TY - JOUR
T1 - Newton solvers for drift-diffusion and electrokinetic equations
AU - Bousquet, Arthur
AU - Hu, Xiaozhe
AU - Metti, Maximilian S.
AU - Xu, Jinchao
N1 - Generated from Scopus record by KAUST IRTS on 2023-02-15
PY - 2018/1/1
Y1 - 2018/1/1
N2 - 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.
AB - 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.
UR - https://epubs.siam.org/doi/10.1137/17M1146956
UR - http://www.scopus.com/inward/record.url?scp=85049478360&partnerID=8YFLogxK
U2 - 10.1137/17M1146956
DO - 10.1137/17M1146956
M3 - Article
SN - 1095-7197
VL - 40
SP - B982-B1006
JO - SIAM Journal on Scientific Computing
JF - SIAM Journal on Scientific Computing
IS - 3
ER -