volume | PIER Journals

Abstract

Electromagnetic scattering by electrically large scatterers usually requires a large number of unknowns. To reduce the matrix size, one expects to choose a small sampling rate for the unknown function. In the method of moments (MoM) scheme, this rate is about 10 unknowns per wavelength for electrically small or medium scatterers. However, this rate may not work well for electrically large scatterers with a concave surface. The concave area on the scatter is observed to be the oscillatory part in the solution domain. The oscillation property requires more samplings to eliminate the numerical noises. The multiscalets with a multiplicity of two are higher-order bases. It is shown that the multiscalets are more suitable to represent the unknown function with oscillatory characteristic. Furthermore, the testing scheme under the discrete Sobolev-type inner product allows the MoM have the derivative sampling which enhances the tracking quality of the multiscalets further. Numerical Examples of scattering by 1000 and 1024 wavelength 2D scatterers demonstrate that the use of multiscalets in the MoM can keep the same discretization size for electrically large scatterers as for electrically small scatterers without losing the accuracy of the solution. In contrast, the traditional MoM and Nyström method require the finer discretization scheme if achieving a stable solution.

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Prof. Mei Song Tong