Fast Fourier transform (FFT)-accelerated, integral-equation-based electromagnetic simulators have gained significant attention due to their ability to compute parasitics of arbitrarily shaped and large-scale voxelized structures on desktop computers. However, FFT-based solvers have limitations as they require voxels of the same size across all Cartesian dimensions. This is a significant limitation, especially for printed circuit boards (PCB)-like geometries of very thin copper layers and much thicker dielectric layers, which leads to an excessive number of voxels, and consequently, a large number of unknowns. In addition, in PCB-like structures, vias represent small details that require finer meshing resolution for proper discretization. This work aims to overcome these limitations by developing a systematic anisotropic strategy for computing matrix-vector products using the FFT-based approach and automatically replacing vias with equivalent R–L lumped elements. Furthermore, a zero-thickness conductor mesh is proposed within the partial element equivalent circuit (PEEC) method framework, which is in turn also suitable for use with other integral-equation-based methods. The accuracy, efficiency, and applicability of the proposed FFT-PEEC solver are demonstrated on three examples.