提出高效计算矩形房间声学格林函数的新方法，支持吸音墙场景。
Evaluation of acoustic Green's function in rectangular rooms with general surface impedance walls
- 基于特征函数展开，引入一阶渐近修正项处理软壁边界。
- 数值测试显示截断阶数增大时误差快速下降，可作仿真基准。
- 适用于需要高精度声场建模的建筑声学与音频仿真研究者。
对于完美反射壁面的矩形房间，声学模式具有闭合表达式，可通过特征函数展开直接计算格林函数。对于接近刚性边界的近似情况也存在一阶近似方法；然而，现有解析方法无法处理更一般的边界条件，例如当墙壁吸声显著时。本文通过引入额外的一阶渐近项，扩展了先前研究，以涵盖软壁边界。此外，提出一种半解析、高效且可靠的格林函数计算方法，并通过数值实验验证。结果表明，当截断阶数足够大时，误差迅速减小，该方法适合作为数值模拟的基准。同时讨论了谱基的正交性与完备性问题，为所提方法的普遍有效性提供了理论框架。
原文摘要 · Abstract (English)
Acoustic room modes admit closed-form expressions for rectangular rooms with perfectly reflecting walls, from which the Green's function can be computed directly through the eigenfunction expansion. First-order approximations also exist for nearly rigid boundaries; however, current analytical methods fail to accommodate more general boundary conditions, e.g., when wall absorption is significant. In this work, we present a comprehensive analysis that extends previous studies by including additional first-order asymptotics that account for soft-wall boundaries. In addition, we introduce a semi-analytical, efficient, and reliable method for computing the Green's function in rectangular rooms, which is described and verified through numerical tests. The resulting error decreases rapidly for sufficiently large truncation order, making the method suitable as a benchmark for numerical simulations. Additional aspects regarding the spectral basis orthogonality and completeness are also addressed, providing a general framework for the validity of the proposed approach.
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