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 - Funding Information:
The work of the authors was supported by DOE grant DE-SC0009249 as part of the Collaboratory on Mathematics for Mesoscopic Modeling of Materials.
Funding Information:
∗Submitted to the journal’s Computational Methods in Science and Engineering section September 12, 2017; accepted for publication (in revised form) March 27, 2018; published electronically June 26, 2018. http://www.siam.org/journals/sisc/40-3/M114695.html Funding: The work of the authors was supported by DOE grant DE-SC0009249 as part of the Collaboratory on Mathematics for Mesoscopic Modeling of Materials. †Department of Mathematics, The Pennsylvania State University, University Park, PA 16802 ([email protected], http://personnal.edu/∼akb5670/, [email protected], http://www.math.psu. edu/xu/). ‡Department of Mathematics, Tufts University, Medford, MA 02155 ([email protected], http: //math.tufts.edu/faculty/xhu/). §Adtile Technologies, San Diego, CA 92121 ([email protected]).
Publisher Copyright:
© 2018 Society for Industrial and Applied Mathematics.
PY - 2018
Y1 - 2018
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.
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U2 - 10.1137/17M1146956
DO - 10.1137/17M1146956
M3 - Article
AN - SCOPUS:85049478360
SN - 1064-8275
VL - 40
SP - B982-B1006
JO - SIAM Journal on Scientific Computing
JF - SIAM Journal on Scientific Computing
IS - 3
ER -