RBF Based on the Modified Fundamental Solutions for High-Frequency Acoustic Problems

Abstract

The conception of modified fundamental solution of the 3-D Helmholtz equation is described in this chapter. Based on the modified fundamental solution, a modified singular boundary and a dual-level method of fundamental solutions are constructed. The merits of the proposed methods are that they inherit the high efficiency and accuracy of the boundary knot method and the method of fundamental solutions, whereas the high stability of the singular boundary method is not affected. For illustration, several acoustic radiation and scattering examples are investigated. Numerical experiments show that the present radial basis function (RBF) method based on the modified fundamental solutions only needs to set about 3 degrees of freedom in one wavelength per direction to produce highly accurate solutions for three-dimensional acoustic problems. At the end of this chapter, the influence of the fictitious boundary on results is analyzed in an appendix.

Keywords: Singular boundary method, Boundary knot method, Method of fundamental solutions, Sound wave propagation.

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