Enriched Constant Elements in the Boundary Element Method for Solving 2D Acoustic Problems at Higher Frequencies

The boundary element method (BEM) is a popular method for solving acoustic wave propagation problems, especially those in exterior domains, owing to its ease in handling radiation conditions at infinity. However, BEM models must meet the requirement of 6–10 elements per wavelength, using the conventional constant, linear, or quadratic elements. Therefore, a large storage size of memory and long solution time are often needed in solving higher-frequency problems. In this work, we propose two new types of enriched elements based on conventional constant boundary elements to improve the computational efficiency of the 2D acoustic BEM. The first one uses a plane wave expansion, which can be used to model scattering problems. The second one uses a special plane wave expansion, which can be used to model radiation problems. Five examples are investigated to show the advantages of the enriched elements. Compared with the conventional constant elements, the new enriched elements can deliver results with the same accuracy and in less computational time. This improvement in the computational efficiency is more evident at higher frequencies (with the nondimensional wave numbers exceeding 100). The paper concludes with the potential of our proposed enriched elements and plans for their further improvement.