An Explicit Time-Difference Scheme with an Adams–Bashforth Predictor and a Trapezoidal Corrector

Kar, Sajal K.

doi:10.1175/mwr-d-10-05066.1

Cited by 7 publications

(4 citation statements)

References 25 publications

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“…(2). The nonlinear terms are discretised with an AdamsÁBashforth-trapezoidal predictorÁcorrector method (Kar, 2012), while a trapezoidal averaging is applied to the linear terms at each stage. With the system written in the form (2), the scheme is given by …”

Section: Model Configurationsmentioning

confidence: 99%

On the use of exponential time integration methods in atmospheric models

Clancy

Pudykiewicz

2013

Tellus A: Dynamic Meteorology and Oceanography

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A B S T R A C T 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.

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Section: Model Configurationsmentioning

confidence: 99%

On the use of exponential time integration methods in atmospheric models

Clancy

Pudykiewicz

2013

Tellus A: Dynamic Meteorology and Oceanography

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“…To remove high frequency components, we define a closed contour C * , the circle centred at the origin with radius ω c (ω c is called the cut-off frequency). We replace C by C * in the integral in (11), yielding the modified inversion…”

Section: Discussionmentioning

confidence: 99%

“…One in particular, labelled T-ABT, uses an implicit trapezoidal (T) averaging for the linear terms, with an AdamsBashforth-Trapezoidal (ABT) method (Kar, 2012) for the nonlinear terms. With X p denoting the intermediate, predicted level, the discretisation for the system (1) is then…”

Section: Nonlinear Termsmentioning

confidence: 99%

“…Clancy and Pudykiewicz () tested a number of two‐stage semi‐implicit methods, in which the nonlinear terms are discretised in time using a predictor–corrector method. One in particular, labelled T‐ABT, uses an implicit trapezoidal (T) averaging for the linear terms, with an Adams–Bashforth‐Trapezoidal (ABT) method (Kar, ) for the nonlinear terms. With X p denoting the intermediate, predicted level, the discretisation for the system is then