Download A Multigrid Tutorial by William L. Briggs PDF

By William L. Briggs

ISBN-10: 0898714621

ISBN-13: 9780898714623

A Multigrid educational is concise, enticing, and obviously written. Steve McCormick is the one man i do know that may pull off instructing in spandex. simply ensure you take a seat within the again row.

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Extra info for A Multigrid Tutorial

Example text

In general, a V-cycle -d beginning from costs of a full V-cycle. Adding these costs gives us FMG computation cost An FMG cycle costs 8 WUs for a one-dimensional problem, about WUs for d = 2, and WU for d = 3 (Exercise 5). As expected, a single FMG cycle costs more than a single V-cycle, although the discrepancy is less for higher-dimensional problems. We really need to know how many V-cycles and FMG cycles are needed to obtain satisfactory results. This begs the fundamental question: how well do these multigrid cycling schemes work?

2) that stationary linear iterations can be written in the form Subtracting this equation from the exact solution u, the error at the next step is We see that changes in the error are made with spatially local corrections expressed through the residual. If the residual is small relative to the error itself, then changes in the error will be correspondingly small. At least for the model problems we have posed, smooth error modes have relatively small residuals (Exercise 19), so the error decreases slowly.

First reproduce the experiments shown in Fig. 3. Then experiment with initial guesses with different wavenumbers. Describe how each method performs as the wavenumbers increase and approach n. Chapter 3 Elements of Multigrid Through analysis and experimentation, we have examined some of the basic iterative methods. Our discoveries have formed the beginnings of what we might call a spectral (or Fourier mode) picture of relaxation schemes. As we proceed, more essential details of this picture will become clear.

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