCT 15 2014

The Poisson-Boltzmann equation (PBE) is one widely-used implicit solvent continuum model in the calculation of electrostatic potential energy for biomolecules in ionic solvent, but its numerical solution remains a challenge due to its strong singularity and nonlinearity caused by its singular distribution source terms and exponential nonlinear terms. To effectively deal with such a challenge, in this paper, new solution decomposition and minimization schemes are proposed, together with a new PBE analysis on solution existence and uniqueness. Moreover, a PBE finite element program package is developed in Python based on the FEniCS program library and GAMer, a molecular surface and volumetric mesh generation program package. Numerical tests on proteins and a nonlinear Born ball model with an analytical solution validate the new solution decomposition and minimization schemes, and demonstrate the effectiveness and efficiency of the new PBE finite element program package. (C) 2014 Elsevier Inc. All rights reserved.

DOI:10.1016/j.jcp.2014.07.012

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