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Spectral Preconditioners for Nonhydrostatic Atmospheric Models. Thomas, Stephen J.; Hacker, Joshua P.; Smolarkiewicz, Piotr K.; Stull, Roland B.
Abstract
The elliptic problems in semi-implicit nonhydrostatic atmospheric models are difficult. Typically, they are poorly conditioned, nonseparable, contain cross-derivative terms, and are often nonsymmetric. Here, the resulting linear system is solved using a preconditioned Krylov subspace method—the generalized conjugate residual (GCR) algorithm. A horizontal spectral preconditioner is developed as an alternative to a more standard and much simpler line Jacobi relaxation scheme. However, the efficacy of the spectral preconditioner requires neglecting the cross-derivative terms and homogenization (e.g., averaging) metric coefficients over the computational domain. Because such a compromise causes a substantial departure of the preconditioner from the original elliptic operator, it is not obvious a priori whether it leads to a competitive solver. The robustness of the proposed approach over a broad range of representative meteorological applications is evaluated, in the context of a three-time-level semi-implicit semi-Lagrangian all-scale weather-prediction/research model. Copyright 2003 American Meteorological Society (AMS). Permission to use figures, tables, and brief excerpts from this work in scientific and educational works is hereby granted provided that the source is acknowledged. Any use of material in this work that is determined to be “fair use” under Section 107 of the U.S. Copyright Act or that satisfies the conditions specified in Section 108 of the U.S. Copyright Act (17 USC §108, as revised by P.L. 94-553) does not require the AMS’s permission. Republication, systematic reproduction, posting in electronic form, such as on a web site or in a searchable database, or other uses of this material, except as exempted by the above statement, requires written permission or a license from the AMS. Additional details are provided in the AMS Copyright Policy, available on the AMS Web site located at (http://www.ametsoc.org/) or from the AMS at 617-227-2425 or copyright@ametsoc.org.
Item Metadata
Title |
Spectral Preconditioners for Nonhydrostatic Atmospheric Models.
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Creator | |
Publisher |
American Meteorological Society
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Date Issued |
2003-10
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Description |
The elliptic problems in semi-implicit nonhydrostatic atmospheric models are difficult. Typically, they are
poorly conditioned, nonseparable, contain cross-derivative terms, and are often nonsymmetric. Here, the resulting
linear system is solved using a preconditioned Krylov subspace method—the generalized conjugate residual
(GCR) algorithm. A horizontal spectral preconditioner is developed as an alternative to a more standard and
much simpler line Jacobi relaxation scheme. However, the efficacy of the spectral preconditioner requires neglecting
the cross-derivative terms and homogenization (e.g., averaging) metric coefficients over the computational
domain. Because such a compromise causes a substantial departure of the preconditioner from the
original elliptic operator, it is not obvious a priori whether it leads to a competitive solver. The robustness of
the proposed approach over a broad range of representative meteorological applications is evaluated, in the
context of a three-time-level semi-implicit semi-Lagrangian all-scale weather-prediction/research model. Copyright 2003 American Meteorological Society (AMS). Permission
to use figures, tables, and brief excerpts from this work in scientific and educational
works is hereby granted provided that the source is acknowledged. Any use of material in
this work that is determined to be “fair use” under Section 107 of the U.S. Copyright Act
or that satisfies the conditions specified in Section 108 of the U.S. Copyright Act (17
USC §108, as revised by P.L. 94-553) does not require the AMS’s permission.
Republication, systematic reproduction, posting in electronic form, such as on a web site
or in a searchable database, or other uses of this material, except as exempted by the
above statement, requires written permission or a license from the AMS. Additional
details are provided in the AMS Copyright Policy, available on the AMS Web site
located at (http://www.ametsoc.org/) or from the AMS at 617-227-2425 or
copyright@ametsoc.org.
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Genre | |
Type | |
Language |
eng
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Date Available |
2011-04-11
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0041844
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URI | |
Affiliation | |
Citation |
Thomas, Stephen J., Hacker, Joshua P., Smolarkiewicz, Piotr K., Stull, Roland B. 2003. Spectral Preconditioners for Nonhydrostatic Atmospheric Models. Monthly Weather Review. 131(10) 2464-2478.
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Peer Review Status |
Reviewed
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Scholarly Level |
Faculty
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Copyright Holder |
Stull, Roland B.
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International