To calculate the dynamic-stiffness matrix at the structure-medium interface of an unbounded medium for the range of frequencies of interest, the consistent infinitesimal finite-element cell method based on finite elements is developed for wave propagation. The derivation makes use of similarity and finite-element assemblage, yielding a nonlinear first-order ordinary differential equation in frequency. The asymptotic expansion for high frequency yields the boundary condition satisfying the radiation condition. In an application only the structure-medium interface is discretized resulting in a reduction of the spatial dimension by one. The boundary condition on the free surface is satisfied automatically. The consistent infinitesimal finite-element cell method is exact in the radial direction and converges to the exact solution in the finite-element sense in the circumferential directions. The extension to the diffusion equation is also discussed. Excellent accuracy results.

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