三維矢量散射分析中奇異積分的準(zhǔn)確計(jì)算方法
THE ACCURATE INTEGRATION METHOD OF SINGULARITY INTEGRATION FOR THREE DIMENSIONAL VECTOR FIELD SCATTERING
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摘要: 在用積分方程和矩量法(MM)或快速多極子法(FMM)分析三維矢量散射時(shí),都要對(duì)有奇異性的被積函數(shù)進(jìn)行積分。如果直接使用高斯積分,則準(zhǔn)確性很低。為了得到準(zhǔn)確的積分結(jié)果,本文在分析了高斯積分原理的基礎(chǔ)上提出了積分區(qū)域分割法。此方法將積分區(qū)域劃分為一個(gè)包含奇異點(diǎn)的部分和若干個(gè)無(wú)奇異點(diǎn)的部分。對(duì)無(wú)奇異點(diǎn)的部分可直接用高斯積分求解,而對(duì)包含奇異點(diǎn)的部分,則可通過(guò)簡(jiǎn)化被積函數(shù),變量代換和加減同階奇異項(xiàng)等方法獲得它的解析表達(dá)式。本文將這種方法用到電場(chǎng)積分方程(EFIE)的矩量法中,以角反射器和導(dǎo)電球目標(biāo)散射特性(RCS)為例,其計(jì)算的結(jié)果與文獻(xiàn)非常吻合。
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關(guān)鍵詞:
- 高斯積分; 奇異性; 積分區(qū)域分割法
Abstract: When three dimensional vector scattering is analyzed by integral equation and the moment method(MM)or the fast multipole method(FMM)，the singular integrand will be done，If it is calculated by Gaussian integration directly,the accuracy will be very poor.In order to get an accurate result，this paper provides a method of integral domain division,which divides the integral domain into several parts with one of them containing the singularity.In the singular part,an analytic result can be derived by simplifying the integral function,replacing the variables,of adding and subtracing a sinlar term．The other can be calculated by Gaussion integration directly.Numerical results for RCS of a corner-reflector antenna and a conducting sphere calculated by this method are in reasonable agereement with that in the references． -
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