Results 141 to 150 of about 12,853 (184)

Energy Optimization of Algebraic Multigrid Bases

Computing, 1999
The authors propose a fast iterative method to optimize coarse basis functions in algebraic multigrid by minimizing the sum of their energies subject to the condition that linear combinations of the basis functions equal to the zero energy modes. Computational results are quite encouraging and will be applied to industrial use.
Mandel, J., Brezina, M., Vaněk, P.
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On Generalizing the Algebraic Multigrid Framework

SIAM Journal on Numerical Analysis, 2004
The authors present a theory that generalizes the algebraic multigrid (AMG) framework to address even broader of problems . This paper will provide a guidance in the development of new AMG methods able to handle difficult problems such as Maxwell's equations. Starting by introducing two new measures in applying the relaxation methods for linear systems,
Falgout, Robert D., Vassilevski, Panayot S.   +1 more
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Generalization of algebraic multiscale to algebraic multigrid

Computational Geosciences, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Silvia Ehrmann, Sebastian Gries, Marc Alexander Schweitzer   +2 more
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Algebraic spectral multigrid methods

Computer Methods in Applied Mechanics and Engineering, 1990
The solution of Helmholtz's equation on a unit square is considered. Many spectral methods lead to linear systems of equations which are much more ill-conditioned than that of a finite difference method with the same number of degrees of freedom. In this paper, a special basis of Jacobi polynomials is chosen and the resulting matrix becomes better ...
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Transition Of Algebraic Multiscale To Algebraic Multigrid

Proceedings, 2018
Summary Algebraic Multiscale (AMS) is a recent development for the construction of efficient linear solvers in certain reservoir simulations. It employs analytical upscaling ideas to coarsen the respective linear system and provides a high amount of inherent parallelism. However, it has the drawback that it can currently only be applied to problems for
S. Ehrmann, S. Gries, M.A. Schweitzer
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Algebraic multigrid (AMG): experiences and comparisons

Applied Mathematics and Computation, 1983
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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An Algebraic Interpretation of Multigrid Methods

SIAM Journal on Numerical Analysis, 1982
The main objective of this paper is to treat the correction cycle of multigrid as a Newton-like method and to analyze it together with relaxation via a natural decomposition of the grid function space. The purpose is to provide a simplified view of multigrid and motivate some general principles for algorithm design.
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Algebraic multigrid / substructuring preconditioners on triangular grids

Russian Journal of Numerical Analysis and Mathematical Modelling, 1991
Summary: A new approach to constructing algebraic multigrid preconditioners for the mesh diffusion operators suggested and studied before by one of the authors for the case of square grids is extended to include the case of triangular hierarchical grids.
Hakopian, Yu. R., Kuznetsov, Yu. A.
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Algebraic analysis of multigrid algorithms

Numerical Linear Algebra with Applications, 1999
This paper deals with the convergence rate of multilevel algorithms from an algebraic point of view. A detailed analysis of the constant in the strengthened Cauchy-Schwarz inequality between the coarse-grid space and a so-called complementary space is presented. Using generalized prewavelets, fast multilevel convergence is proved.
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Efficient Algebraic Multigrid Algorithms and Their Convergence

SIAM Journal on Scientific Computing, 2002
The authors present 8 new interpolation formulae for use in algebraic multigrid algorithms. For this aim, they separate suitably defined strongly and weakly connected unknowns and exploit Gauss-Seidel or Jacoby iteration-type ideas. In the scetch of a convergence theory, the authors refer strongly to earlier work by \textit{J. W.
Chang, Qianshun, Huang, Zhaohui
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