A first-order system least-squares finite element method for the Poisson-Boltzmann equation

The Poisson-Boltzmann equation is an important tool in modeling solvent in biomolecular systems. In this paper, we focus on numerical approximations to the electrostatic potential expressed in the regularized linear Poisson-Boltzmann equation. We expose the flux directly through a first-order system form of the equation. Using this formulation, we propose a system that yields a tractable least-squares finite element formulation and establish theory to support this approach. The least-squares finite element approximation naturally provides an a posteriori error estimator and we present numerical evidence in support of the method. The computational results highlight optimality in the case of adaptive mesh refinement for a variety of molecular configurations. In particular, we show promising performance for the Born ion, Fasciculin 1, methanol, and a dipole, which highlights robustness of our approach. Key words: Poisson-Boltzmann, implicit solvent, finite elements, least-squares,...

• Type: Journal
• Year: 2010
• Where: JCC
• Authors: Stephen D. Bond, Jehanzeb Hameed Chaudhry, Eric C. Cyr, Luke N. Olson
• Keywords: JCC 2010, Linear Poisson-boltzmann Equation, Poisson-Boltzmann Equation, finite Elements