The fast multipole method for the direct E/MEG problem

Reconstructing neuronal activity from MEG and EEG measurements requires the accurate calculation of the electromagnetic field inside the head. The boundary element formulation of this problem leads to a dense linear system which is too large to be solved directly. We propose to accelerate the computations via the fast multipole method. This method approximates the electromagnetic interaction between surface elements by performing multipole expansions at a coarse resolution. It significantly reduces the computational complexity of the matrix-vector products needed for the iterative solution of the linear system, and avoids the storage of its matrix. We describe the single-level fast multipole method and present several experiments demonstrating its accuracy and performance.