(untitled) (Advances in Applied Mathematics and Mechanics, 2022)
With the rapid development of computer technology, numerical simulation has become the third scientific research tool besides theoretical analysis and experimental research. As the core of numerical simulation, constructing efficient, accurate and 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 acoustic problems. In practical application, the key issue is to construct efficient and accurate numerical methodology to calculate the large-scale and high-frequency sound field. This article focuses on the following two research areas. They are how to discretize partial differential equations into more appropriate linear equations, and how to solve linear equations more efficiently. The bottleneck problems encountered in the computational acoustics are used as the technical routes, i.e., efficient solution of dense linear system composed of ill-conditioned matrix and stable simulation of wave propagation at low sampling frequencies. The article reviews recent advances in emerging applications of the singular boundary method for computational acoustics. This collection can provide a reference for simulating other more complex wave propagation.