Advances in implementation, theoretical motivation, and numerical results for the nested iteration with range decomposition algorithm

Summary This paper studies a low‐communication algorithm for solving elliptic PDEs on high‐performance machines, the nested iteration with range decomposition (NIRD) algorithm. Previous work has shown that NIRD converges to a high level of accuracy within a small, fixed number of iterations (usually...

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Veröffentlicht in:Numerical linear algebra with applications Jg. 25; H. 3
Hauptverfasser: Mitchell, Wayne, Manteuffel, Tom
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Oxford Wiley Subscription Services, Inc 01.05.2018
Wiley Blackwell (John Wiley & Sons)
Schlagworte:
Accuracy
Algorithms
Computer simulation
Convergence
Decomposition
elliptic PDE solvers
Error analysis
Iterative methods
low‐communication
nested iteration
Parallel computers
Preprocessing
range decomposition
Test procedures
ISSN:1070-5325, 1099-1506
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Beschreibung
Zusammenfassung:Summary This paper studies a low‐communication algorithm for solving elliptic PDEs on high‐performance machines, the nested iteration with range decomposition (NIRD) algorithm. Previous work has shown that NIRD converges to a high level of accuracy within a small, fixed number of iterations (usually one or two) when applied to simple elliptic problems. This paper makes some improvements to the NIRD algorithm (including the addition of adaptivity during preprocessing, wider choice of partitioning functions, and modified error measurement) that enhance the method's accuracy and scalability, especially on more difficult problems. In addition, an updated convergence proof is presented based on heuristic assumptions that are supported by numerical evidence. Furthermore, a new performance model is developed that shows increased performance benefits for NIRD when problems are more expensive to solve using traditional methods. Finally, extensive testing on a variety of elliptic problems provides additional insight into the behavior of NIRD and additional evidence that NIRD achieves excellent convergence on a wide class of elliptic PDEs and, as such, should be a very competitive method for solving PDEs on large parallel computers.
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USDOE
(SC) DE-FC02-03ER25574; (NNSA) DE-NA0002376
ISSN:1070-5325
1099-1506
DOI:10.1002/nla.2149