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

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.