Such imposed SPD constraints may complicate the construction of the preconditioner, e. Multigrid methods can be generalized in many different ways. They can be applied naturally in a time-stepping solution of parabolic partial differential equations , or they can be applied directly to time-dependent partial differential equations. Another set of multiresolution methods is based upon wavelets. These wavelet methods can be combined with multigrid methods. Adaptive multigrid exhibits adaptive mesh refinement , that is, it adjusts the grid as the computation proceeds, in a manner dependent upon the computation itself.
Practically important extensions of multigrid methods include techniques where no partial differential equation nor geometrical problem background is used to construct the multilevel hierarchy.
In classical AMG, the levels of the hierarchy are simply subsets of unknowns without any geometric interpretation. More generally, coarse grid unknowns can be particular linear combinations of fine grid unknowns. Thus, AMG methods become black-box solvers for certain classes of sparse matrices. AMG is regarded as advantageous mainly where geometric multigrid is too difficult to apply,  but is often used simply because it avoids the coding necessary for a true multigrid implementation.
While classical AMG was developed first, a related algebraic method is known as smoothed aggregation SA. Multigrid methods have also been adopted for the solution of initial value problems. The well known Parareal parallel-in-time integration method can also be reformulated as a two-level multigrid in time.
Multigrid method - Wikipedia
From Wikipedia, the free encyclopedia. Practical Fourier analysis for multigrid methods. Multigrid: Basics, Parallelism and Adaptivity Free download. Book file PDF easily for everyone and every device. This Book have some digital formats such us :paperbook, ebook, kindle, epub, fb2 and another formats. Lemke, M. Melson, T. Manteuffel, and S. McCormick, eds.
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