MATLAB Implementation of the Boundary Element Method for Acoustic Analysis

The Boundary Element Method (BEM) is a numerical technique that calculates physical fields using discrete nodes distributed along boundaries. In acoustic analysis, BEM is commonly employed for sound field simulation, which involves computing the distribution of sound waves in various environments. Sound field simulation serves as a predictive computational approach for modeling how sound waves propagate through different spaces. Sound pressure error calculation provides a quantitative assessment of simulation accuracy by comparing differences between computational results and actual measurements. Key implementation aspects in MATLAB include: - Discretizing boundary surfaces using triangular or quadrilateral elements - Formulating boundary integral equations for Helmholtz equation governing acoustic waves - Implementing numerical integration schemes (e.g., Gaussian quadrature) for singular and regular integrals - Constructing system matrices through collocation or Galerkin methods - Solving linear systems using direct solvers (backslash operator) or iterative methods (GMRES) for large-scale problems - Validating results through error norms comparing simulated and measured sound pressure values - Visualizing acoustic field distributions using contour plots and 3D surface representations The MATLAB implementation typically involves functions for mesh generation, matrix assembly, equation solving, and result validation, providing a comprehensive framework for acoustic boundary element analysis.