In order to accelerate the speed of matrix-vector product (MVP) in iteration process for adaptive integral method (AIM), a virtual grids technique (VGT) with the multi-dimensional fast Fourier transform (FFT) is proposed. By adding some uniform virtual grids outside the original region, the indexes of nonzeros in the projection matrix are modified so as to eliminate the padding and unpadding procedures in MVP. The advantages of this method are that first it will not occupy any extra memory, and second it makes the Green's function vector compressed from (2Nx - 1)(2Ny - 1)(2Nz - 1) to 8(Nx - 1)(Ny - 1)(Nz - 1) because of its symmetrical block-Toeplitz property. Numerical results show that per iteration time could be reduced more than 30% by applying this method in comparison with the conventional AIM, without losing accuracy. In addition, the peak memory consumption could also be reduced because the intermediate vectors are eliminated.
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