Analysis of three-dimensional interior acoustic fields by using the localized method of fundamental solutions

Abstract

• Applying the localized method of fundamental solutions for 3D interior acoustic fields. • The behavior of the present method for oscillating solution is first investigated. • Acoustic fields in a high-speed train and a room with complicated geometries are solved successfully. The traditional method of fundamental solutions has a full interpolation matrix, and thus its solution is computationally expensive, especially for large-scale problems with complicated domains. In this paper, we make a first attempt to apply the localized method of fundamental solutions for analysis of 3D interior acoustic fields. The present method first divides the whole computational domain into some overlapping subdomains, and then expresses physical variables as linear combinations of the fundamental solution in each subdomain. Finally, the method forms a sparse and banded system matrix by satisfying both governing equations at interior nodes and boundary conditions at boundary nodes. We provide four numerical experiments to verify the accuracy and the stability of the method. Comparisons of numerical results and computational time are also made between the present method, the method of fundamental solutions, and the COMSOL software.