The inverse source problem where an unknown source is to be identified from the knowledge of its radiated wave is studied. The focus is placed on the effect that multifrequency data has on establishing uniqueness. In particular, it is shown that data obtained from finitely many frequencies is not sufficient. On the other hand, if the frequency varies within a set with an accumulation point, then the source is determined uniquely, even in the presence of highly heterogeneous media. In addition, an algorithm for the reconstruction of the source using multi-frequency data is proposed. The algorithm, based on a subspace projection method, approximates the minimum-norm solution given the available multifrequency measurements. A few numerical examples are presented.

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We devise a new high order local absorbing boundary condition (ABC) for radiating problems and scattering of time-harmonic acoustic waves from obstacles of arbitrary shape. By introducing an artificial boundary S enclosing the scatterer, the original unbounded domain Ω is decomposed into a bounded computational domain Ω − and an exterior unbounded domain Ω + . Then, we define interface conditions at the artificial boundary S , from truncated versions of the well-known Wilcox and Karp farfield expansion representations of the exact solution in the exterior region Ω + . As a result, we obtain a new local absorbing boundary condition (ABC) for a bounded problem on Ω − , which effectively accounts for the outgoing behavior of the scattered field. Contrary to the low order absorbing conditions previously defined, the order of the error induced by this ABC can easily match the order of the numerical method in Ω − . We accomplish this by simply adding as many terms as needed to the truncated farfield expansions of Wilcox or Karp. The convergence of these expansions guarantees that the order of approximation of the new ABC can be increased arbitrarily without having to enlarge the radius of the artificial boundary. We include numerical results in two and three dimensions which demonstrate the improved accuracy and simplicity of this new formulation when compared to other absorbing boundary conditions.

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Potential flow past a porous body of arbitrary shape with constant physical permeability k0, as well as the flow in the corresponding porous medium, are analysed by means of a pair of linear Fredholm integral equations of the second kind. As an example for verification of the proposed general method, the case of a two-dimensional porous circular cylinder is worked out in detail.

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The current work sets forth a practical approach to numerically solve two-dimensional direct acoustic scattering problems from complexly shaped scatterers with severe singularities, such as corners and cusps. First, boundary conforming coordinates are generated. This generation is performed through an elliptic grid generator algorithm, including control of the coordinate lines. The grid line control solely depends on the initial distribution of grid points. Following the grid generation process, the initial boundary value problem, modelling the scattering phenomenon, is formulated in terms of the new curvilinear coordinates, and a finite-difference time domain method is implemented. The presence of the boundary singularities causes instability of the numerical method. However, by appropriately controlling the distance between grid lines in the vicinity of these singularities, stability and convergence are achieved. A semianalytical formula for the differential scattering cross-section is obtained from the discrete Fourier transform of the computed scattered pressure field. The method is successfully applied to several interesting scatterers of various shapes.