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This paper demonstrates a novel frequency domain analysis (FDA) to evaluate the scattering behavior of a waveguide mode at arbitrary scattering geometries by a time harmonic simulation based on the finite element method (FEM). To this end, we add an injection-damping mechanism (IDM) to avoid interference at the acoustic input port. The IDM can be easily constructed by a numerical operation. Our approach offers improved time consumption and calculation power necessary over the established method in the time domain. After checking the validity of the proposed method, we discuss the importance of considering wave scattering phenomena in film bulk acoustic wave resonator (FBAR) devices by applying the proposed method to two simplified models of an FBAR device.