The symmetric BEM: bringing in more variables for better accuracy

Electrophysiological modeling of Magneto- and Electro-encephalography (MEG and EEG) rely on accurate forward solvers that relate source activities to sensor measurements. In comparing a Boundary Element (BEM) and a Finite Element Method (FEM) for forward electroencephalography, in our early numerical experiments, we found the FEM to have a better accuracy than the BEM. This triggered a quest to improve the accuracy of Boundary Element Methods and led us to study the extended Green representation theorem.