Download A Multigrid Tutorial by William L. Briggs PDF

Download A Multigrid Tutorial by William L. Briggs PDF

By William L. Briggs

A Multigrid educational is concise, attractive, and obviously written. Steve McCormick is the one man i do know that could pull off educating in spandex. simply ensure you sit down within the again row.

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6(b) shows the schedule of grids for = 2 and the resulting W-cycle. We refer to a V-cycle with v1 relaxation sweeps before the correction step and v2 relaxation sweeps after the correction step as a V(v 1 , v2)-cycle, with a similar notation for W-cycles. We originally stated that two ideas would lead to multigrid. So far we have developed only the correction scheme. The nested iteration idea has yet to be explored. Recall that nested iteration uses coarse grids to obtain improved initial guesses for fine-grid problems.

We now use these few basic schemes and develop them into far more powerful methods. 11: Gauss-Seidel iteration matrix applied to the model problem with n = 64 points. The initial guesses consist of (a) the eigenvectors of the iteration matrix RG with wavenumbers 1 k 63 and (b) the eigenvectors of A with wavenumbers I k 63. The figure shows the number of iterations required to reduce the norm of the initial error by a factor of 100 for each initial guess. A Multigrid Tutorial 27 Exercises 1. Residual vs.

We may have obtained some improvement by using the coarse grids, but the final iteration will stall if smooth components still remain. We return to these questions and find answers that will allow us to use nested iteration in a very powerful way. A second strategy incorporates the idea of using the residual equation to relax on the error. It can be represented by the following procedure: • Relax on Au = f on h to obtain an approximation vh. • Compute the residual r = f — Avh. Relax on the residual equation Ae = r on an approximation to the error e2h.

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