Simple and robust solver for the Poisson-Boltzmann equation Export

@article{citeulike:5305070, abstract = {A variational approach is used to develop a robust numerical procedure for solving the nonlinear Poisson-Boltzmann equation. Following Maggs and Rossetto [Phys. Rev. Lett. 88, 196402 (2002)], we construct an appropriate constrained free energy functional such that its Euler-Lagrange equations are equivalent to the Poisson-Boltzmann equation. This is a formulation that searches for a true minimum in function space, in contrast to previous variational approaches that rather searched for a saddle point. We then develop, implement, and test an algorithm for its numerical minimization, which is quite simple and unconditionally stable. The analytic solution for planar geometry is used for validation. Some results are presented for a charged colloidal sphere surrounded by counterions and optimizations based upon fast Fourier transforms and hierarchical preconditioning are briefly discussed.}, author = {Baptista, M. and Schmitz, R. and D\"{u}nweg, B.}, citeulike-article-id = {5305070}, citeulike-linkout-0 = {http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PLEEE8000080000001016705000001&idtype=cvips&gifs=yes}, citeulike-linkout-1 = {http://link.aps.org/abstract/PRE/v80/e016705}, citeulike-linkout-2 = {http://dx.doi.org/10.1103/PhysRevE.80.016705}, day = {22}, doi = {10.1103/PhysRevE.80.016705}, journal = {Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)}, keywords = {algorithm, boltzmann, equation, euler, lagrange, poisson, solver}, month = {July}, number = {1}, pages = {016705+}, posted-at = {2009-07-30 17:55:26}, priority = {5}, publisher = {APS}, title = {Simple and robust solver for the Poisson-Boltzmann equation}, url = {http://dx.doi.org/10.1103/PhysRevE.80.016705}, volume = {80}, year = {2009} }

TY - JOUR ID - citeulike:5305070 L3 - citeulike-article-id:5305070 N2 - A variational approach is used to develop a robust numerical procedure for solving the nonlinear Poisson-Boltzmann equation. Following Maggs and Rossetto [Phys. Rev. Lett. 88, 196402 (2002)], we construct an appropriate constrained free energy functional such that its Euler-Lagrange equations are equivalent to the Poisson-Boltzmann equation. This is a formulation that searches for a true minimum in function space, in contrast to previous variational approaches that rather searched for a saddle point. We then develop, implement, and test an algorithm for its numerical minimization, which is quite simple and unconditionally stable. The analytic solution for planar geometry is used for validation. Some results are presented for a charged colloidal sphere surrounded by counterions and optimizations based upon fast Fourier transforms and hierarchical preconditioning are briefly discussed. IS - 1 JF - Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) TI - Simple and robust solver for the Poisson-Boltzmann equation PB - APS VL - 80 SP - 016705 KW - algorithm KW - boltzmann KW - equation KW - euler KW - lagrange KW - poisson KW - solver AU - Baptista, M AU - Schmitz, R AU - Dünweg, B PY - 2009/07/22/ UR - http://dx.doi.org/10.1103/PhysRevE.80.016705 ER -