Compactly supported radial basis functions for the acoustic 3D eigenanalysis using the particular integral method

This paper discusses the efficiency of several Compactly Supported Radial Basis Functions (CSRBFs) for the eigenanalysis of 3D acoustic cavities using the Particular Integral Method. Starting with the two most popular CSRBF families due to Wendland and Wu, a third family proposed by Buhmann is suggested. Results on rectangular parallelepiped highlight the benefit of CSRBFs compared to the classical conical function, especially when dealing with cavities discretized by few elements. On the other hand, when the mesh is refined, numerical difficulties arise and particular attention should be paid to the order of the employed CSRBF. Indeed, and while the conical function is likely to be the most robust function, high-order CSRBFs should be avoided. However, the proposed Buhmann's functions appear to bring significant improvements on eigenanalysis when compared to their Wendland and Wu counterparts.