Coupling finite elements and Helmholtz integral equations for solving radiation and scattering problems

Abstract

Radiation and scattering problems encountered in fluid‐structure interaction can be solved through a total finite‐element formulation, or through a mixed formulation. In the first case, both the interacting body and the acoustic medium are modeled using finite elements. This approach leads to a linear equation system of large size when, for example, the overall dimensions of the transducer being analyzed are large compared with the wavelength of the radiated or scattered waves. In the second case, the body is modeled with finite elements and the fluid domain is implicitly represented through an integral equation. This completely eliminates the need for modeling the fluid, drastically reducing the size of the system to be solved. In this paper attention is focused on one combination for the mixed formulation, namely the coupling of the finite‐element code ATILA [J. N. Decarpigny et al., J. Acoust. Soc. Am. 78, 1499–1507 (1985)] and the Combined Helmholtz Integral Equation Formulation code CHIEF [H. A. Schenck, J. Acoust. Soc. Am. 44, 41 (1968)]. Results of test cases for both axisymmetrical and 3‐D structures are presented. [Work partially supported by DRET.]