| Description |
1 online resource (20 pages) : color illustrations. |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
| Series |
NREL/CP ; 2C00-80343 |
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Conference paper (National Renewable Energy Laboratory (U.S.)) ; 2C00-80343.
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| Note |
"February 2022." |
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"Presented at SISC Copper Mountain Special Section, March 25-31, 2021"--Cover. |
| Bibliography |
Includes bibliographical references (pages 19-20). |
| Funding |
U.S. Department of Energy DE-AC36-08GO28308 |
| Note |
Description based on online resource; title from PDF title page (NREL, viewed June 27, 2022). |
| Summary |
A low-synchronization MGS-GMRES Krylov solver employing a truncated Neumann series for the inverse compact WY MGS correction matrix T is presented. A corollary to the backward stability result of Paige et al. [1] establishes that T = I - Lk is sufficient for convergence of GMRES when kLkp F = O("p)_p F (B), where the strictly lower triangular matrix L is defined by the inner products of Krylov vectors V T 1:k-2 vk-1. The preconditioner is the classical Ruge-Stuben AMG algorithm with compatible relaxation and inner-outer Gauss-Seidel smoother. This smoother may also be expressed as a truncated Neumann series. Drop tolerances are applied to the lower triangular matrices arising in the smoother in order to reduce the number of non-zeros and accelerate the time to solution. The number of small matrix elements are found to increase from fine to coarse levels and thus the effciency gains are greater for large problems with many levels in the V -cycle. The solver is applied to the pressure continuity equation for the incompressible Navier-Stokes equations. Unlike the inner-outer iteration, the solver convergence rate with the standard Gauss-Seidel smoother deteriorates with dropping. The solver compute time is reduced by up to 50% without a change in the convergence rate. |
| Subject |
Engineering mathematics.
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Algebras, Linear.
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Mathématiques de l'ingénieur.
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Algèbre linéaire.
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Algebras, Linear
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Engineering mathematics
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| Indexed Term |
Gauss-Seidel smoother |
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inner-outer iterations |
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Krylov solver |
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MGS-GMRES |
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Neumann series |
| Added Author |
National Renewable Energy Laboratory (U.S.), issuing body.
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| Standard No. |
1845270 OSTI ID |
| Gpo Item No. |
0430-P-04 (online) |
| Sudoc No. |
E 9.17:NREL/CP-2 C 00-80343 |
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