Adaptive and Iterative Methods for Simulations of Nanopores with the PNP-Stokes Equations
| Autor: | Mitscha-Baude, Gregor, Buttinger-Kreuzhuber, Andreas, Tulzer, Gerhard, Heitzinger, Clemens |
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| Rok vydání: | 2016 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jcp.2017.02.072 |
| Popis: | We present a 3D finite element solver for the nonlinear Poisson-Nernst-Planck (PNP) equations for electrodiffusion, coupled to the Stokes system of fluid dynamics. The model serves as a building block for the simulation of macromolecule dynamics inside nanopore sensors. We add to existing numerical approaches by deploying goal-oriented adaptive mesh refinement. To reduce the computation overhead of mesh adaptivity, our error estimator uses the much cheaper Poisson-Boltzmann equation as a simplified model, which is justified on heuristic grounds but shown to work well in practice. To address the nonlinearity in the full PNP-Stokes system, three different linearization schemes are proposed and investigated, with two segregated iterative approaches both outperforming a naive application of Newton's method. Numerical experiments are reported on a real-world nanopore sensor geometry. We also investigate two different models for the interaction of target molecules with the nanopore sensor through the PNP-Stokes equations. In one model, the molecule is of finite size and is explicitly built into the geometry; while in the other, the molecule is located at a single point and only modeled implicitly -- after solution of the system -- which is computationally favorable. We compare the resulting force profiles of the electric and velocity fields acting on the molecule, and conclude that the point-size model fails to capture important physical effects such as the dependence of charge selectivity of the sensor on the molecule radius. Comment: 28 pages, 12 figures |
| Databáze: | arXiv |
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