LAUSR

Summary It is well-known that the traditional finite element method (FEM) fails to provide accurate results to the Helmholtz equation with the increase of wave number due to the “pollution error” caused by numerical dispersion. In order to overcome this deficiency, a gradient-weighted finite element method (GW-FEM) that combines Shepard interpolation and linear shape functions is proposed in this work. Three-node triangular and four-node tetrahedral elements that can be generated automatically are first used to discretize the problem domain in 2D and 3D spaces, respectively. For each independent element, a compacted support domain is then formed based on the element itself and its adjacent elements sharing common edges (or faces). With the aid of Shepard interpolation, a weighted acoustic gradient field is then formulated, which will be further used to construct the discretized system equations through the generalized Galerkin weakform. Numerical examples demonstrate that the present algorithm can significantly reduces the dispersion error in computational acoustics.