Special Finite Elements for Dipole Modelling

This thesis focuses on the solution of the EEG forward problem, using the finite element method. The goal is to compare different dipole models for a current source in the human head, with a focus on Whitney type basis functions. For the current sources in the head a widely used model is the mathematical or current dipole. Its strong singularity poses a problem for numerical methods. Therefore we investigate a less singular dipole model based on Whitney forms. In the first part of the thesis we give an overview of the EEG forward problem and the theory behind Whitney elements. Then we investigate methods for representing a mathematical dipole in Whitney formulation, in order to validate the Whitney approach. The following comparison of the available models on tetrahedral and hexahedral meshes shows, that the Whitney model achieves the highest accuracy if the local mesh geometry can represent the dipole moment well. Otherwise interpolation techniques have to be used, which worsen the accuracy, making the Whitney approach inferior to the other methods in the general case.