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 instructing in spandex. simply ensure you sit down within the again row.

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For instance, what does it mean to relax on Ae = r on ? 2: Interpolation of a vector on coarse grid to fine grid h . 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.

Specifically, the wavenumber of the initial error is plotted against the number of iterations required to reduce the norm of the initial error by a factor of 100. This experiment is done for weighting factors of w = 1 and w = . With w = 1, both the high- and low-frequency components of the error are damped very slowly. Components with wavenumbers near are damped rapidly. This behavior is consistent with the eigenvalue curves of Fig. 7. We see a quite different behavior in Fig. 8(b) with w — . Recall that w = was chosen to give preferential damping to the oscillatory components.

The coarse-grid problem is not much different from the original problem. Therefore, we can apply the two-grid correction scheme to the residual equation on , which means relaxing there and then moving to 4h for the correction step. We can repeat this process on successively coarser grids until a direct solution of the residual equation is possible. 5: Coarse-grid correction for —u" = 0 on a grid with n = 64. Top left: The initial guess, (w16 + W40)/2. Top right: The error after one sweep of weighted Jacobi.

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