Nested fast adaptive cross approximation algorithm for solving electromagnetic scattering problems

In this paper, 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 Nested Cross Approximation (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.This work was supported in part by the National Nature Science Foundation of China under Grant 61871219, Grant 61771238, and Grant 61501227; in part by the Post-Graduate Research and Practice Innovation Program of Jiangsu Province under Grant KYCX18_0289; in part by the China Scholarship Council under Grant 201906830042; in part by the Spanish Ministerio de Ciencia e Innovacion (MICINN) under Project TEC2016-78028-C3-1-P, Project PID 2019-107885GB-C31, Project TEC2017-83343-C4-2-R, and Project MDM2016-0600; and in part by the Catalan Research Group 2017 SGR 219.Peer ReviewedPostprint (author's final draft