Finite element-boundary element methods for dielectric relaxation spectroscopy

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-BEMcoupling 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.