Analytical numerical matching (ANM) is an analysis method that separates problems into high-resolution local and low-resolution global solutions. A method is presented to treat discontinuities, such as structural attachments, within the ANM local solution by high-resolution solid modeling using finite element analysis. The global problem, which is subjected only to smooth distributed forces, can then be solved by lower order methods, such as shell theory. Both the local and global solutions are more easily solved than the original problem, and the resulting composite solution is very computationally efficient. The approach is a novel way to embed local highly refined solutions within a broader problem. The method is illustrated by several sample problems including a vibrating beam with constraints, and acoustic scattering from a fluid loaded shell.