Comparação entre as técnicas do Método dos Elementos de Contorno com Interpolação Direta e com Múltipla Reciprocidade em problemas governados pela Equação de Helmholtz

Abstract

This work deals with the application of the Boundary Element Method (BEM) to solve problems governed by the Helmholtz Equation. For this, we first use the auxiliary procedure called Direct Interpolation Self-regularized (DIBEM-2), which applies radial basis functions to solve the integral term referring to the inertia in the Helmholtz Equation. This new technique originated from the formulation Direct Interpolation (DIBEM). However, the DIBEM-2 technique establishes an auxiliary function, which consists of the fundamental solution of the Laplace problem subtracted from a function associated with the Galerkin Tensor and, in this way, ignores the execution of the regularization procedure, since it avoids the singularity produced in the fundamental solution due to the coincidence between the source points and the field points. In a second step, the BEM formulation is proposed by extending the application of Multiple Reciprocity (MRBEM) which strategically uses a sequence of fundamental higherorder solutions, collaborating to convert the domain integral term to the exact contour only using the proposed formulation. Thus, numerical experiments are implemented on twodimensional problems in order to evaluate the performance of the two proposals by solving the response problem, which corresponds to sweeping different excitation frequencies. In general, simulations are compared with analytical solutions to generate benchmark information.