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with the surface integral equation method in classical electromagnetics at certain stage. Reid et al method reduces the problem to a search of the all eigenvalues of the impedance matrix. Our method reduces the problem to solving a set of matrix equation, with the same impedance matrix as in Reid et al method. Reid et al method calculates energy directly while our method calculates the force distribution directly. The complexity of both method could be reduced to O ( N log N ) at best by using fast algorithms, where N is the number of surface unknowns. The drawback of the path integral method is that we need to differentiate the total energy with respect to displacement in a certain direction to get the force. This operation changes the problem into a generalized eigenvalue problem which increases the cost and complexity. Another drawback is that the force distribution on the surface is not available from the method. On the contrary, for stress tensor approach, force distribution is required before we obtain the total force. The tradeoff is that an additional surface integral needs to be performed compared to the path integral method. 

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[3] H. B. Chan, V. A. Aksyuk, R. N. Kleiman, D. J. Bishop, and F. Capasso, Science 291, 1941 (2001). 

