Paper Info
Title
Asynchronous Fast Adaptive Composite-Grid Methods for Elliptic Problems: Theoretical Foundations
Abstract
Accurate numerical modeling of complex physical, chemical, and biological systems requires numerical simulation capability over a large range of length scales, with the ability to capture rapidly varying phenomena localized in space and/or time. Adaptive mesh refinement (AMR) is a numerical process for dynamically introducing local fine resolution on computational grids during the solution process, in response to unresolved error in a computation. Fast adaptive composite-grid (FAC) methods are a class of algorithms that exploit the multilevel structure of AMR grids to solve elliptic problems efficiently. This paper develops a theoretical foundation for AFACx, an asynchronous FAC method. A new multilevel condition number estimate establishes that the convergence rate of the AFACx algorithm does not degrade as the number of refinement levels in the AMR hierarchy increases.
Year
DOI
Venue
2004
10.1137/S0036142902400767
SIAM J. Numerical Analysis
Keywords
Field
DocType
afacx algorithm,afac,amr hierarchy increase,afacx,fast adaptive composite-grid,asynchronous fast adaptive composite-grid,elliptic solvers,adaptive composite-grid,accurate numerical modeling,numerical simulation capability,theoretical foundations,fac,adaptive mesh refinement,asynchronous,asynchronous fac method,multilevel structure,elliptic problems,amr grid,numerical process,condition number,length scale,biological systems,numerical simulation
Asynchronous communication,Condition number,Mathematical optimization,Computer simulation,Algorithm,Adaptive mesh refinement,Rate of convergence,Numerical analysis,Mathematics,Grid,Computation
Journal
Volume
Issue
ISSN
42
1
0036-1429
Citations 
PageRank 
References 
2
0.39
6
Authors
4
Name
Order
Citations
PageRank
Barry Lee1485.29
STEPHEN F. MCCORMICK225830.70
Bobby Philip3759.67
Daniel J. Quinlan465280.13