Abstract
We apply the finite element-boundary element method (FEM-BEM) for a smooth approximation of a curvilinear interior interface in a finite domain. This avoids unphysical singularities at the interface due to a piece-wise linear boundary. This type of FEM-BEM coupling arises from simulating the biophysical problem of dielectric relaxation spectroscopy of solvated proteins. Boundary elements convert the linear Poisson problem due to the intramolecular charges of the protein into a boundary condition at the protein-solvent interface. The electro-diffusion of ions in the solvent is modeled as a set of convection-diffusion equations. The spatial distributions of the ion species induce an electrostatic potential which solves a Poisson problem. The gradient of the potential constitutes the convective flow field. The link to experiments is given by computing the stationary ionic current through the system. This requires Robin-type boundary conditions at the electrodes.
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Kramer, S.C., Lube, G. (2015). Finite Element-Boundary Element Methods for Dielectric Relaxation Spectroscopy. In: Abdulle, A., Deparis, S., Kressner, D., Nobile, F., Picasso, M. (eds) Numerical Mathematics and Advanced Applications - ENUMATH 2013. Lecture Notes in Computational Science and Engineering, vol 103. Springer, Cham. https://doi.org/10.1007/978-3-319-10705-9_4
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DOI: https://doi.org/10.1007/978-3-319-10705-9_4
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