New PDF release: A Multigrid Tutorial

By William L. Briggs

ISBN-10: 0898714621

ISBN-13: 9780898714623

A Multigrid instructional 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 take a seat within the again row.

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Write a short program that performs weighted Jacobi (with variable w), Gauss-Seidel, and red-black Gauss-Seidel for the one-dimensional model problem. 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.

Middle right: The fine-grid error after one sweep of weighted Jacobi on the coarse-grid problem. Bottom left: The fine-grid error after three sweeps of weighted Jacobi on the coarsegrid problem. Bottom right: The fine-grid error after the coarse-grid correction is followed by three weighted Jacobi sweeps on the fine grid. 40 Chapter 3 To facilitate the description of this procedure, some economy of notation is desirable. The same notation is used for the computer implementation of the resulting algorithm.

8. Eigenvalues of the model problem. Compute the eigenvalues of the matrix A of the one-dimensional model problem. (Hint: Write out a typical equation of the system Aw = Aw with wo = wn — 0. ) How many distinct eigenvalues are there? Compute I, A2, n _2, n_i when n = 32. 9. Eigenvectors of the model problem. Using the results of the previous problem, find the eigenvectors of the one-dimensional model problem matrix A. 10. Jacobi eigenvalues and eigenvectors. Find the eigenvalues of the weighted Jacobi iteration matrix when it is applied to the one-dimensional model problem matrix A.

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A Multigrid Tutorial by William L. Briggs

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