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 (akb5670@psu.edu, http://personnal.edu/∼akb5670/, xu@math.psu.edu, http://www.math.psu. edu/xu/). ‡Department of Mathematics, Tufts University, Medford, MA 02155 (xiaozhe.hu@tufts.edu, http: //math.tufts.edu/faculty/xhu/). §Adtile Technologies, San Diego, CA 92121 (maxx@adtile.me).
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 -