2.5D singular boundary method for exterior acoustic radiation and scattering problems

In this paper, a numerical methodology based on a two-and-a-half-dimensional (2.5D) singular boundary method (SBM) to deal with acoustic radiation and scattering problems in the context of longitudinally invariant structures is proposed and studied. In the proposed 2.5D SBM, the desingularisation provided by the subtracting and adding-back technique is used to determine the origin intensity factors (OIFs). These OIFs are derived by means of the OIFs of the Laplace equation. The feasibility, validity and accuracy of the proposed method are demonstrated for three acoustic benchmark problems, in which detailed comparisons with analytical solutions, the 2.5D boundary element method (BEM) and the 2.5D method of fundamental solutions (MFS) are performed. As a novelty of the present study, it is found that the 2.5D SBM provides a higher numerical accuracy than the 2.5D linear-element BEM and lower than the 2.5D quadratic-element BEM. Although the results obtained depict that a nodal approximation of the boundary geometry leads to a significant reduction in the accuracy of the 2.5D SBM, the delivered errors are still acceptable. For complex geometries, the 2.5D SBM is found to be simpler and more robust than the 2.5D MFS, since no optimization procedure is required.Peer ReviewedPostprint (published version

A regularized approach evaluating origin intensity factor of singular boundary method for Helmholtz equation with high wavenumbers

Evaluation of the origin intensity factor of the singular boundary method for Helmholtz equation with high wavenumbers has been a difficult task for a long time. In this study, a regularized approach is provided to bypass this limitation. The core idea of the subtraction and adding-back technique is to substitute an artificially constructed general solution of the Helmholtz equation into the boundary integral equation or the hyper boundary integral equation to evaluate the non-singular expressions of the fundamental solutions at origin. The core difficulty is to derive the appropriate artificially constructed general solution. The regularized approach avoids the unstable inverse interpolation and has strict mathematical derivation process. Therefore, it is easy-to-program and free of mesh dependency. Numerical experiments show that the proposed technique can be used successfully to avoid singularity and hyper singularity difficulties encountered in the boundary element method and the singular boundary method.The work was supported by the Fundamental Research Funds for the Central Universities (Grant Nos. 2018B40714, 2016B06214, 2017B709X14), the National Science Funds of China 11572111, 11772119), the Foundation for Open Project of State Key Laboratory of Structural Analysis for Industrial Equipment (Grant No. GZ1707), the Postgraduate Research & Practice Innovation Program of Jiangsu Province (Grant No. KYCX17_0488) and the Postgraduate Scholarship Program from the China Scholarship Council (Grant No. 201706710107)