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A Multigrid Method for the Helmholtz Equation with Optimized Coarse Grid Corrections

2014
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SIAM Journal on Scientific Computing
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We study the convergence of multigrid schemes for the Helmholtz equation, focusing in particular on the choice of the coarse scale operators. Let G_c denote the number of points per wavelength at the coarse level. If the coarse scale solutions are to approximate the true solutions, then the oscillatory nature of the solutions implies the requirement G_c > 2. However, in examples the requirement is more like G_c >= 10, in a trade-off involving also the amount of damping present and the number of

doi:10.1137/13092349x
fatcat:xxqqrzmgf5aivo5fnbv3w5rze4