Sponsor
This material is based upon work supported by the U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research Program. The author benefited also from the Research Training Group (RTG) activities under NSF grant DMS-2136228.
Published In
Numerical Linear Algebra with Applications
Document Type
Pre-Print
Publication Date
12-1-2025
Subjects
Fractional order hierarchical decompositions, multigrid, fractional order -- white noise sampling
Abstract
Motivated by the fractional order multilevel decompositions of finite element spaces developed previously, we exploit additive representations of popular multigrid (MG) cycles to design fractional order MG decompositions. The additive representations enable us to scale the individual hierarchical components thus ending up with fractional order hierarchical decompositions that are based on the readily available MG components. This results in a highly efficient and scalable (in terms of high-performance) fractional order hierarchical MG decompositions that we tested in the setting of finite element white noise sampling as an alternative to PDE-based white noise sampling using fractional order shifted Laplacians.
Rights
© Copyright the author(s) 2025
DOI
10.1002/nla.70048
Persistent Identifier
https://archives.pdx.edu/ds/psu/44311
Citation Details
Vassilevski, P. S. (2025). Fractional Order Hierarchical Decompositions Using Multigrid Components. Numerical Linear Algebra with Applications, 32(6). Portico.
Description
This is the author’s version of a work that was accepted for publication. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published as: Fractional Order Hierarchical Decompositions Using Multigrid Components. Numerical Linear Algebra with Applications, 32(6). Portico.