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The Helmholtz problem is hard to solve in heterogeneous media, in particular, when the wave number is real and large. The problem is neither coercive nor Hermitian symmetric. This article concerns the V -cycle multigrid (MG) method for high-frequency solutions of the Helmholtz problem. Since we need to choose at least 10-12 grid points per wavelength for stability, the coarse grid problem is still large. To solve the coarse grid problem efficiently, a nonoverlapping domain decomposition methoddoi:10.1137/s1064827501385426 fatcat:dx3jzxtpezeshnwwi4opf2ijo4