A fast and stable solver for acoustic scattering problems based on the nonuniform grid approach

Area of Science:

• Computational physics
• Acoustics
• Numerical methods

Background:

• Solving external acoustic scattering problems is computationally intensive.
• Traditional boundary element methods (BEM) can face convergence and efficiency challenges, especially for large-scale problems.
• Accurate modeling of high-frequency acoustic phenomena like creeping waves and diffractions remains a challenge.

Purpose of the Study:

• To develop a fast and stable boundary element method (BEM) algorithm for external acoustic scattering problems.
• To enhance computational efficiency and accuracy for complex scatterer geometries and high-frequency effects.
• To demonstrate the algorithm's capability in handling large acoustic scatterers and piecewise smooth surfaces.

Main Methods:

• Utilized the Burton-Miller integral equation for stable iterative solver convergence.
• Implemented a generalized multilevel nonuniform grid (MLNG) algorithm for rapid field integral evaluation.
• Employed MLNG for computational bottleneck removal and regularization of hyper-singular integral kernels.
• Applied low-order basis functions for integral kernel regularization.

Main Results:

• The developed BEM algorithm demonstrates fast and stable convergence for acoustic scattering problems.
• Accurate calculation of scattered fields for large, including nonconvex, acoustic scatterers with piecewise smooth surfaces.
• Successfully incorporated high-frequency effects such as creeping waves and multiple-edge diffractions.
• Achieved computational complexity close to O(N log N) for computation time and storage.

Conclusions:

• The novel BEM algorithm provides an efficient and accurate solution for external acoustic scattering.
• The MLNG approach significantly reduces computational bottlenecks and enhances stability.
• The method is suitable for analyzing complex acoustic scattering scenarios, including high-frequency phenomena.