Fast solution of electromagnetic integral equations using adaptive waveletpacket transform

The adaptive wavelet packet transform is applied to sparsify moment matrice s for the fast solution of electromagnetic integral equations, In the algor ithm, 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 packe t basis and the moment matrix transformation are implemented by the repeate d two-channel filtering of the original moment matrix with a pair of quadra ture filters. It is found that the sparsified matrix has above-threshold el ements that grow only as O(N-1.4) for typical scatterers. Consequently the operations to solve the transformed moment equation using the conjugate gra dient method scales as O(N-1.4). The additional computational cost for carr ying out the adaptive wavelet packet transform is evaluated and discussed.