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Multigrid methods are well suited to large massively parallel computer architectures because they are mathematically optimal and display excellent parallelization properties. Since current architecture trends are favoring regular compute patterns to achieve high performance, the ability to express structure has become much more important. The hypre software library provides high-performance multigrid preconditioners and solvers through conceptual interfaces, including a semi-structured interface that describes matrices primarily in terms of stencils and logically structured grids. This paper presents a new semi-structured algebraic multigrid (SSAMG) method built on this interface. The numerical convergence and performance of a CPU implementation of this method are evaluated for a set of semi-structured problems. SSAMG achieves significantly better setup times than hypre's unstructured AMG solvers and comparable convergence. In addition, the new method is capable of solving more complex problems than hypre's structured solvers.