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The paper addresses the handling of frequency-dependent, local admittance boundary conditions in acoustic transient finite/infinite-element models. The proposed approach avoids the evaluation of a convolution integral along the related boundary. Based on a similar technique developed in an aeroacoustic/finite difference context, the spatially local boundary condition is rewritten in a discrete form that involves normal accelerations and pressure time derivatives at the current time step and few steps before. The incorporation of such a discrete (in time) boundary condition in a finite/infinite-element context is addressed. The infinite-element scheme selected for that purpose relies on the conjugated Astley-Leis formulation. Implementation aspects cover the handling of frequency-dependent boundary conditions along both finite- and infinite-element edges. Numerical examples (waveguide, single source in a half-space bounded by an impedance plane, diffraction by an acoustically treated screen) are presented in order to demonstrate the efficiency of the proposed approach.

Many acoustic problems (especially in environmental acoustics) involve half-space domains bounded by a plane subjected to normal admittance boundary conditions. In the "low" frequency domain, the numerical treatment of such problems usually relies on boundary element methods based on a particular Green's function suited for the half-(admittance) plane. In the present paper, an alternative hybrid finite/infinite element scheme is proposed. The method relies on a direct treatment of nonhomogeneous boundary conditions along infinite element edges (or faces). The procedure is validated through comparisons with an available reference solution.

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