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The precorrected-FFT method is applied to the fast solution of the volume integral equation for lossy, inhomogeneous dielectric bodies. The volume of the dielectric body is discretized into tetrahedron elements and the SWG basis functions are employed to expand the unknown electric flux density. The basis functions are then projected onto a uniform grid surrounding the nonuniform mesh, enabling the FFTs to be used to speed up the matrix-vector multipliers in the iterative solution of the matrix equation. The resultant method has a computational complexity and memory requirement of O(N log N) and O(N) respectively.