Newton Solvers for Drift-Diffusion and Electrokinetic Equations
| Autor: | Arthur Bousquet, Xiaozhe Hu, Maximilian S. Metti, Jinchao Xu |
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| Rok vydání: | 2018 |
| Předmět: |
Work (thermodynamics)
Applied Mathematics 010103 numerical & computational mathematics Solver 01 natural sciences Stability (probability) Finite element method 010101 applied mathematics Computational Mathematics Electrokinetic phenomena Nonlinear system Computer Science::Systems and Control Linearization Applied mathematics 0101 mathematics Diffusion (business) Mathematics |
| Zdroj: | SIAM Journal on Scientific Computing. 40:B982-B1006 |
| ISSN: | 1095-7197 1064-8275 |
| DOI: | 10.1137/17m1146956 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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