On a Fast Solution Strategy for a Surface-Wire Integral Formulation of the Anisotropic Forward Problem in Electroencephalography

This work focuses on a quasi-linear-in-complexity strategy for a hybrid surface-wire integral equation solver for the electroencephalography forward problem. The scheme exploits a block diagonally dominant structure of the wire self block— that models the neuronal fibers self interactions—and of the surface self block—modeling interface potentials. This structure leads to two Neumann iteration schemes further accelerated with adaptive integral methods. The resulting algorithm is linear up to logarithmic factors. Numerical results confirm the performance of the method in biomedically relevant scenarios.