Spectral method for modified Poisson-Boltzmann equation on different geometries

• Main Authors: Chen, Yi-Ting, 陳奕廷
• Other Authors: Lin, Te-Sheng
• Format: Others
• Language: en_US
• Published: 2019
• Online Access: http://ndltd.ncl.edu.tw/handle/g9mfvy

碩士 === 國立交通大學 === 應用數學系所 === 107 === To investigate the structure of the electrical double layer (EDL) in electrolyte solutions, we visit modified Poisson-Boltzmann (MPB) equation over different geometries, like polar, elliptical, annular, and rectangular geometries, and verify a theoretical prediction numerically. First, we consider the linear Poisson equation △φ = f and state how we solve it with Chebyshev- Fourier spectral method. Second, we describe how we solve nonlinear MPB equation with Newton’s method. The advantage of our approach is that the grid points are clustered close to the domain boundary so that we can capture the behavior of the boundary layer accurately.