This paper presents a fast-multipole surface-charge-simulation method for calculating three-dimensional Laplacian fields in voxel models. This method treats a surface of a voxel that has different inside and outside conductivities as a surface element of the indirect BEM (boundary element method). The main features of the proposed method are as follows. (1) An O(D2) performance in the memory capacity and operation cost is provided by applying the diagonal form fast multipole method (FMM), when the number of voxels is about D3. (2) The boundary matching is imposed by the continuity of the total flux passing through each element, which guarantees the solution globally satisfying Gauss's law; therefore the solution is globally stabilized.
This method is successfully applied to calculate the electric field induced by an applied homogeneous ELF (extremely low frequency) magnetic field in a human head model that has 1 mm ×1 mm 1 mm voxel size. © 2008 Wiley Periodicals, Inc. Electr Eng Jpn, 165(4): 1–10, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20529