Recent Advances and Emerging Applications of the Singular Boundary Method for Large-Scale and High-Frequency Computational Acoustics (Advances in Applied Mathematics and Mechanics, 2022)
With the rapid development of computer technology, numerical simulationhas become the third scientific research tool besides theoretical analysis and experimental research. As the core of numerical simulation, constructing efficient, accurateand stable numerical methods to simulate complex scientific and engineering problems has become a key issue in computational mechanics. The article outlines the application of singular boundary method to the large-scale and high-frequency acousticproblems. In practical application, the key issue is to construct efficient and accuratenumerical methodology to calculate the large-scale and high-frequency sound field.This article focuses on the following two research areas. They are how to discretizepartial differential equations into more appropriate linear equations, and how to solvelinear equations more efficiently. The bottleneck problems encountered in the computational acoustics are used as the technical routes, i.e., efficient solution of dense linearsystem composed of ill-conditioned matrix and stable simulation of wave propagationat low sampling frequencies. The article reviews recent advances in emerging applications of the singular boundary method for computational acoustics. This collectioncan provide a reference for simulating other more complex wave propagation.