电磁散射研究中的自适应修正特征基函数法

Adaptively Modified Characteristic Basis Function Method for Electromagnetic Scattering Study

该文提出了一种新的特征基函数法——自适应修正特征基函数法(Adaptively Modified Characteristic Basis Function Method,AMCBFM)。首先在分块子域上构建初次基函数,并计算出基函数的系数以及各块的初次电流;而后用块间互阻抗、各块的初次电流以及初次基函数系数的模来构造反映块间耦合的二次基函数,计算出其系数以及更为精确的电流,高次基函数的求解依此类推,应用一种新的精度判断方法方便地控制电流误差以停止计算更高次的基函数。讨论了不同模型时,不同特征基函数法的精度收敛性能,AMCBFM在基函数阶数较低时收敛性能优于已有的方法。还分析了在尽可能提高计算速度时分块数目与未知数个数的关系。数值结果表明,AMCBFM具有有效降低计算矩阵的尺寸,精度高,计算速度快,误差易控制等优点。

In this paper, an Adaptively Modified Characteristic Basis Function Method （AMCBFM） based on partitioning object geometry into blocks is proposed. Firstly, the primary CBFs arising from the self-interaction within the self-block are generated, then the primary current vector is elicited; subsequently, the second CBFs which account for the mutual coupling effects from the other distinct domains expect the own ones by using the inter-impedances, primary current vectors and the modulus of the primary CBFs coefficients, is gotten. And a more accurate current vector is obtained. The higher CBFs can be also derived with the same way. The difference of the currents＇ convergence speeds between the new CBFM and conventional CBFMs under diverse models via a new convenient method of controlling the result precision is discussed, and the results show that the new CBFM is better than those of conventional ones. Finally, the relationship between the block number and the unknowns under the condition of improving calculating speed is analyzed. The numerical results indicate that the new method has a series of merits： reducing the size of the matrix equation into a small level, the satisfying precision, high calculating speed and simple error control condition.