ANÁLISE DE DESEMPENHO DE ALGUMAS FUNÇÕES DE BASE RADIAL COM A TÉCNICA DE INTERPOLAÇÃO DIRETA PARA CALCULAR FREQUÊNCIAS NATURAIS EM PROBLEMAS ACÚSTICOS TRIDIMENSIONAIS

Resumo

Direct Interpolation Boundary Element Method (DIBEM) has been an effective alternative to
other techniques aimed at transforms domain integrals in boundary integrals since it solves problems
modeled by non-adjoint differential operators. The DIBEM was successfully applied to two-dimensional
problems involving the solution of Poisson, Helmholtz, and Diffusion-advection equations. The reason
for its better performance is based, above all, on the fact that the approximation is given by on the use
of radial functions whose mathematical model is more similar to an interpolation procedure, compared
to other techniques. Intended to further improve the knowledge about the particularities of DIBEM, in
this work, an extension of the technique to the three-dimensional eigenvalue problems was done,

focusing on the performance analysis of the various classic radial basis functions, widely used in two-
dimensional problems. Some radial functions have already been used satisfactorily in the solution of

three-dimensional problems, but in this work, the tests are performed with a broader spectrum of radial
functions. To evaluate the accuracy of the results, the natural frequencies are calculated numerically and
comparison with the available analytical solutions.