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Abstract: Bond, Chaudry, Cyr, Olson, JCC 2010

Citation

S.D. Bond, J.H. Chaudhry, E.C. Cyr and L.N. Olson, A First-Order Systems Least-Squares Finite Element Method for the Poisson-Boltzmann Equation, Journal of Computational Chemistry, 31:1625-1635, 2010.

Abstract

The Poisson-Boltzmann equation is an important tool in modeling solvent in biomolecular systems. In this article, 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.

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Eric C. Cyr


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E-mail: Eric C. Cyr
(505)844-0360 (Phone)

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University of Illinois
Clemson University