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[21]: 

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where E and H are the total field in the space and E i and H i are the incident field generated by an external source. The operators are defined as 

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where g ( r , r $^{′}$) = e ik 0 | r − r $^{$^{′}$|}$/ 4 π | r − r $^{′}$| . The total tangential electric field vanishes on the surface of the PEC object. Enforcing Eqn. (13) on the surface we obtain the electric field integral equation(EFIE): 

<img src='content_image/330212.jpg'>

By expanding the unknown current with RWG basis [12], J ( r $^{′}$) = ∑ $_{n}$a$_{n}$ J$_{n}$ ( r $^{′}$) and us- ing Galerkin’s method, the integral equation (15) could be cast into a matrix equation [ Z$_{mn}$ ][ a$_{n}$ ] = [ g$_{m}$ ], where 

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If the sources listed in Table I are used to generate the incident field, then the evaluation of g$_{m}$ involves integrals containing some super-hyper singularities. The treatment of these singularities has been discussed in detail in [22]. 

Now we would present some numerical results obtained from this method. They are compared with either analytical results or other’s calculation. First we would start with the evaluation of the Casimir force between two spheres, since they are the simplest 3D objects and the analytical expression of the Casimir energy is available in [9]. We assume that the radius of both spheres is R and their minimum distance is Z , the product of the force and 

