skip to: onlinetools | mainnavigation | content | footer

Stephen D. Bond

Citation:

Stephen D. Bond, Jehanzeb Hameed Chaudhry, Eric C. Cyr and Luke N. Olson, A First-Order Systems Least-Squares Finite Element Method for the Poisson-Boltzmann Equation, Journal of Computational Chemistry 31:8 (2010) 1625-1635.

Abstract:

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.

Full Text:

DOI: 10.1002/jcc.21446

Preprint:

A First-Order Systems Least-Squares Finite Element Method for the Poisson-Boltzmann Equation (564K, PDF)

Bibtex:
@article{BCCO2010,
  author  = {Stephen D. Bond and Jehanzeb Hameed Chaudhry and Eric C. Cyr and
             Luke N. Olson},
  title   = {A First-Order Systems Least-Squares Finite Element Method for
             the {P}oisson-{B}oltzmann Equation},
  journal = {Journal of Computational Chemistry},
  volume  = 31,
  number  = 8,
  year    = 2010,
  pages   = {1625--1635},
  doi     = {10.1002/jcc.21446},
  note    = {SAND Number 2009-3266 J}
}

Stephen Bond