Formulação do método dos elementos de contorno para resolver problemas de Helmholtz usando funções de interpolação de base radial em regularização

Abstract

The objective of this work is to propose a new formulation for the Boundary Element Method named here with MECID-2 (Direct Interpolation Boundary Elements Method without Regularization), which uses the radial basis functions to interpolate domain integrals, but which has a different solution strategy of the model presented in the formulation already successfully validated named as MECID Regularized. Five problems governed by the Helmholtz Equation for the validation of this formulation were solved in which the results of the MECID-2 will be compared with the MECID Regularized, taking as parameter the analytical solution of the problem, if any, or the approximate solution by the Finite Element Method (FEM). Another important parameter evaluated in the results is the mesh refinement importance on the boundaries and the number of internal points inserted in the domain. Performance curves are generated by calculating the mean percentage error for each mesh, demonstrating the convergence and precision of each method.