A simple and efficient technique to accelerate the computation of a nonlocal dielectric model for electrostatics of biomolecule

Abstract

<p style='text-indent:20px;'>The nonlocal modified Poisson-Boltzmann equation (NMPBE) is one important variant of a commonly-used dielectric continuum model, Poisson-Boltzmann equation (PBE). In this paper, we use a nonlinear block relaxation method to develop a new nonlinear solver for the nonlinear equation of <inline-formula><tex-math id="M1">\begin{document} $\Phi $ \end{document}</tex-math></inline-formula> and thus a new NMPBE solver, which is then programmed as a software package in <inline-formula><tex-math id="M2">\begin{document} $\texttt{C}\backslash\texttt{C++}$ \end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M3">\begin{document} $\texttt{Fortran}$ \end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M4">\begin{document} $\texttt{Python}$ \end{document}</tex-math></inline-formula> for computing the electrostatics of a protein in a symmetric 1:1 ionic solvent. Numerical tests validate the new package and show that the new solver can improve the efficiency by at least <inline-formula><tex-math id="M5">\begin{document}$ 40\%$ \end{document}</tex-math></inline-formula> than the finite element NMPBE solver without compromising solution accuracy.