Two novel aggregation-based algebraic multigrid methods
نویسندگان
چکیده
منابع مشابه
Algebraic analysis of aggregation-based multigrid
Convergence analysis of two-grids methods based on coarsening by (unsmoothed) aggregation is presented. For diagonally dominant symmetric (M-)matrices, it is shown that the analysis can be conducted locally; that is, the convergence factor can be bounded above by computing separately for each aggregate a parameter which in some sense measures its quality. The procedure is purely algebraic and c...
متن کاملAn aggregation-based algebraic multigrid method
An algebraic multigrid method is presented to solve large systems of linear equations. The coarsening is obtained by aggregation of the unknowns. The aggregation scheme uses two passes of a pairwise matching algorithm applied to the matrix graph, resulting in most cases in a decrease of the number of variables by a factor slightly less than four. The matching algorithm favors the strongest nega...
متن کاملGeneralizing Smoothed Aggregation-based Algebraic Multigrid
Smoothed aggregation-based (SA) algebraic multigrid (AMG) is a popular and effective solver for systems of linear equations that arise from discretized partial differential equations. While SA has been effective over a broad class of problems, it has several limitations and weaknesses that this thesis is intended to address. This includes the development of a more robust strength-of-connection ...
متن کاملAlgebraic Multigrid Methods
This paper is to give an overview of AMG methods for solving large scale systems of equations such as those from the discretization of partial differential equations. AMG is often understood as the acronym of “Algebraic Multi-Grid”, but it can also be understood as “Abstract Muti-Grid”. Indeed, as it demonstrates in this paper, how and why an algebraic multigrid method can be better understood ...
متن کاملAggregation-Based Algebraic Multigrid for Convection-Diffusion Equations
We consider the iterative solution of large sparse linear systems arising from the upwind finite difference discretization of convection-diffusion equations. The system matrix is then an M-matrix with nonnegative row sum, and, further, when the convective flow has zero divergence, the column sum is also nonnegative, possibly up to a small correction term. We investigate aggregationbased algebra...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Miskolc Mathematical Notes
سال: 2013
ISSN: 1787-2405,1787-2413
DOI: 10.18514/mmn.2013.344