Analysis of Minimal Residual Smoothing in Multigrid
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Acceleration and stabilization properties of minimal residual smoothing technique in multigrid
We analyze the standard multigrid method accelerated by a minimal residual smoothing (MRS) technique. We show that MRS can accelerate the convergence of the slow residual components, thus accelerates the overall multigrid convergence. We prove that, under certain hypotheses, MRS stabilizes the divergence of certain slow residual components and thus stabilizes the divergent multigrid iteration. ...
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We introduce some inexact versions of the minimal residual smoothing (IMRS) technique to accelerate the standard multigrid convergence. These are modiied versions of the minimal residual smoothing (MRS) technique introduced in an earlier paper 26]. The IMRS acceleration schemes minimize the residual norm of the multigrid iterate in a subspace and reduce the cost of the standard MRS acceleration...
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We analyze the two-level method accelerated by a minimal residual smoothing (MRS) technique. The two-grid analysis is suucient for our purpose because our MRS acceleration scheme is only applied on the nest level of the multigrid method. We prove that the MRS acceleration scheme is a semi-iterative method with respect to the underlying two-level iteration and that the MRS accelerated two-level ...
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