Solving Helmholtz problems with the boundary element method using direct radial basis function interpolation

In the present study, a direct interpolation technique that uses radial basis functions is applied to the boundary element method integral term, which refers to inertia, in the Helmholtz equation; consequently, free vibration frequencies and corresponding amplitudes can be determined from an eigenvalue problem solution. The proposed method, which has already been successfully applied to scalar problems governed by the Poisson equation, does not require standard domain integration procedures, which employ cell discretisation, and is more robust than the dual-reciprocity technique. Although similar to the latter in some aspects, because it uses radial basis functions and their primitives for interpolation, the proposed methodology is more general. It allows the immediate use of interpolation functions of any type, and there are no convergence or monotonicity problems as the number of basis points is increased.