快速提升小波变换在介质体散射中的运用

Application of fast lifting wavelet transform to dielectric scattering problems

推导一种用于求解介质体散射问题的面积分方程,它克服了内谐振现象,且同体积分方程相比,获得了更小的阻抗矩阵维数。一种新的基于提升法的类小波变换预处理算子的使用,降低了矩阵向量积的计算复杂度和求逆过程中的迭代次数。数值结果表明,与传统方法相比,提升法消减了预处理矩阵的多余内存,并且节省了约1倍的计算时间。

A surface integral equation is derived for solving dielectric scattering problems. It avoids the internal resonance phenomenon, and smaller dimensions of the impedance matrix are obtained by comparison with the volume integral equation. In order to reduce the computation complexity of the matrix-vector product and the iterative times in the process of matrix inversing, a new wavelet-like preconditioning operator based on the lifting scheme is used. Numerical results suggest that compared with the traditional method, the lifting scheme cuts down the auxiliary memory for preconditioning matrices and saves about half compution time.