Multigrid with Inexact Minimal Residual Smoothing Acceleration
نویسنده
چکیده
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 by about 40% for two dimensional problems and frequently achieve even faster convergence. Numerical experiments are employed to compare the performance of the exact and the inexact minimal residual smoothing schemes.
منابع مشابه
Multi-level minimal residual smoothing: a family of general purpose multigrid acceleration techniques
We employ multi-level minimal residual smoothing (MRS) as a pre-optimization technique to accelerate standard multigrid convergence. The MRS method is used to improve the current multigrid iterate by smoothing its corresponding residual before the latter is projected to the coarse grid. We develop di erent schemes for implementing MRS technique on the nest grid and on the coarse grids, and seve...
متن کاملAcceleration 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. ...
متن کاملTwo-grid analysis of minimal residual smoothing as a multigrid acceleration technique
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 ...
متن کاملAccelerated Multigrid High Accuracy Solution of theConvection - Di usion Equation with High Reynolds Number
A fourth-order compact nite diierence scheme is employed with the multigrid algorithm to obtain highly accurate numerical solution of the convection-diiusion equation with very high Reynolds number and variable coeecients. The multigrid solution process is accelerated by a minimal residual smoothing (MRS) technique. Numerical experiments are employed to show that the proposed multigrid solver i...
متن کاملAccelerated Multigrid High Accuracy Solution of the Convection-diiusion Equation with High Reynolds Number
A fourth-order compact nite diierence scheme is employed with the multigrid algorithm to obtain highly accurate numerical solution of the convection-diiusion equation with very high Reynolds number and variable coeecients. The multigrid solution process is accelerated by a minimal residual smoothing (MRS) technique. Numerical experiments are employed to show that the proposed multigrid solver i...
متن کامل