A meshless Galerkin least-square method for the Helmholtz equation

The Helmholtz equation always suffers the so-called ‘pollution effect’, which is directly related to the dispersion for high wavenumber. The element-free Galerkin method (EFGM) has been successfully applied to acoustic problems and significantly reduced the dispersion error. Unfortunately, it is computationally expensive. In this paper, a two-dimensional (2-D) dispersion analysis is performed on the meshless Galerkin least-square (MGLS) method. This method is based on the EFGM at the domain boundary and the least-square method in the interior. Numerical examples on an L-shaped cavity demonstrate that while retaining the accuracy of the EFGM, the computational cost can be significantly reduced.