By William L. Briggs
A Multigrid educational is concise, attractive, and obviously written. Steve McCormick is the single man i do know that may pull off instructing in spandex. simply ensure you sit down within the again row.
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Extra resources for A Multigrid Tutorial
On and transfer it to . We also need to know how to relax on and what initial guess should be used. Moreover, how do we transfer the error estimate from back to ? These questions suggest that we need mechanisms for transferring information between the grids. We now turn to this important consideration. In our discussion of intergrid transfers, we consider only the case in which the coarse grid has twice the grid spacing of the next finest grid. This is a nearly universal practice, because there is usually no advantage in using grid spacings with ratios other than 2.
How is the mode with wavenumber k = represented on the grid? How is the mode with wavelength = represented on the grid? Make sketches for these two examples. 13. Optimal Jacobi. Show that when the weighted Jacobi method is used with (w — |, the smoothing factor is . Show that if u is chosen to damp the smooth modes effectively, then the oscillatory modes are actually amplified. 14. Gauss—Seidel eigenvalues and eigenvectors. (a) Show that the eigenvalue problem for the Gauss-Seidel iteration matrix, RGw — Aw, may be expressed in the form Uw = (D — L) w, where U, L, D are defined in the text.
For problems in two or more dimensions, the requirement drops to less than | of thefine-gridproblem along (Exercise 3). Thus, the storage costs of multigrid algorithms decrease relatively as the dimension of the problem increases. 1: Illustration of the course of a four-level (n = 16) V-cycle showing changes in the data arrays. The v and f arrays hold the solution vectors and rightside vectors, respectively, in the four grids. We may use similar reasoning to estimate the computational cost of multigrid methods.
A Multigrid Tutorial by William L. Briggs