Performance Comparison between the Multiple Reciprocity and Direct Interpolation Boundary Element Method in Problems Governed by the Helmholtz Equation

Resumo

In this work, response problems applied and governed by the Helmholtz equation are analyzed. The
formulation Multiple Reciprocity Boundary Element Method (MRBEM) can be seen as an extension of the
formulation with Dual Reciprocity (DRBEM) because the original problem as a whole is modeled by a sequence
of fundamental solutions of a higher-order, while the formulation of the DRBEM uses a sequence of radial-based
functions to approximate the kernel the domain integrals. Although both techniques apply the reciprocity
theorem, the idea behind each method is essentially different. For the validation of this formulation, problems
governed by the Helmholtz equation are solved, in which the MRBEM results were compared to a new
formulation of the Boundary Element Method (BEM), denoted in this work as DIBEM-2 (Direct Interpolation
Boundary Element Method without Regularization). DIBEM-2 makes use of radial basis functions to
approximate domain integrals. Performance curves are generated by calculating the average percentage error for
each mesh, demonstrating the convergence and precision of each method.