A coupled FE and boundary integral equation method based on exterior domain decomposition for fluid-structure interface problems

Abstract

A coupled finite element and exterior domain decomposition-based boundary integral formulations for the solutions of two- or three-dimensional time-harmonic fluid-structure interaction problems is described in this paper. It is known that the memory limitation of computers has been one of the major obstacles for solving large scale high frequency fluid-structure interface systems using various existing nonlocal finite element and boundary integral equation coupling techniques due to the fully populated resultant matrix generated from the boundary integral equation representation. The essence of this study is to decompose, through domain decomposition of the exterior region, the original exterior problem into arbitrary subproblems with data sharing only at the interfaces. By decomposing the exterior infinite domain into an appropriate number of infinite subdomains, this method not only ensures the validity of the formulation for all frequencies but also leads to a diagonalized, blockwise-banded system of discretized equations. The size of an individual submatrix (i.e. a block) that is associated with an exterior subdomain may be decided by the user, and may be selected such that the restriction due to the memory limitation of a given computer may be accommodated. In addition, the method is suited for parallel processing since the data associated with each subdomain (impedance matrices, load vectors, etc.) may be generated in parallel, and the communication needed will be only for the interface values. Most significantly, unlike the existing coupled finite element and boundary integral equation techniques that are valid for all frequencies, our method avoids the use of both the hypersingular operator and the double integrals, therefore reducing the computational complexity. Numerical experiments have been performed for elastic cylindrical shells subjected to a plane incident wave. The results have demonstrated the accuracy of the method for wavenumbers ranging from 0 to 30, both directly on the shell and in the far field, and have confirmed that the procedure is valid for all frequencies.