Broadband Electromagnetic Scattering In The Frequency Domain And Efficient Algorithm

The wide band electromagnetic scattering is very important in many fields such as modern radar target recognizing, microwave imaging and microwave remote sensing. However most traditional wide band methods are not valid when the object is complex in structure or electrically large. In order to meet the practical engineering requirement, the multilevel fast multipole algorithm (MLFMA) and the higher order vector basis function, which is based on modified Legendre polynomials and good for the rapid frequency sweep, are first combined to calculate the electromagnetic scattering at frequency samples. Then an improved interpolation method based on the normalized induced current is used to share the above calculated information to obtain the scattering at other frequencies. In this way the wide band electromagnetic analysis from the scatter with complex structure and large electrical size is performed accurately and efficiently in the frequency domain.There are several related techniques to be presented, such as the geometrical modeling, the orthogonalization of the higher order basis functions and the skill to deal with the singular integral met in the computation of the impedance matrix, before the higher order basis functions are used in MLFMA. Then the effect of several basic parameters on the memory cost, accuracy and efficiency is discussed, and the referenced principle is given. Because the number of unknowns is greatly reduced when the higher order basis fuctions are used, much less memory and CPU time are needed when the higher order MLFMA is used to calculate the electromagnetic scattering from the object with complex structure and large electrical size, compared with the low order MLFMA.When the higher order MLFMA is used to solve the wide band electromagnetic scattering problem, only one invariant mesh system, usually got at the lowest frequency, is required for all different frequency samples at which the scattering should be calculated, and only the order of the basis function has to be adjusted with frequency change. Therefore this method requires much less geometrical modeling work and less unknowns to be solved at each frequency sample than traditional wide-band methods, so the memory cost and computational complexity are both decreased. The interpolation method for the rapid frequency sweep, which is based on the normalized induced current at the Gauss integral points located in the basis domain instead of at the center of the basis domain, is not only more accurate but also valid in the higher order method. Moreover, it does not require the same number of unknowns at different frequency samples, so it is easy to be combined with the higher order MLFMA to solve the wide band scattering problem efficiently and accurately.The typical numerical examples in this paper have shown that the frequency domain method presented here, based on the higher order MLFMA and the interpolation of the normalized induced current, is more universal, more efficient and more available for wide band scattering analysis compared with other wide band methods.