Anisotropic and Optimized FFT-Based Iterative Electromagnetic Solver for the PEEC Method

Fast Fourier transform (FFT)-accelerated integral-equation-based electromagnetic (EM) simulators have gained attraction for their capability to compute parasitics of arbitrarily shaped and large-scale voxelized structures on a desktop computer. Yet, FFT-based solvers have limitations due to the necessity of using voxels of the same size in all three Cartesian dimensions and suffer in the case of geometries with far-apart objects that require meshing also the air between them, resulting in a huge number of voxels and, thus, of unknowns. This work aims to overcome both these limitations by developing a systematic anisotropic strategy to compute matrix–vector products using the FFT-based approach and to remove the air existing between objects without sacrificing the desirable features of the FFT-based approach. The proposed approach is presented in the framework of the partial element equivalent circuit (PEEC) method, but it is well suited to be used also with other integral equation-based methods. The accuracy, efficiency, and applicability of the proposed anisotropic and optimized FFT (aoFFT)-based PEEC solver are demonstrated in the example of two structures requiring to use voxels of different sizes along the three Cartesian dimensions and with a large portion of air between the objects.