Analysis of two-dimensional acoustic radiation problems using the finite element with cover functions

Abstract

Due to the pollution errors in acoustic analysis, the requirement of very refined meshes at high wavenumbers limits the practical application of the conventional finite element method (FEM). In this work, the three-node linear triangular element with linear interpolation cover functions (FEwC) is applied to solve acoustic radiation problems in two dimensions. The present FEwC has considerable generality since the polynomial interpolation cover functions can be easily implemented without changing the mesh topology. As the original linear approximation space is enriched by the cover functions, the FEwC can significantly alleviate the pollution errors and increase the convergence rate of the original low-order element in acoustic computation. We show the proper imposition of the Dirichlet boundary conditions in acoustic problems and illustrate an effective iterative algorithm to resolve the system equations with a singular coefficient matrix. The Dirichlet-to-Neumann mapping technique is used to truncate the infinite problem domain into a bounded computational domain for the exterior problems and the Sommerfeld radiation condition then can be satisfied at infinity. Several numerical experiments demonstrate that the present scheme is a promising numerical tool for acoustic radiation problems.