A TRILINEAR IMMERSED FINITE ELEMENT METHOD FOR SOLVING THE ELECTROENCEPHALOGRAPHY FORWARD PROBLEM

This article describes a trilinear immersed finite element method for solving the electroencephalography forward problem, which is a three-dimensional elliptic interface problem in the head geometry. The method uses hexahedral Cartesian meshes independent of the interfaces between head tissues, thus avoiding the sometimes difficult task of generating geometry fitting meshes. The interfaces are represented with level sets, and the finite element space is locally modified to better approximate the discontinuities of the solution. Numerical results show that this method achieves the same accuracy as the standard linear finite element method with geometry fitting mesh.