Name
Abstract | ||
|---|---|---|
Algebraic-based multilevel solution methods (e.g. classical Ruge-Stuben and smoothed aggregation style algebraic multigrid) attempt to solve or precondition sparse linear systems without knowledge of an underlying geometric grid. The automatic construction of a multigrid hierarchy relies on strength-of connection information to coarsen the matrix graph and to determine sparsity patterns for the inter-grid transfer operators. Strength-of-connection as a general concept is not well understood and the first task of this paper is therefore on understanding existing strength-of-connection measures and their limitations. In particular, we present a framework to interpret and clarify existing measures through differential equations. This framework leads to a new procedure for making pointwise strength-of-connection decisions that combines knowledge of local algebraically smooth error and of the local behavior of interpolation. The new procedure effectively addresses a variety of challenges associated with strength-of-connection and when incorporated within an algebraic multigrid procedure gives rise to a robust and efficient solver. Copyright (C) 2009 John Wiley & Sons, Ltd. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1002/nla.669 | NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS |
Keywords | Field | DocType |
algebraic multigrid (AMG),smoothed aggregation (SA),algebraic coarsening | Mathematical optimization,Algebraic number,Linear system,Interpolation,Theoretical computer science,Precondition,Operator (computer programming),Solver,Multigrid method,Mathematics,Pointwise | Journal |
Volume | Issue | ISSN |
17 | 4 | 1070-5325 |
Citations | PageRank | References |
9 | 0.68 | 5 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Luke Olson | 1 | 235 | 21.93 |
| Jacob Schroder | 2 | 9 | 0.68 |
| Raymond S. Tuminaro | 3 | 145 | 15.07 |