Hybrid finite element modelling of conformal antenna and array structures utilizing fast integral methods

Abstract

Hybrid finite element methods (FEM) which combine the finite element and boundary integral methods have been found very successful for the analysis of conformal finite and periodic arrays embedded on planar or curved platforms. A key advantage of these hybrid methods is their capability to model inhomogeneous and layered material without a need to introduce complicated Green's functions. Also, they offer full geometrical adaptability and are thus of interest in general-purpose analysis and design. For the proposed hybrid FEM, the boundary integral is only used on the aperture to enforce the radiation condition by employing the standard free space Green's function. The boundary integral truncation of the FEM volume domain, although necessary for rigor, is also the cause of substantial increase in CPU complexity. In this paper, we concentrate on fast integral methods for speeding-up the computation of these boundary integrals during the execution of the iterative solver. We consider both the adaptive integral method (AIM) and the fast multipole method (FMM) to reduce the complexity of boundary integral computation down to 𝒪(Nα) with α<1.5. CPU and memory estimates are given when the AIM and FMM accelerations are employed as compared to the standard 𝒪(N2) algorithms. In addition, several examples are included to demonstrate the practicality and application of these fast hybrid methods to planar finite and infinite arrays, frequency selective surfaces, and arrays on curved platforms. Copyright © 2000 John Wiley & Sons, Ltd.