A novel high‐order collocation indirect boundary element method based on the Leis formulation for three‐dimensional high frequency exterior acoustic problems

Abstract

AbstractHigh‐order finite element method (FEM) has recently achieved significant success in solving acoustic problems and has proved to be accurate, robust, and capable of reducing the pollution effect. Inspired by the high‐order FEM, this study presents a novel high‐order collocation indirect BEM for solving three‐dimensional high‐frequency exterior acoustic problems. Due to the difficulty of evaluating hypersingular integrals on curved surface elements with complex density functions, the high‐order BEM scheme for acoustic problems has long been a challenging task, especially for relatively large‐scale problems. In the developed scheme, the Leis formulation is used to overcome the well‐known nonuniqueness problem in the indirect BEM, and an auxiliary integral equation method is presented and employed to regularize the hypersingular integrals in this formulation. The derived regularized boundary integral formulation is mathematically simple and amenable to the elements of arbitrary shape and arbitrary variable interpolation order, and leads to a simple, efficient, and robust algorithm for the calculation of all integrals. Several benchmark examples are investigated to verify the performance of the proposed method. Results demonstrate that the present method is very effective in stimulating the far‐field solution with large wavenumber.