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Title: Multicloud: Multigrid convergence with a meshless operator

Abstract

The primary objective of this work is to develop and test a new convergence acceleration technique we call multicloud. Multicloud is well-founded in the mathematical basis of multigrid, but relies on a meshless operator on coarse levels. The meshless operator enables extremely simple and automatic coarsening procedures for arbitrary meshes using arbitrary fine level discretization schemes. The performance of multicloud is compared with established multigrid techniques for structured and unstructured meshes for the Euler equations on two-dimensional test cases. Results indicate comparable convergence rates per unit work for multicloud and multigrid. However, because of its mesh and scheme transparency, multicloud may be applied to a wide array of problems with no modification of fine level schemes as is often required with agglomeration techniques. The implication is that multicloud can be implemented in a completely modular fashion, allowing researchers to develop fine level algorithms independent of the convergence accelerator for complex three-dimensional problems.

Authors:
 [1];  [1]
  1. Department of Aeronautics and Astronautics, Stanford University, Durand Building, 496 Lomita Mall, Stanford, CA 94305 (United States)
Publication Date:
OSTI Identifier:
21308098
Resource Type:
Journal Article
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 228; Journal Issue: 14; Other Information: DOI: 10.1016/j.jcp.2009.04.023; PII: S0021-9991(09)00199-5; Copyright (c) 2009 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9991
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ACCELERATION; ALGORITHMS; CONVERGENCE; ENERGY LEVELS; EQUATIONS; FUNCTIONS; MATHEMATICAL OPERATORS; MODIFICATIONS; PERFORMANCE; THREE-DIMENSIONAL CALCULATIONS; TWO-DIMENSIONAL CALCULATIONS

Citation Formats

Katz, Aaron, and Jameson, Antony. Multicloud: Multigrid convergence with a meshless operator. United States: N. p., 2009. Web. doi:10.1016/j.jcp.2009.04.023.
Katz, Aaron, & Jameson, Antony. Multicloud: Multigrid convergence with a meshless operator. United States. https://doi.org/10.1016/j.jcp.2009.04.023
Katz, Aaron, and Jameson, Antony. 2009. "Multicloud: Multigrid convergence with a meshless operator". United States. https://doi.org/10.1016/j.jcp.2009.04.023.
@article{osti_21308098,
title = {Multicloud: Multigrid convergence with a meshless operator},
author = {Katz, Aaron and Jameson, Antony},
abstractNote = {The primary objective of this work is to develop and test a new convergence acceleration technique we call multicloud. Multicloud is well-founded in the mathematical basis of multigrid, but relies on a meshless operator on coarse levels. The meshless operator enables extremely simple and automatic coarsening procedures for arbitrary meshes using arbitrary fine level discretization schemes. The performance of multicloud is compared with established multigrid techniques for structured and unstructured meshes for the Euler equations on two-dimensional test cases. Results indicate comparable convergence rates per unit work for multicloud and multigrid. However, because of its mesh and scheme transparency, multicloud may be applied to a wide array of problems with no modification of fine level schemes as is often required with agglomeration techniques. The implication is that multicloud can be implemented in a completely modular fashion, allowing researchers to develop fine level algorithms independent of the convergence accelerator for complex three-dimensional problems.},
doi = {10.1016/j.jcp.2009.04.023},
url = {https://www.osti.gov/biblio/21308098}, journal = {Journal of Computational Physics},
issn = {0021-9991},
number = 14,
volume = 228,
place = {United States},
year = {2009},
month = {8}
}