A nonuniform cartesian grid algorithm for fast field evaluation on elongated domains

A fast algorithm for field evaluation of time harmonic fields of two-dimensional source constellation with elongated geometry is presented. The algorithm relies on sampling the phase- and amplitude - compensated fields produced by finite size radiating sources. Such fields behave as essentially bandlimited functions, which can be sampled over sparse nonuniform left- and right - Cartesian grids. These grids are employed for both outgoing and incoming fields. Henceforth, the algorithm uses hierarchical subdivision of the complete scatterer into a binary tree of sub-domains. The required fields are gradually aggregated via a multilevel process passing up and down the tree. The algorithm attains linear computational complexity.