中文摘要：

特征基函数的构造是特征基函数法的关键步骤之一，传统方法在构造特征基函数时，需要在每个子域设置足够多的入射波激励，生成的特征基函数个数较多，奇异值分解时间较长。为了加快特征基函数的构造，本文提出了一种改进的特征基函数法。该方法充分考虑每个子域之间的耦合作用，求出每个子域的次要特征基函数，从而降低入射波激励的个数，大大减少了特征基函数的个数；并且结合自适应交叉近似算法加速阻抗矩阵元素的计算，提高了次要特征基函数求解和缩减矩阵构建过程中的矩阵矢量相乘的速度。数值结果证明了本文方法的精确性和高效性。

英文摘要：

Constructing characteristic basis functions （CBFs） is a key step of characteristic basis function method （CBFM）. But it is required to set adequate plane wave excitations in each sub-block, which leads to the increased number of characteristic basis functions and the longer time consumed in singular value decomposition of traditional method. In order to accelerate the construction of CBFs, an improved CBFM is presented, which fully considers the mutual coupling effects among sub-blocks and then the secondary level characteristic basis function （SCBF） is obtained, therefore the number of plane wave excitations is reduced greatly, and so is the number of characteristic basis functions. The adaptive cross approximation algorithm is also used to accelerate the matrix-vector multiplication procedure of generating SCBF and constructing the reduced matrix. Numerical results demonstrate that the proposed method is accurate and efficient.