NEWTON SOLVERS FOR DRIFT-DIFFUSION AND ELECTROKINETIC EQUATIONS

作者：Bousquet Arthur^*; Hu Xiaozhe; Metti Maximilian S; Xu Jinchao

来源：SIAM Journal on Scientific Computing, 2018, 40(3): B982-B1006.

DOI：10.1137/17M1146956

• finite elements
• Poisson-Nernst-Planck
• stability analysis
• numerical solvers

A Newton solver for equations modeling drift-diffusion and electrokinetic phenomena is investigated. For drift-diffusion problems, modeled by the nonlinear Poisson-Nernst-Planck (PNP) equations, the linearization of the model equations is shown to be well-posed. Furthermore, a fast solver for the linearized PNP and electrokinetic equations is proposed and numerically demonstrated to be effective on some physically motivated benchmarks. This work builds on a formulation of the PNP and electrokinetic equations that is investigated in [M. S. Metti, J. Xu, and C. Liu, J. Comput. Phys., 306 (2016), pp. 1-18] and shown to have some favorable stability properties.

• 出版日期2018