Analysis of a meshless boundary integral equation method for acoustic problems

Abstract

In this paper, a meshless boundary integral equation method, the Galerkin boundary element-free method, is proposed to solve acoustic problems. The existence, uniqueness, and optimal asymptotic error estimate of the solution are analyzed theoretically. In the method, the system matrix is symmetric and positive definite, boundary conditions are satisfied directly and exactly, approximation and discretization only use boundary nodes, and computational formulas are suitable for both interior and exterior acoustic problems. Numerical results verify the effectiveness of the method and the theoretical analysis.