A multigrid tutorial

By W. Briggs. 1987

Subfields: Numerical Methods & Scientific Computing

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Citations in the corpus

Deep Residual Learning for Image Recognition (2015, methodology): “ctors [17] is shown to be more effective than encoding original vectors. In low-level vision and computer graphics, for solving Partial Differential Equations (PDEs), the widely used Multigrid method [3] reformulates the system as subproblems at multiple scales, where each subproblem is responsible ”
Rethinking Atrous Convolution for Semantic Image Segmentation (2017, methodology): “Motivated by multigrid methods which employ a hierarchy of grids of different sizes [4, 69, 5, 57] and following [72, 16], we adopt different atrous rates within block4 to block7 in the proposed model.”
Artificial neural networks for solving ordinary and partial differential equations (1997, methodology): “For a linear differential equation, accuracy control can be obtained using the following iterative improvement procedure [ 11 ].”
Wavelets and Subband Coding (2013, methodology): “The multigrid methods used for the solution of partial differential equations [39] are an example.”
Algebraic multigrid for higher-order finite elements (2005, methodology): “We refer to [24,25] for a more indepth discussion of these details, only mentioning that we adhere the RS approach for nearly all choices in defining interpolation.”
Algorithm 866: IFISS, a Matlab toolbox for modelling incompressible flow (2007, background): “(See, for example, Briggs et al. [2000], Hackbusch [1985], or Wesseling [1992] for definitions and properties of multigrid.) There is a choice of smoothing operator: weighted Jacobi, ILU and point or line versions of Gauss-Seidel. The number of pre- and post-smoothing steps is selected by the user. ”
Optimal Model Management for Multifidelity Monte Carlo Estimation (2016, background): “…techniques have a long and successful history in computational science and engineering, e.g., multigrid for solving systems of equations [8, 25, 9], multilevel discretizations for representing functions [50, 18, 10], and multi-level Monte Carlo and multilevel stochastic collocation for…”
Survey of multifidelity methods in uncertainty propagation, inference, and optimization (2018, methodology): “chniques that fall into these three categories in Section 2. Comparison to multilevel methods. Multilevel methods have a long history in computational science and engineering, e.g., multigrid methods [28, 93, 30, 142, 204], multilevel preconditioners [27, 55], and multilevel function representations”
Preconditioning discretizations of systems of partial differential equations (2011, background): “Multigrid and domain decomposition preconditioners for elliptic problems, like I − , have been studied by many authors, consider, for example [11, 46–48] and references given there.”
Locally adapted hierarchical basis preconditioning (2006, background): “Figure 2 shows a sample set of input data values d i and weights w i , which we can think of points pulling on the final surface f i with strong springs.”
Numerical Aspects of the Application of Recursive Filters to Variational Statistical Analysis. Part II: Spatially Inhomogeneous and Anisotropic General Covariances (2003, methodology): “General discussions of such methods can be found in Brandt (1977) and an excellent introductory exposition of the method is Briggs (1987) .”