A self-regularized Scheme for solving Helmholtz problems using the boundary element direct integration technique with radial basis functions

摘要

This work presents a self-regularized scheme of the Direct Interpolation Boundary Element Technique with Radial Basis Functions (DIBEM) for the solution of Helmholtz problems. Said scheme avoids the singularity produced by the fundamental solution due to the coincidence between source points and the interpolation basis points, eliminating the necessity for regularization procedure. The mathematical model is based on the proposal of a new auxiliary function consisting of the classic Laplace's fundamental solution and a function associated with the Galerkin Tensor for potential problems. The performance of the new proposal is evaluated by applying it to five two-dimensional response problems, which consists of scanning different excitation frequencies in a chosen interval. Overall, resonance points were detected with better precision and presented smaller errors than the regularized DIBEM scheme.