An enriched finite element method with interpolation cover functions for acoustic analysis in high frequencies

Abstract

At present, the conventional finite element method (FEM) still has some defects for solving acoustic problems governed by the Helmholtz equation. Owing to the numerical dispersion error, the standard FEM always fails to provide sufficiently satisfactory results in high frequency range. To cure this drawback, an enriched finite element method (E-FEM) with interpolation cover functions is presented to deal with 2D and 3D acoustic problems in this work. In the present E-FEM, the nodal interpolation functions from the standard FEM are enriched by the additional interpolation cover functions over patches of elements to improve the performance (such as convergence rate and computation accuracy) of the standard FEM and the original mesh (such as the conventional triangular and tetrahedral mesh) in the standard FEM can still be used. In addition, the high gradient components of the considered field variable can be captured and the inter-element gradient jumps can be smoothed out by the used interpolation cover functions, so the present E-FEM is able to provide a smoother and more accurate acoustic field for acoustic analyses. Several numerical examples demonstrate that higher computational efficiency and accuracy can be obtained for analyzing acoustic problems compared to the conventional FEM. Moreover, the E-FEM can effectively suppress the dispersion error at high frequencies, so it can make an effective prediction for practical engineering problems.