Hybrid boundary element and finite difference method for solving the nonlinear Poisson-Boltzmann equation

@article{citeulike:3831825, abstract = {A hybrid approach for solving the nonlinear Poisson-Boltzmann equation (PBE) is presented. Under this approach, the electrostatic potential is separated into (1) a linear component satisfying the linear PBE and solved using a fast boundary element method and (2) a correction term accounting for nonlinear effects and optionally, the presence of an ion-exclusion layer. Because the correction potential contains no singularities (in particular, it is smooth at charge sites) it can be accurately and efficiently solved using a finite difference method. The motivation for and formulation of such a decomposition are presented together with the numerical method for calculating the linear and correction potentials. For comparison, we also develop an integral equation representation of the solution to the nonlinear PBE. When implemented upon regular lattice grids, the hybrid scheme is found to outperform the integral equation method when treating nonlinear PBE problems. Results are presented for a spherical cavity containing a central charge, where the objective is to compare computed 1D nonlinear PBE solutions against ones obtained with alternate numerical solution methods. This is followed by examination of the electrostatic properties of nucleic acid structures. {\copyright} 2004 Wiley Periodicals, Inc. J Comput Chem 25: 935-955, 2004}, address = {Continuum Dynamics, Inc., 34 Lexington Avenue, Ewing, NJ 08618-2302; Institute of Molecular Biophysics, Florida State University, Tallahassee, FL 32306}, author = {Boschitsch, Alexander H. and Fenley, Marcia O.}, citeulike-article-id = {3831825}, doi = {10.1002/jcc.20000}, journal = {Journal of Computational Chemistry}, keywords = {electrostatics, mathematics}, number = {7}, pages = {935--955}, posted-at = {2008-12-28 15:25:38}, priority = {0}, title = {Hybrid boundary element and finite difference method for solving the nonlinear Poisson-Boltzmann equation}, url = {http://dx.doi.org/10.1002/jcc.20000}, volume = {25}, year = {2004} }

TY - JOUR ID - citeulike:3831825 L3 - citeulike-article-id:3831825 N2 - A hybrid approach for solving the nonlinear Poisson-Boltzmann equation (PBE) is presented. Under this approach, the electrostatic potential is separated into (1) a linear component satisfying the linear PBE and solved using a fast boundary element method and (2) a correction term accounting for nonlinear effects and optionally, the presence of an ion-exclusion layer. Because the correction potential contains no singularities (in particular, it is smooth at charge sites) it can be accurately and efficiently solved using a finite difference method. The motivation for and formulation of such a decomposition are presented together with the numerical method for calculating the linear and correction potentials. For comparison, we also develop an integral equation representation of the solution to the nonlinear PBE. When implemented upon regular lattice grids, the hybrid scheme is found to outperform the integral equation method when treating nonlinear PBE problems. Results are presented for a spherical cavity containing a central charge, where the objective is to compare computed 1D nonlinear PBE solutions against ones obtained with alternate numerical solution methods. This is followed by examination of the electrostatic properties of nucleic acid structures. © 2004 Wiley Periodicals, Inc. J Comput Chem 25: 935-955, 2004 IS - 7 JF - Journal of Computational Chemistry AD - Continuum Dynamics, Inc., 34 Lexington Avenue, Ewing, NJ 08618-2302; Institute of Molecular Biophysics, Florida State University, Tallahassee, FL 32306 EP - 955 TI - Hybrid boundary element and finite difference method for solving the nonlinear Poisson-Boltzmann equation VL - 25 SP - 935 KW - electrostatics KW - mathematics AU - Boschitsch, Alexander AU - Fenley, Marcia PY - 2004/// UR - http://dx.doi.org/10.1002/jcc.20000 ER -