Domain Decomposition for Coupling Finite and Boundary Element Methods in EEG

The forward problem in electroencephalography aims to simulate on the scalp the potential V of an electromagnetic field generated by a simulated source. It must fit precisely with the electromagnetic propagation in the patient head. Yet, the skull anisotropy happens to be highly anisotropic, and must then be modeled. Although boundary element methods cannot deal with anisotropy like finite element methods, the symmetric BEM offers a higher accuracy than FEM wherever the conductivity can be considered as constant (i.e. for the brain and the scalp). A domain decomposition (DD) framework allows to split the global system into several ones with smaller computational domains. Then, one method (BEM or FEM) can be used per volume. This work presents such a coupling formulation of a 3-DD method solving iteratively a BEM for the brain, a FEM for the skull layer, and finally a BEM for the scalp.