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

## Palavras-chave:

Boundary Element Method, Dual Reciprocity, Direct Interpolation## 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.