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# The Characteristic Basis Function Method: A New Technique for Fast Solution of Radar Scattering Problems

Raj Mittra1, V.V.S. Prakash1
EE Dept., PSU, University Park, PA, U.S.A 16802.

Computer Modeling in Engineering & Sciences 2004, 5(5), 435-442. https://doi.org/10.3970/cmes.2004.005.435

### Abstract

In this paper, we introduce a novel approach for the efficient solution of electromagnetic scattering problems from objects that can be represented in terms of facets. The approach is based on the use of the Characteristic Basis Functions (CBFs), which are high-level basis functions of special types, and whose domains are not bound by the conventional Rao, Wilton and Glisson (RWG) discretization using triangular patches that are typically$\lambda$/10 to$\lambda$/20 in size. In contrast, the CBFs are defined over much larger-size domains, even tens of wavelengths in size, with no limit placed on the dimensions of the facets. The use of these basis functions leads to relatively small-size matrices, typically orders of magnitude smaller than the conventional ones generated by the RWG bases; and yet, the reduced matrices are sparse and well-conditioned in nature, which is typically not the case when conventional entire domain basis functions are used instead. A novel technique for the construction of CBFs, which is based on the Windowed Plane Wave Spectrum (WPWS) approach that totally bypasses the RWG discretization, associated matrix generation, or its solution, is presented in the paper. Some representative examples that illustrate the accuracy of the CBF approach are included, and the numerical efficiency of the CBF approach over the conventional integral equation formulation and matrix solution, including the Fast Multipole Method (FMM), is demonstrated for a class of problems whose geometries can be represented in terms of facets.

### Keywords

Characteristic basis functions, Method of Moments, Electromagnetic Scattering, Radar Cross Section (RCS).

Mittra, R., Prakash, V. (2004). The Characteristic Basis Function Method: A New Technique for Fast Solution of Radar Scattering Problems. CMES-Computer Modeling in Engineering & Sciences, 5(5), 435–442.

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