A new local boundary integral equation method for meshless acoustic computations

The local boundary integral equation (LBIE) method has been introduced approximately three-decades ago, and has been successfully used in engineering problems such as elasticity, acoustics and electrodynamics. The method is based on writing the local weak form of the governing equation. If an appropriate form of the Green’s function can be found considering the governing equation in subdomains, the local integral equation may have a convenient form, e.g. without domain integrals or the flux term on the subdomain boundaries. Considering the application of the methods to acoustic problems, four different test functions have been employed so far in the literature. All of the resulting formulations contain domain integrals. In this paper, we present a new form of Green’s function to be used in LBIE method for acoustic calculations, which yields a simple form of the local integral equation without domain integrals. This feature provides significant improvement in terms of the computational time (CPU) requirements. The efficiency and the accuracy of the new method are presented and compared with a Finite Element Method.