On the use of exponential time integration methods in atmospheric models

Exponential integration methods offer a highly accurate approach to the time integration of large systems of differential equations. In recent years, they have attracted increased attention in a number of diverse fields due to advances in their computational efficiency. This has been as a result of...

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Main Authors: Colm Clancy, Janusz A. Pudykiewicz
Format: Article
Language:English
Published: Taylor & Francis Group 2013-12-01
Series:Tellus: Series A, Dynamic Meteorology and Oceanography
Subjects:
Online Access:http://www.tellusa.net/index.php/tellusa/article/download/20898/pdf_1
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spelling doaj-96f7197beb234742a164ff6bbbd445512020-11-25T01:56:58ZengTaylor & Francis GroupTellus: Series A, Dynamic Meteorology and Oceanography0280-64951600-08702013-12-0165011610.3402/tellusa.v65i0.20898On the use of exponential time integration methods in atmospheric modelsColm ClancyJanusz A. PudykiewiczExponential integration methods offer a highly accurate approach to the time integration of large systems of differential equations. In recent years, they have attracted increased attention in a number of diverse fields due to advances in their computational efficiency. This has been as a result of the use of Krylov subspace methods for the approximation of the matrix exponentials which typically arise. In this work, we investigate the potential of exponential integration methods for use in atmospheric models. Two schemes are implemented in a shallow water model and tested against reference explicit and semi-implicit methods. In a number of experiments with standard test cases, the exponential methods are found to yield very accurate solutions with time-steps far longer than even the semi-implicit method allows. The relative efficiency of the exponential integrators, which depends mainly on the choice of the specific algorithm used for the calculation of the matrix exponent, is also discussed. The future work aimed at further improvements of the proposed methodology is outlined.http://www.tellusa.net/index.php/tellusa/article/download/20898/pdf_1numerical weather predictiontime integrationexponential methodsshallow water equationsadvection schemesicosahedral grid
collection DOAJ
language English
format Article
sources DOAJ
author Colm Clancy
Janusz A. Pudykiewicz
spellingShingle Colm Clancy
Janusz A. Pudykiewicz
On the use of exponential time integration methods in atmospheric models
Tellus: Series A, Dynamic Meteorology and Oceanography
numerical weather prediction
time integration
exponential methods
shallow water equations
advection schemes
icosahedral grid
author_facet Colm Clancy
Janusz A. Pudykiewicz
author_sort Colm Clancy
title On the use of exponential time integration methods in atmospheric models
title_short On the use of exponential time integration methods in atmospheric models
title_full On the use of exponential time integration methods in atmospheric models
title_fullStr On the use of exponential time integration methods in atmospheric models
title_full_unstemmed On the use of exponential time integration methods in atmospheric models
title_sort on the use of exponential time integration methods in atmospheric models
publisher Taylor & Francis Group
series Tellus: Series A, Dynamic Meteorology and Oceanography
issn 0280-6495
1600-0870
publishDate 2013-12-01
description Exponential integration methods offer a highly accurate approach to the time integration of large systems of differential equations. In recent years, they have attracted increased attention in a number of diverse fields due to advances in their computational efficiency. This has been as a result of the use of Krylov subspace methods for the approximation of the matrix exponentials which typically arise. In this work, we investigate the potential of exponential integration methods for use in atmospheric models. Two schemes are implemented in a shallow water model and tested against reference explicit and semi-implicit methods. In a number of experiments with standard test cases, the exponential methods are found to yield very accurate solutions with time-steps far longer than even the semi-implicit method allows. The relative efficiency of the exponential integrators, which depends mainly on the choice of the specific algorithm used for the calculation of the matrix exponent, is also discussed. The future work aimed at further improvements of the proposed methodology is outlined.
topic numerical weather prediction
time integration
exponential methods
shallow water equations
advection schemes
icosahedral grid
url http://www.tellusa.net/index.php/tellusa/article/download/20898/pdf_1
work_keys_str_mv AT colmclancy ontheuseofexponentialtimeintegrationmethodsinatmosphericmodels
AT januszapudykiewicz ontheuseofexponentialtimeintegrationmethodsinatmosphericmodels
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