Domain Decomposition Method Using Integral Equations and Adaptive Cross Approximation IE-ACA-DDM for Studying Antenna Radiation and Wave Scattering From Large Metallic Platforms

• Published in: IEEE transactions on antennas and propagation Vol. 63; no. 12; pp. 5698 - 5708
• Main Authors: Maurin, Julien, Barka, Andre, Gobin, Vincent, Juvigny, Xavier
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-12-2015; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: adaptive cross approximation; antenna radiation patterns; Antennas; Approximation algorithms; Approximation methods; Calculus; Domain decomposition; Integral equations; Matrix decomposition; radar cross section; Surface impedance; Wires; integral equations; radar cross section (RCS); antenna radiation patterns; domain decomposition; Adaptive cross approximation
• ISSN: 0018-926X; 1558-2221
• DOI: 10.1109/TAP.2015.2481931

In this paper, we present a new methodology for a nonoverlapping domain decomposition method using boundary integral equations and adaptive cross approximation in the frequency domain (IE-ACA-DDM). This paper proposes two main novelties. First, the IE-DDM condition number is improved with the development of a formulation based on electric field integral equation (EFIE) implementation over the entire subdomains and on a simplification of the magnetic field integral equation (MFIE) on the interfaces. As a consequence, the number of matrix-vector products is significantly reduced during the iterative resolution. Then, this paper proves that the ACA can be applied and efficiently implemented in IE-DDM methods. Moreover, a hierarchical LU (HLU) decomposition is proposed to accelerate the ACA solver. The IE-ACA-DDM is very suitable for the resolution of multiple excitations and to bypass the low-frequency breakdown. The flexibility, accuracy, and efficiency of IE-ACA-DDM are demonstrated by comparing with reference integral equation solutions and scaled mock-up measurements.