On a class of predefined wavelet packet bases for efficient representation of electromagnetic integral equations

A general wavelet packet tree is proposed to design predefined wavelet packet (PWP) bases for the efficient representation of electrodynamic integral equations. The wavelet packet decomposition tree is constructed by zooming in along the spectral oscillatory frequency of the free-space Green´s function. Numerical results show that for typical two dimensional (2-D) scatterers the number of above-threshold elements in the PWP-based moment matrix is on the order of O(N^1.3) and tends to grow at a rate of O(N·log N) for large-scale problems. Therefore, the complexity of solving the moment equations can be reduced accordingly. Furthermore, it is shown that the elements of the moment matrix based on the PWP bases can be computed directly at approximately the same complexity as the fast wavelet transform approach. Consequently, with on-the-fly thresholding of the matrix elements, the O(N²) memory bottleneck in the formation of the PWP-based moment matrix can be circumvented