Abstract:

A boundary-integral equation (BIE) method is described for computing the acoustic field scattered by a 3-D object with a smooth, optionally penetrable, boundary in a layered fluid--solid medium. The medium is assumed to be horizontally homogeneous, with the extreme layers consisting of homogeneous rigid or penetrable half-spaces. The incident field is excited by a monofrequent point or line source, and the the Green's function of the layered medium is computed by an adaptive transform integral technique. The BIE is solved by a point-collocation technique using high-order B splines (BSP) and high-order numerical integration. The discretized equations are solved by an iterative method, enhanced by preconditioning with the LU factors of a related linear system for spline interpolation or spline smoothing on the scatterer surface. Numerical examples are given at frequencies of a few kHz, representative, e.g., for a seabed-penetrating parametric transducer. A benchmark example is included, in which the field from a scatterer with super-ellipsoidal shape in a homogeneous medium is computed with the BSP method, with a standard BEM technique with quadratic elements, and with the null-field (NFL) method. The BSP method is shown to be highly efficient with performance gains growing as frequency increases and/or accuracy requirements are tightened.