  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.
