By William L. Briggs
ISBN-10: 0898714621
ISBN-13: 9780898714623
A Multigrid instructional is concise, enticing, and obviously written. Steve McCormick is the single man i do know which may pull off educating in spandex. simply ensure you sit down within the again row.
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Additional resources for A Multigrid Tutorial
Example text
C) Demonstrate that one V-cycle based on red-black Gauss-Seidel and full weighting is a direct (exact) solver for the one-dimensional model problem. 8. FMG cost. The difference in cost between FMG and a single V-cycle is the cost of all but the last V-cycle on £lh in the FMG scheme. Estimate the cost of these extra V-cycles. , n/2. Assume also that i/o = 1. Chapter 4 Implementation The preceding chapter was devoted to the development of several multigrid schemes. We now turn to the practical issues of writing multigrid programs and determining whether they work.
If 1 k < -, its components may be written as Notice that superscripts have been used to indicate the grids on which the vectors are defined. 1: Wave with wavenumber k = 4 on h (n = 12 points) projected onto 2h (n = 6 points). The coarse grid "sees" a wave that is more oscillatory on the coarse grid than on the fine grid. mode on ; this fact is easier to understand by noting that there are half as many modes on as there are on . The important consequence of this fact is that in passing from the fine grid to the coarse grid, a mode becomes more oscillatory.
At this point, the 2-norm of the error is about 1% of its original value. This experiment demonstrates that relaxation, when done on two grids and applied to both the original and the residual equation, can be very powerful. The two-grid correction scheme, as outlined above, leaves one looming procedural question: what is the best way to solve the coarse-grid problem A2he2h = r2/l? The answer may be apparent, particularly to those who think recursively. The coarse-grid problem is not much different from the original problem.
A Multigrid Tutorial by William L. Briggs
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