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)