Scattering analysis accelerated by a 3-D multilevel non-uniform grid field evaluation algorithm

A fast algorithm for computing the scattering cross section of arbitrary shaped large rigid bodies using an iterative method of moments solver has been presented. The main computational bottleneck of such iterative solvers stems from the need to perform at each iteration at least one matrix‐vector product. If performed directly, matrix‐vector multiplication, which is equivalent to field evaluation for a given source distribution, is characterized by O(N2) complexity (N being the number of unknowns). To that end, a multilevel non‐uniform grid (MLNG) algorithm for 3‐D fast field evaluation has been proposed, developed, and tested on representative examples of elongated, quasi‐planar, and full 3‐D scatterers. The algorithm relies on hierarchical domain decomposition, field evaluation on highly sparse non‐uniform grids, and multilevel field aggregation through phase‐compensated interpolations. Computational complexity and memory requirements of O(N<th>log10<th>N) have been achieved by the MLNG without affecting the convergence of the iterative solver. Complexity of the MLNG is similar to that of the multilevel fast multipole algorithm [S. Ko and W. C. Chew, J. Acoust. Soc. Am. 103, 721–734 (1998)]. The MLNG approach is inherently geometrically adaptive, provides seamless transition from the high frequency to quasi‐static regime, and is quite easy to implement.