Finite Element–Boundary Element Acoustic Backscattering with Model Reduction of Surface Pressure Based on Coherent Clusters

Computing backscattering of harmonic acoustic waves from underwater elastic targets of arbitrary shape is a problem of considerable practical significance. The finite element method is commonly applied to the discretization of the target; on the other hand, the boundary element method naturally incorporates the radiation boundary condition at infinity. The coupled model tends to be expensive, primarily due to the need to manipulate large, dense, and complex matrices and to repeatedly solve systems of complex linear algebraic equations of significant size for each frequency of interest. In this article, we develop a model reduction transformation based on the notion of coherence applied to the surface pressures, which considerably reduces the size of the systems to be solved. We found that the proposed model reduction approach delivers acceptably accurate results at a fraction of the cost of the full model. A typical speedup of an order of magnitude was realized in our numerical experiments. Our approach enables backscattering computations with considerably larger models than have been feasible to date.