Xie, Dexuan New solution decomposition and minimization schemes for Poisson-Boltzmann equation in calculation of biomolecular electrostatics. (English) Zbl 1349.78077 J. Comput. Phys. 275, 294-309 (2014). Summary: 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. Cited in 29 Documents MSC: 78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory 78A30 Electro- and magnetostatics 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 92C40 Biochemistry, molecular biology Keywords:Poisson-Boltzmann equation; finite element method; variational minimization; biomolecular electrostatics; FEniCS project Software:CHARMM; F2PY; APBS; NAMD; DOLFIN; TNPACK; FEniCS; GAMER; tabipb; TABI; DelPhi Web Server; PDB2PQR; PBEQ-Solver PDFBibTeX XMLCite \textit{D. Xie}, J. Comput. 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