{'fraction_non_alphanumeric': 0.025441696113074206, 'fraction_numerical': 0.0014134275618374558, 'mean_word_length': 5.495412844036697, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Time-domain impedance boundary condition modeling with the discontinuous Galerkin method for room acoustics simulations.

The time-domain nodal discontinuous Galerkin (TD-DG) method is emerging as a potential wave-based method for three-dimensional (3D) room acoustics modeling, where high-order accuracy in the low frequency range, geometrical flexibility, and accurate modeling of boundary conditions are of critical importance. This paper presents a formulation of broadband time-domain impedance boundary conditions (TDIBCs) of locally-reacting surfaces in the framework of the TD-DG method. The formulation is based on the approximation of the plane-wave reflection coefficient at normal incidence in the frequency domain using a sum of template rational functions, which can be directly transformed to the time-domain. The coupling of the TDIBCs with the discontinuous Galerkin discretization is achieved through the characteristic waves of the upwind flux along the boundary, where a series of first-order auxiliary differential equations is time-integrated in a high-order way. To verify the performance of the formulation, various numerical tests of single reflection scenarios are shown to demonstrate the cost efficiency and memory-efficiency of high-order basis functions, among which a 3D application to an impedance boundary of rigidly backed glass-wool baffle for room acoustic purposes is presented.