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This study extends the integral equation fast Fourier transform (IE-FFT) algorithm to the method of moments solution of a nonconformal volume integral equation. The algorithm relies on the interpolation of Green's function by Lagrangian polynomials on a uniform Cartesian tensor grid. Hence, the matrix-vector product in the iterative solver can be computed via the fast Fourier transform. The memory requirement and the computational complexity of the algorithm tend to stay close to O(N) and O(NlogN), respectively, where N is the number of unknowns.