3D Multilevel Non-Uniform Grid Algorithm for Fast Field Evaluation

The analysis of large scattering problems is often performed using iterative method-of-moments (MoM) solvers. The main computational bottleneck of such iterative solvers stems from the need to perform at each iteration at least one matrix-vector product, which is equivalent to field evaluation for a given source distribution. The O(N
²
) complexity and memory needs of direct matrix-vector multiplication (N being the number of unknowns), underscores the need for fast field evaluation techniques. The multilevel fast multipole algorithm (MLFMA) achieves an O(NlogN) complexity for dynamic frequency domain problems. Also, the recently introduced non-uniform grid (NG) algorithm promises to achieve a similar asymptotic complexity and storage requirements while allowing analysis time-domain problems as well as virtually seamless transition from dynamic to quasi-static regime. In comparison with the MLFMA, the implementation of the NG is straightforward. This paper presents a 3D dynamic scalar field evaluation performed at O(NlogN) operations using a multilevel NG (MLNG) algorithm. The scalar case allows us to explore the main features of the MLNG while somewhat simplifying the formulation