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.

翻译：本文聚焦于一种准线性复杂度的混合面-线积分方程求解器，用于脑电图正问题。该方案利用了线自块（模拟神经纤维自身相互作用）和面自块（模拟界面电势）的块对角占优结构。这一结构催生了两种进一步通过自适应积分方法加速的诺伊曼迭代方案。所得算法的复杂度在考虑对数因子时呈线性。数值结果验证了该方法在生物医学相关场景中的性能。