Analytical method for radiation and scattering problems in noncanonical domains

Abstract

One of the tendencies in modern acoustics is to use analytical solutions of the Helmholtz equation to present the sound field around radiators and scatterers of noncanonical shapes. The T matrix and internal source density methods are examples. In the present paper a method called a partial domain method is discussed. An essential point of the method is the notion of general solution of the boundary-value problem for the Helmholtz equation. The boundaries of the objects under consideration are parts of coordinate surfaces in separable systems. However, surfaces may be either coordinate surfaces of different types (as in the case of a finite cylinder) or coordinate surfaces of different systems (as in the case of a cylinder with spherical lids). Theoretical problems of both the method and numerical implementation of one are discussed. Consideration of such aspects of the method as singularity of the field near corner points, nonuniqueness of the wave functions, and extension of boundary conditions gives a basis to make the computation process more effective. The numerical results for some cases of radiation by finite cylinder and cylinder with hemispherical lids are used to illustrate the method.