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Stephen D. Bond

Citation:

Jehanzeb Hameed Chaudhry, Stephen D. Bond and Luke N. Olson, A Weighted Adaptive Least-Squares Finite Element Method for the Poisson-Boltzmann Equation, Applied Mathematics and Computation 218:9 (2012) 4892-4902.

Abstract:

The finite element methodology has become a standard framework for approximating the solution to the Poisson Boltzmann equation in many biological applications. In this article, we examine the numerical efficacy of least-squares finite element methods as an alternative to the traditional Galerkin finite element approach. In particular, we highlight the utility of a first-order form, noting optimality, control of the flux variables, and flexibility in the formulation, including the choice of elements. We explore the impact of weighting and the choice of elements on conditioning and adaptive refinement. In a series of numerical experiments, we compare the finite element methods when applied to the problem of computing the solvation free energy for realistic molecules of varying size.

Full Text:

DOI: 10.1016/j.amc.2011.10.054

Preprint:

A Weighted Adaptive Least-Squares Finite Element Method for the Poisson-Boltzmann Equation (1.2M, PDF)

Bibtex:
@article{CBO2012,
  author  = {Jehanzeb Hameed Chaudhry and Stephen D. Bond and Luke N. Olson},
  title   = {A Weighted Adaptive Least-Squares Finite Element Method for the
             {P}oisson-{B}oltzmann Equation},
  journal = {Applied Mathematics and Computation},
  volume  = 218,
  number  = 9,
  year    = 2012,
  pages   = {4892--4902},
  doi     = {10.1016/j.amc.2011.10.054},
  note    = {SAND Number 2011-3810 J}
}

Stephen Bond