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.

这项工作提出了具有径向基函数的直接插值边界元技术（DIBEM）的自正则化方案，用于解决亥姆霍兹问题。该方案避免了由于源点和内插基点之间的重合而由基本解产生的奇异性，从而消除了进行正则化过程的必要性。该数学模型基于新辅助功能的建议，该功能包括经典拉普拉斯的基本解以及与潜在问题的Galerkin张量相关的功能。通过将新建议书应用于五个二维响应问题来评估新建议书的性能，这些问题包括在选定间隔内扫描不同的激励频率。总体，