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Low-Communication, Parallel Multigrid Algorithms for Elliptic Partial Differential Equations.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Low-Communication, Parallel Multigrid Algorithms for Elliptic Partial Differential Equations./
Author:	Mitchell, Wayne Bradford.
Description:	1 online resource (109 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 79-02(E), Section: B.
Contained By:	Dissertation Abstracts International79-02B(E).
Subject:	Applied mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9780355231755

Low-Communication, Parallel Multigrid Algorithms for Elliptic Partial Differential Equations.
Mitchell, Wayne Bradford.

Low-Communication, Parallel Multigrid Algorithms for Elliptic Partial Differential Equations. - 1 online resource (109 pages)

Source: Dissertation Abstracts International, Volume: 79-02(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

When solving elliptic partial differential equations (PDE's) multigrid algorithms often provide optimal solvers and preconditioners capable of providing solutions with O(N) computational cost, where N is the number of unknowns. As parallelism of modern super computers continues to grow towards exascale, however, the cost of communication has overshadowed the cost of computation as the next major bottleneck for multigrid algorithms. Typically, multigrid algorithms require O((log P)2) communication steps in order to solve a PDE problem to the level of discretization accuracy, where P is the number of processors. This has inspired the development of new algorithms that employ novel paradigms for parallelizing PDE problems, and this thesis studies and further develops two such algorithms.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9780355231755Subjects--Topical Terms:

1069907
Applied mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Low-Communication, Parallel Multigrid Algorithms for Elliptic Partial Differential Equations.
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300 $a 1 online resource (109 pages)
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500 $a Source: Dissertation Abstracts International, Volume: 79-02(E), Section: B.
500 $a Advisers: Thomas A. Manteuffel; Stephen F. McCormick.
502 $a Thesis (Ph.D.) $c University of Colorado at Boulder $d 2017.
504 $a Includes bibliographical references
520 $a When solving elliptic partial differential equations (PDE's) multigrid algorithms often provide optimal solvers and preconditioners capable of providing solutions with O(N) computational cost, where N is the number of unknowns. As parallelism of modern super computers continues to grow towards exascale, however, the cost of communication has overshadowed the cost of computation as the next major bottleneck for multigrid algorithms. Typically, multigrid algorithms require O((log P)2) communication steps in order to solve a PDE problem to the level of discretization accuracy, where P is the number of processors. This has inspired the development of new algorithms that employ novel paradigms for parallelizing PDE problems, and this thesis studies and further develops two such algorithms.
520 $a The nested iteration with range decomposition (NIRD) algorithm is known to achieve accuracy similar to that of traditional methods in only a single iteration with log P communication steps for simple elliptic problems. This thesis makes several improvements to the NIRD algorithm and extends its application to a much wider variety of problems, while also examining and updating previously proposed convergence theory and performance models.
520 $a The second method studied is the algebraic multigrid with domain decomposition (AMG-DD) algorithm. Though previous work showed only marginal benefits when comparing convergence factors for AMG-DD against standard AMG V-cycles, this thesis studies the potential of AMG-DD as a discretization-accuracy solver. In addition to detailing the first parallel implementation of this algorithm, this thesis also shows new results that study the effect of different AMG coarsening and interpolation strategies on AMG-DD convergence and show some evidence to suggest AMG-DD may achieve discretization accuracy in a fixed number of cycles with O(log P) communication cost even as problem size increases.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Applied mathematics. $3 1069907
655 7 $a Electronic books. $2 local $3 554714
690 $a 0364
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a University of Colorado at Boulder. $b Applied Mathematics. $3 1182498
773 0 $t Dissertation Abstracts International $g 79-02B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10615220 $z click for full text (PQDT)