Nested Fast Adaptive Cross Approximation Algorithm for Solving Electromagnetic Scattering Problems

In this article, a nested fast adaptive cross approximation (NFACA) algorithm is presented to accelerate the solution of electromagnetic scattering problems. It is based on the fast adaptive cross approximation (FACA) and the nested cross approximation (NCA). In the NFACA, the FACA is applied instead of the ACA or the Chebyshev nodes, to enhance the efficiency. It is shown to have O(N) storage and computational complexity for electrically small problems. Different from the conventional NCA or the fast NCA (FNCA), the pivot selection does not rely on a preliminary selection with Chebyshev nodes or ACA for each group. The NFACA permits the selection of the optimum pivots independently at each level to make the accuracy controllable. Numerical results of several objects are presented to demonstrate the performance of this method. Compared with the FACA and NCA in solving the electromagnetic scattering problems, the NFACA is more efficient both in computational cost and storage. Compared with the FNCA, the NFACA is both faster and more accurate.