Using the method of fundamental solutions in conjunction with the degenerate kernel in cylindrical acoustic problems

Abstract

This paper proposes applications of the method of fundamental solutions (MFS) to exterior acoustic radiation and scattering problems. By using the two‐point function of fundamental solutions, the coefficients of influence matrices are easily determined. It is found that this method also pordoces irregular frequencies as well as the boundary element method does. The position of the irregular frequency depends on the source point location. To avoid this numerical instability, the mixed‐layer potential method is employed to deal with the problem. Based on the circulant properties and degenerate kernels, an analytical scheme in the discrete system of a cylinder is achieved to demonstrate the existence of irregular frequencies. Three numerical examples of uniform radiation, nonuniform radiation and scattering problems of a circular cylinder are examined and are compared with the results by using direct BEM.

Key words:

• method of fundamental solutions
• two‐point function
• irregular frequency
• circulant
• degenerate kernels