A Comparison between Dual Reciprocity and Direct Interpolation Techniques for Solving the Helmholtz Problem by Frequency Scanning

Resumo

The identification of the modal content of a dynamical system through the excitation frequency
scanning procedure is a very common procedure, especially with regard to experimental models. In terms of
numerical simulation, this technique is also very accessible and computationally inexpensive. In the case of the
Boundary Element Method (BEM), this procedure is much simpler than the direct solution of the associated
eigenvalue problem, if the fundamental solution is frequency-dependent since the problem becomes nonlinear. In
order to simplify the solution of these problems with the BEM, which are stationary acoustics problems
governed by the Helmholtz equation, techniques were developed that use simpler fundamental solutions. Among
these are the well-known dual reciprocity technique (DRBEM) and the more recent direct interpolation
technique (DIBEM). Both are characterized by employing radial basis functions and thus avoiding domain
integrations generated by the reactive term of the governing equation; however, Dual Reciprocity interpolates
only the primal variable of the problem, while the Direct Interpolation technique approximates the entire kernel
of the domain integral. Although they allow the direct solution of the eigenvalue problem, this article compares
the two techniques mentioned to solve the problem of stationary acoustics, through scanning of imposed
frequencies. The stationary data was obtained in a chosen frequency range. Error curves are obtained by
comparing numerical solutions and available analytical solutions for a more accurate assessment.