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The finite-element boundary element method has been successfully used to provide proper truncation for numerical computation in an unbounded region. The information of the exterior environment can be incorporated whenever the corresponding Green's function is available. In this paper, we extend the method by computing Green's functions numerically so that general exterior environments can also be incorporated into the boundary element computation. Once the numerical Green's function is computed for a given environmental configuration, it can be reused for other instances of electromagnetic devices. This method is especially beneficial if a small portion of geometry needs to be repeatedly changed.