By William L. Briggs
A Multigrid educational is concise, enticing, and obviously written. Steve McCormick is the single man i do know that could pull off instructing in spandex. simply ensure you take a seat within the again row.
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Extra resources for A Multigrid Tutorial
Clearly, we have achieved another reduction in the error by moving to the coarse grid; the norm of the error is now 26% of the initial error norm. This improvement occurs because the smooth error components, inherited from the fine grid, appear oscillatory on the coarse grid and are quickly removed. The error after three coarse-grid relaxation sweeps is shown in the bottom left figure. The norm of the error is now about 8% of its initial value. The coarse-grid approximation to the error is now used to correct the fine-grid approximation.
The experience of many practitioners suggests that such programs should be highly modular. This allows them to evolve from simple relaxation programs and makes them much easier to check and debug. Also, the various components of the program (for example, relaxation, interpolation, and restriction subroutines) can be replaced individually. Choosing a manageable data structure for a multigrid program is essential. Modern programming languages are replete with devices that make data management easy.
Because the error is smooth, interpolation should work very well and the correction of the fine-grid solution should be effective. Numerical example. A numerical example will be helpful. Consider the weighted Jacobi method with w =| applied to the one-dimensional model problem Au = 0 on a grid with n = 64 points. We use an initial guess, consisting of the k = 16 and k = 40 modes. The following two-grid correction scheme is used: 38 Chapter 3 • Relax three times on Ahuh = 0 on fth with initial guess vh.
A Multigrid Tutorial by William L. Briggs