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Abstract Time-harmonic acoustic waves interact with a scatterer: this interaction is calculated using linear, first-order theory. However, there are quadratic, second-order quantities that are of interest. These include the scattering cross-section and the steady radiation force; these quantities can be expressed as integrals of products of first-order quantities over a sphere. These integrals are evaluated exactly. The results are infinite series of products of the coefficients in the spherical multipole expansions of the incident and scattered fields; they do not depend on the radius of the spherical integration surface. For a specific scattering problem, the coefficients can be connected by an appropriate T -matrix. In most previous work, the spherical surface is moved to infinity so that far-field quantities can be introduced: it is shown that this process is not straightforward and it may introduce spurious difficulties. Highlights • Exact computation of scattering cross-section. • Exact computation of radiation force. • All computations done in the near field. [ABSTRACT FROM AUTHOR]

Acoustic scattering by three-dimensional obstacles is considered, using boundary integral equations, null-field equations and the T-matrix. Connections between these techniques are explored. It is shown that solving a boundary integral equation by a particular Petrov–Galerkin method leads to the same algebraic system as obtained from the null-field equations. It is also emphasised that the T-matrix can be constructed by solving boundary integral equations rather than by solving the null-field equations. [Copyright &y& Elsevier]

The development of the method of fundamental solutions (MFS) and related methods for the numerical solution of scattering and radiation problems in fluids and solids is described and reviewed. A brief review of the developments and applications in all areas of the MFS over the last five years is also given. Future possible areas of applications in fields related to scattering and radiation problems are identified. [Copyright &y& Elsevier]