Localized boundary knot method for 3D inhomogeneous acoustic problems with complicated geometry

Abstract

This paper reports the first attempt to extend a novel localized boundary knot method to the 2D and 3D acoustic problems with complicated geometry. The solution of original partial differential equation with inhomogeneous term is firstly described as a sum of a particular solution and a homogeneous one. Secondly, the Chebyshev interpolation technique is applied to the approximation of particular solution. The interpolation approach adopts the Chebyshev-Gauss-Lobatto nodes to offer the spectral convergence and high accuracy. And then the numeircal solution of homogeneous equation is obtained by applying the localized boundary knot method with non-singular general solutions. As a localized meshless method, the localized boundary knot method in conjunction with the interpolation technique is very simple mathematically, accurate numerically, and particularly feasible for large-scale computation in a complicated geometry. Numerical experiments including 2D and 3D models verify the performance of the proposed method for solving inhomogeneous Helmholtz-type equations.