A finite volume method to solve the Poisson equation with jump conditions and surface charges: application to electroporation. (English) Zbl 07842850
Summary: Efficient numerical schemes for solving the Poisson equation with jump conditions are of great interest for a variety of problems, including the modeling of electroporation phenomena and filamentary discharges. In this paper, we propose a modification to a finite volume scheme, namely the discrete dual finite volume method, in order to account for jump conditions with surface charges, i.e. with a source term. Our numerical tests demonstrate second-order convergence even with highly distorted meshes. We then apply the proposed method to model electroporation phenomena in biological cells by proposing a model that considers the thickness of the cell membrane as a separate domain, which differs from the literature. We show the advantages of the proposed method in this context through numerical experiments.
MSC:
| 65Nxx | Numerical methods for partial differential equations, boundary value problems |
| 65Mxx | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |
| 35Jxx | Elliptic equations and elliptic systems |
Keywords:
Poisson equation; jump conditions; surface charges; finite volume method; DDFV; cell modelingReferences:
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