Adaptive spatial resolution for spatial spectral integral equations

Fast formulations for domain integral equations exist for decades. Two popular discretization strategies for them are voxel-grids [1] and Schaubert-Wilton-Glisson-functions (SWGs) [2]. The main advantage of a voxel-grid is that the continuous translation symmetry of the physical problem translates to a discrete translation symmetry in the discretized problem. This allows for a quick computation of the interaction matrix and fast, FFT-based matrix-vector-products. However, voxel-grids do not allow for refinement, and voxels are a somewhat crude approximation to the continuous electromagnetic fields. SWGs do much better at the latter aspect, since they allow for local refinement, and are an order more continuous. But, in general, SWG-discretized objects do not have a discrete translation symmetry, leading to significantly larger computational efforts.