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Interior three-dimensional acoustic modeling and modal analysis using wavelet-based finite-element approach
Zexi Sun1, Guoyong Jin1, Tiangui Ye1
1College of Power and Energy Engineering, Harbin Engineering University, Harbin 150001, People's Republic of China.
The Journal of the Acoustical Society of America
|August 20, 2024
Summary
The wavelet finite-element method (WFEM) offers accurate 2D and 3D acoustic modeling by reducing errors and computational load. This novel approach provides stable and efficient solutions for acoustic pressure and modal analysis.
Area of Science:
- Computational physics
- Acoustics
- Numerical analysis
Background:
- Acoustic modeling and modal analysis are crucial for understanding sound propagation and vibration phenomena.
- Traditional methods like the standard finite-element method (FEM) can suffer from high computational costs and dispersion errors, especially in high-frequency ranges.
Purpose of the Study:
- To introduce and evaluate the wavelet finite-element method (WFEM) for 2D and 3D acoustic modeling and modal analysis.
- To demonstrate the advantages of WFEM over standard FEM in terms of accuracy, stability, and computational efficiency.
Main Methods:
- The study employs the wavelet finite-element method (WFEM) using B-spline wavelets for parameterizing and analyzing acoustic domains governed by the Helmholtz equation.
- Multi-resolution analysis is utilized to construct elements with varying numbers of nodes.
- Numerical examples include 2D acoustic problems (tube) and 3D acoustic problems (cubic and L-shaped rooms).
Main Results:
- WFEM significantly reduces interpolation errors and computational burden compared to standard FEM.
- The method shows stability, being insensitive to internal mesh size variations.
- WFEM effectively controls pollution (dispersion) error in high-frequency ranges and reduces interpolation errors in low-frequency domains.
Conclusions:
- The wavelet finite-element method (WFEM) presents a stable and efficient alternative for 2D and 3D acoustic modeling and modal analysis.
- WFEM offers superior accuracy and reduced computational cost, particularly in high-frequency acoustic problems.
- The B-spline wavelet elements demonstrate effectiveness in error control and numerical stability.
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