A New Test Function for Acoustic Computations with Meshless Methods

The meshless local Petrov-Galerkin (MLPG) and the local boundary integral equation (LBIE) methods has been introduced approximately three decades ago. These methods are based on writing the local weak form of the governing equation and performing subsequent numerical integration and interpolations in the local subdomains. A key step is the choice of the test function in the local weak form, which has historically led to several different formulations regarding the final form of the local integrals. Considering the application of the methods to acoustics, four different test functions have been employed so far in the literature; all of these approaches resulted in formulations which contain domain integrals. In this paper, we present a new test function to be used in meshless methods, which yields a simple form of the local integral equation without domain integrals and provides significant improvement in terms of the computational time and CPU requirements. The efficiency and the accuracy of the new method are presented and compared with the previous methods.