Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 40, Issue 3, Pages B982-B1006Publisher
SIAM PUBLICATIONS
DOI: 10.1137/17M1146956
Keywords
finite elements; Poisson-Nernst-Planck; stability analysis; numerical solvers
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Funding
- DOE as part of the Collaboratory on Mathematics for Mesoscopic Modeling of Materials [DE-SC0009249]
- U.S. Department of Energy (DOE) [DE-SC0009249] Funding Source: U.S. Department of Energy (DOE)
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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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