Fast solution of electromagnetic integral equations using adaptive wavelet packet transform

The adaptive wavelet packet transform is applied to sparsify the moment matrices for the fast solution of electromagnetic integral equations. In the algorithm, a cost function is employed to adaptively select the optimal wavelet packet expansion/testing functions to achieve the maximum sparsity possible in the resulting transformed system. The search for the best wavelet packet basis and the moment matrix transformation are implemented by repeated two-channel filtering of the original moment matrix with a pair of quadrature filters. It is found that the sparsified matrix has above-threshold elements that grow only as O(N^1.4) for typical scatterers. Consequently the operations to solve the transformed moment equation using the conjugate gradient method scales as O(N^1.4). The additional computational cost for carrying out the adaptive wavelet packet transform is evaluated and discussed