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The hybrid finite-element/boundary-element (FE/BE) computational scheme is advantageous in that it satisfies boundary conditions at infinity while avoiding meshing and computations in the air regions. Of numerous hybrid schemes, one using the fundamental solution of Poisson's equation as the weighting function has been employed successfully in many fields. Analyses in electromagnetic (EM) launch usually involve strong coupling among EM, thermal, and structural equations. The hybrid method has the added benefit that it may be fashioned to incorporate the effect of structural deformations on EM fields. Here, a three-dimensional (3-D) hybrid algorithm using the fundamental solution of Poisson's equation as the weighting function is investigated and implemented in the parallel version of the code Electromechanical Analysis Program in 3D (EMAP3D). The method is validated using two examples with semianalytical solutions: a 3-D ring conductor with rectangular cross section carrying uniform current, and a quadrupole configuration with four independent, closed-ring conductors excited by imposed potential differences. The solutions obtained using the hybrid method match the semianalytical solutions within approximately 4% deviations.