SUMMARYThe variational indirect boundary element method is widely used in many acoustical problems such as simulation of scattering and radiation phenomena. Although it has many advantageous features in dealing with those problems, it su ers from the singularity problem when the double surface integral is done over the same element. In this paper, a straightforward technique for computing the singularity 1=R over triangular element is presented. It is based on a generalized polar co-ordinates transformation to transform the triangular master element into a square one. The singularity factor is taken as weight function. Consequently, a single straightforward implementation without any special treatment of singularity is possible for meshes involving both quadrilateral and triangular elements of higher order. The e ciency of the proposed method is demonstrated for some numerical examples.
In this paper, FD formulations in cylindrical coordinates are used to model the field radiated, by a circular source, in fluid and solid media. The stability of the used schemes is controlled by a proper choice of time and space steps. Absorbing boundary conditions are introduced to satisfy the assumption of a propagation in a half space medium. In order to minimize the CPU time, calculations are limited for regions disturbed by the propagating ultrasonic pulse then the calculus zone is incremented. Some numerical results are presented to illustrate the effect of the medium nature, source vibration profiles and eventually the presence of targets in the acoustic field. A spatio-temporal description of the diffraction phenomena is given. The radiated field is interpreted in terms of plane and edge waves. For solid media, this interpretation allows the determination of the arrival times which are compared with those numerically predicted. Numerical results corresponding to fluid media are compared to those obtained by the Impulse Response Method. The good agreement obtained justifies the choice of the FDM for the modeling of the wave propagation problems.
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