Evaluation of acoustic Green's function in rectangular rooms with general surface impedance walls

2026-02-10

AI Summary

This study addresses the challenge of efficiently computing the acoustic Green’s function in rectangular rooms with non-rigid boundaries characterized by sound-absorbing surface impedances—a task that existing methods struggle to accomplish with both accuracy and computational efficiency. To overcome this limitation, the authors propose a semi-analytical approach that integrates high-order asymptotic expansions with modal superposition, thereby extending the classical modal expansion method to general impedance boundary conditions. A rigorous theoretical foundation is established, including proofs of orthogonality and completeness for the associated spectral basis. The resulting formulation achieves high accuracy while significantly improving computational efficiency, with negligible errors even at high truncation orders, making it suitable as a benchmark solution for numerical simulations. Numerical experiments confirm the method’s reliability and broad applicability across diverse acoustic scenarios.

Technology Category

• Machine Learning: Efficient ML / Green AI
• Natural Language Processing: Language Grounding & Multi-modal NLP
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

Acoustic room modes and the Green's function mode expansion are well-known for rectangular rooms with perfectly reflecting walls. 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 validated through numerical tests. With a sufficiently large truncation order, the resulting error becomes negligible, 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.

Problem

• acoustic Green's function
• rectangular rooms
• general surface impedance
• room acoustics
• boundary conditions

Innovation

• Green's function
• rectangular rooms
• general surface impedance
• semi-analytical method
• asymptotic expansion