三维目标电磁散射矢量有限元/边界元法的公式研究

A Study of the Formulations of Hybrid Vector FEM/BEM for EM Scattering from 3-D Objects

研究应用于三维目标电磁散射分析的矢量有限元/边界元混合方法不同公式.分析表明,混合公式系统矩阵的条件数随边界元采用不同公式有很大差异,从而导致混合公式的稳定性有很大不同.并讨论了混合方法中边界元部分的单一检验基函数方法和组合检验基函数方法.认为组合检验基函数方法仍可被视为单一检验基函数方法;通过比较边界元部分使用单一检验基函数法和组合检验基函数法时所得计算结果,纠正了只有使用组合检验基函数,有限元/边界元混合方法才能得到精确结果的结论.综合考虑计算结果可靠性、精度及对内部谐振的免疫力等因素,给出了所推荐使用的有限元/边界元混合方法公式.

We study the different formulations of the hybrid vector FEM/BEM （Finite Element Method/Boundary Element Method） for 3-D scattering. It is shown that the condition number of matrices from different hybrid formulations varies greatly with different BEM formulations used, and therefore, the stability of the hybrid formulations varies correspondingly. Issues of combined testing function method and single testing function method for BEM are also discussed. We show that the combined testing function method can be viewed as the single testing function method. And the accuracy of the results obtained by the two methods is compared, which rectified the conclusion that accurate results can be obtained by the hybrid method only when the combined testing function method is employed. Based on the reliability, accuracy, and ability to immune to the corruption of interior resonance, the formulation of hybrid vector FEM/ BEM for 3-D scattering is recommended.