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A large body with cracks and cavities is a typical structure widely existing in realistic targets. In this paper, a newly developed fast and accurate finite-element boundary-integral (FA-FE-BI) method is applied to compute scattering by this kind of scatterer. A thorough analysis on this FA-FE-BI numerical technique is presented, clearly demonstrating that this technique has computational complexity O(N log N) and memory requirement O(N) (N is the total number of surface unknowns). An inward-looking approach is employed as a preconditioner to speed up the rate of convergence of iterative solvers for this structure. Under these techniques, a powerful code is developed for this kind of scatterer whose accuracy, efficiency, and capability is well confirmed by various numerical results.