In this article, we introduce a novel integral equation (IE) solver for inductance extraction that incorporates both Fast Multipole Method (FMM) and Fast Fourier Transform (FFT) acceleration. Crucially, FMM allows to deal with arbitrary polyhedral grids and thus with both tetrahedral and voxelized grids, whereas FFT requires exclusively voxelized grids. The FFT acceleration in the proposed framework differs from other FFT-accelerated approaches thanks to the use of element-wise constant basis functions, which reduce the computational cost and enable a simple singularity extration. We demonstrate pros and cons of three different combinations of acceleration method and type of grid, namely FMM-Tetrahedra (FMM-Tet), FMM-Voxel and FFT-Voxel, by applying them to a set of toyproblems as well as a real-world structure of a printed circuit board involving millions of unknowns. The results point out two inherent limitations of FFT methods, due to the necessity of using voxels of the same size along fixed Cartesian directions: the poor geometric approximation accuracy of curved geometries, and the high matrix fill-in resulting from the modeling of thin structures immersed in air. We conclude that FFT acceleration is better suited as a specialized tool in a more general framework, to be used only when its strict favorable conditions are met. This conclusion puts in perspective the performance gains of alternative methods proposed in literature that employ FFTacceleration on voxelized grids for the case of thin and curved geometries, thus suggesting new future directions of research.
