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A Block Forward Backward (BFB) method is described for the computation of electromagnetic fields scattered from a collection of inhomogeneous bodies. The electric field volume integral equation is used to formulate the problem. It is discretised using the method of moments and a discrete FFT is used to accelerate the matrix vector multiplications at the heart of the BFB method. Numerical results confirm that the convergence rate achieved can be greatly in excess of that obtained using Krylov methods.