Implementation of spectral basis functions in BEM/FEM/GSM Domain Decomposition Methods devoted to scattering and radiation applications

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Abstract

In this paper, we discuss several improvements of a substructuring Domain Decomposition Method (DDM) devoted to Electromagnetic computations, based on the Boundary Element Method (BEM) and the Finite Element Method (FEM). This computation procedure is applied to the analysis of antenna performance on board vehicles as well as Radar Cross Section (RCS). The benefits of the subdomain Computational Electromagnetic Method are mainly the ability to deal with collaborative studies involving several companies, and the reduction of the computation costs by one or more orders of magnitude, especially in the context of parametric studies. Furthermore, this paper proposes a Spectral Basis Function (SBF) defined on fictitious surfaces surrounding equipment, to deal with both the computation of antenna far field patterns and RCS in a multi-domain mode. By masking the complexity of the equipment (wires, thin surfaces, materials, supply network, weapons) the external domain of the vehicle can be closed so that the Combined Field Integral Equation (CFIE) can be used, which is better conditioned than the Electric Field Integral Equation (EFIE). This calculation procedure leads to a faster convergence when using iterative Multi Level Fast Multiple Algorithms (MLFMA). The accuracy and efficiency of this technique is assessed by performing the computation of the diffraction and radiation of several test-objects in a multi-domain way cross compared with reference integral equation results.

Section snippets

Domain Decomposition Methods applied to radiation and scattering of electromagnetic waves

Domain Decomposition Methods (DDMs) constitute flexible and powerful techniques for numerically solving Partial Differential Equations (PDEs) and Integral Equations (EIs). Many references are available in the literature [1], [2], [3], [4], [5], [6], [7], [8]. They can be used as a process of distributing data from a computational domain among the machines of a cluster of PCs, or for the separation of the physical domain into regions which occurs when using different and adapted solving methods,

A GSM substructuring DDM technique

The calculation of the Radar Cross Section of equipment (weapons, antennas) as well as the radiation of complex antenna systems mounted on large structures, such as ships or aircrafts, is separated into several subdomains, which will be connected at the end of the process.

Let us consider an object Ω whose boundary is denoted by ∂V. The subdomain formulation applied to 3D objects consists in splitting the geometry Ω in 2 subdomains or volumes (V0 and V1) connected together with 1 fictitious

Numerical results on test-objects

In this section, various computations are discussed with the objectives of validating the multi-domain technique with reference to Boundary Element Methods and analyzing the truncation of the spectral functions expansion on Γ. Note that the validations are carried out for higher frequencies (UHF and X band), than the VHF band investigated in [7]. For the three test-cases considered, the tangent electromagnetic fields are expanded with the Dirichlet and Neumann spectral functions on a

Conclusion

We have presented a substructuring Domain Decomposition Method (DDM) devoted to Electromagnetic computations, based on the Boundary Element Method (BEM) and the Finite Element Method (FEM). This computation procedure is applied to the analysis of antenna performance onboard vehicles as well as Radar Cross Section. Spectral Basis Functions have been used and validated for expanding the electromagnetic fields on 3D interfaces separating the subdomains. This way, by masking the equipment on the

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