Newton solvers for drift-diffusion and electrokinetic equations

Arthur Bousquet, Xiaozhe Hu, Maximilian S. Metti, Jinchao Xu

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)B982-B1006
JournalSIAM Journal on Scientific Computing
Volume40
Issue number3
DOIs
StatePublished - Jan 1 2018

Fingerprint

Drift-diffusion
Linearization
Nonlinear equations
Diffusion Problem
Nonlinear Equations
Benchmark
Formulation
Modeling

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

Cite this

Bousquet, Arthur ; Hu, Xiaozhe ; Metti, Maximilian S. ; Xu, Jinchao. / Newton solvers for drift-diffusion and electrokinetic equations. In: SIAM Journal on Scientific Computing. 2018 ; Vol. 40, No. 3. pp. B982-B1006.
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Newton solvers for drift-diffusion and electrokinetic equations. / Bousquet, Arthur; Hu, Xiaozhe; Metti, Maximilian S.; Xu, Jinchao.

In: SIAM Journal on Scientific Computing, Vol. 40, No. 3, 01.01.2018, p. B982-B1006.

Research output: Contribution to journalArticle

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