Smoothed aggregation adaptive spectral elementbased algebraic multigrid
Abstract
SAAMGE provides parallel methods for building multilevel hierarchies and solvers that can be used for elliptic equations with highly heterogeneous coefficients. Additionally, hierarchy adaptation is implemented allowing solving multiple problems with close coefficients without rebuilding the hierarchy.
 Publication Date:
 Research Org.:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1232073
 Report Number(s):
 SAAMGE V1.0; 003358WKSTN00
LLNLCODE667435
 DOE Contract Number:
 AC5207NA27344
 Resource Type:
 Software
 Software Revision:
 00
 Software Package Number:
 003358
 Software Package Contents:
 Media Directory; Software Abstract; Media includes Source Code; / 1 CDROM
 Software CPU:
 WKSTN
 Open Source:
 No
 Source Code Available:
 Yes
 Country of Publication:
 United States
Citation Formats
. Smoothed aggregation adaptive spectral elementbased algebraic multigrid.
Computer software. Vers. 00. USDOE. 20 Jan. 2015.
Web.
. (2015, January 20). Smoothed aggregation adaptive spectral elementbased algebraic multigrid (Version 00) [Computer software].
. Smoothed aggregation adaptive spectral elementbased algebraic multigrid.
Computer software. Version 00. January 20, 2015.
@misc{osti_1232073,
title = {Smoothed aggregation adaptive spectral elementbased algebraic multigrid, Version 00},
author = {},
abstractNote = {SAAMGE provides parallel methods for building multilevel hierarchies and solvers that can be used for elliptic equations with highly heterogeneous coefficients. Additionally, hierarchy adaptation is implemented allowing solving multiple problems with close coefficients without rebuilding the hierarchy.},
doi = {},
year = 2015,
month = 1,
note =
}

Consider the linear system Ax = b, where A is a large, sparse, real, symmetric, and positive definite matrix and b is a known vector. Solving this system for unknown vector x using a smoothed aggregation multigrid (SA) algorithm requires a characterization of the algebraically smooth error, meaning error that is poorly attenuated by the algorithm's relaxation process. For relaxation processes that are typically used in practice, algebraically smooth error corresponds to the nearnullspace of A. Therefore, having a good approximation to a minimal eigenvector is useful to characterize the algebraically smooth error when forming a linear SA solver. Thismore »


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We present an improved analysis of the smoothed aggregation (SA) alge braic multigrid method (AMG) extending the original proof in [SA] and its modification in [Va08]. The new result imposes fewer restrictions on the aggregates that makes it eas ier to verify in practice. Also, we extend a result in [Van] that allows us to use aggressive coarsening at all levels due to the special properties of the polynomial smoother, that we use and analyze, and thus provide a multilevel convergence estimate with bounds independent of the coarsening ratio. 
Adaptive Algebraic Multigrid for Finite Element Elliptic Equations with Random Coefficients
This thesis presents a twogrid algorithm based on Smoothed Aggregation Spectral Element Agglomeration Algebraic Multigrid (SA{rho}AMGe) combined with adaptation. The aim is to build an efficient solver for the linear systems arising from discretization of secondorder elliptic partial differential equations (PDEs) with stochastic coefficients. Examples include PDEs that model subsurface flow with random permeability field. During a Markov Chain Monte Carlo (MCMC) simulation process, that draws PDE coefficient samples from a certain distribution, the PDE coefficients change, hence the resulting linear systems to be solved change. At every such step the system (discretized PDE) needs to be solved and themore »
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