Robustness analysis of direct interpolation boundary element method solving special scalar dynamic problems

Presented as a promising alternative for solving various scalar field problems, and having already demonstrated superior performance over the dual reciprocity boundary element method (DRBEM) for this mathematical model, this work aims to confirm the robustness of the direct interpolation boundary element method (DIBEM) for solving dynamic problems, such as two-dimensional acoustic wave motion. To this end, examples were chosen whose numerical solution is more challenging: situations in which the discrete system is subjected to variable excitations of higher frequencies, cases in which loads are applied to increasingly specific regions, stimulating higher modal contents, and also evaluating the response in curvilinear problems with thin geometry, in which the boundary dimensions become prominent relative to the domain involved and the generated wavelengths become shorter. The accuracy of the proposed formulation was assessed by comparison with analytical solutions and, whenever unavailable, with the finite volume method. The results demonstrate that DIBEM accurately captures the dynamic response in all cases analyzed, confirming its robustness and reliability for transient acoustic wave problems.