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A first-order system least-squares finite element method for the Poisson-Boltzmann equation
Stephen D Bond1, Jehanzeb Hameed Chaudhry, Eric C Cyr
1Department of Computer Science, University of Illinois, Urbana, Illinois 61801, USA.
Journal of Computational Chemistry
|November 13, 2009
Summary
This study introduces a novel least-squares finite element method for solving the regularized linear Poisson-Boltzmann equation, improving biomolecular solvent modeling. The approach offers an effective error estimator and demonstrates robust performance across various molecular systems.
Area of Science:
- Computational chemistry
- Biophysics
- Applied mathematics
Background:
- The Poisson-Boltzmann equation is crucial for modeling solvent effects in biomolecular systems.
- Accurate electrostatic potential calculations are vital for understanding molecular interactions.
Purpose of the Study:
- To develop and analyze a tractable least-squares finite element formulation for the regularized linear Poisson-Boltzmann equation.
- To provide a robust numerical method for approximating electrostatic potentials in biomolecular modeling.
Main Methods:
- Reformulation of the Poisson-Boltzmann equation into a first-order system.
- Development of a least-squares finite element method (LSFEM).
- Establishment of theoretical underpinnings for the LSFEM approach.
- Implementation of an a posteriori error estimator.
Main Results:
- The proposed LSFEM provides a tractable and theoretically supported method.
- The method naturally incorporates an a posteriori error estimator.
- Numerical results demonstrate optimal performance with adaptive mesh refinement.
- The approach shows robust and promising performance for various molecular configurations, including the Born ion, Fasciculin 1, methanol, and a dipole.
Conclusions:
- The least-squares finite element method offers an efficient and accurate approach for solving the regularized linear Poisson-Boltzmann equation.
- This method enhances the modeling of electrostatic potentials in complex biomolecular systems.
- The demonstrated robustness across diverse molecular models validates the approach for broad applicability in computational biophysics.
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