On the use of exponential time integration methods in atmospheric models
By: Colm Clancy and Janusz A. Pudykiewicz
References
-
. Algorithms for the matrix exponential and its Fréchet derivative. 2010; University of Manchester, Manchester, UK: Faculty of Engineering and Physical Sciences. 155. PhD Thesis. -
, , . A new class of time discretization schemes for the solution of nonlinear PDEs. J. Comput. Phys. 1998; 147: 362– 387. -
. Exponential integrators for multiple time scale problems of environmental fluid dynamics. Innovative Integrators Workshop 27–30 October 2010. 2010; Austria: Universität Innsbruck. -
, . Laplace transform integration of the shallow-water equations. Part I: Eulerian formulation and Kelvin waves. Q. J. Roy. Meteorol. Soc. 2011; 137: 792– 799. -
, . A class of semi-implicit predictor–corrector schemes for the time integration of atmospheric models. J. Comput. Phys. 2013; 250: 665– 684. -
, . Exponential time differencing for stiff systems. J. Comput. Phys. 2002; 176: 430– 455. -
. The development of efficient time integration schemes using model normal modes. Mon. Weather Rev. 1980; 108: 100– 110. -
. Numerical Methods for Wave Equations in Geophysical Fluid Dynamics. 1999; New York: Springer. -
, , . Variational iterative methods for nonsymmetric systems of linear equations. SIAM J. Numer. Anal. 1983; 20: 345– 357. -
, , . An initial-value problem for testing numerical models of the global shallow-water equations. Tellus A. 2004; 56: 429– 440. -
, . On Krylov subspace approximations to the matrix exponential operator. SIAM J. Numer. Anal. 1997; 34: 1911– 1925. -
, , . Exponential integrators for large systems of differential equations. SIAM J. Sci. Comput. 1998; 19: 1552– 1574. -
, , , , , . The pros and cons of diffusion, filters and fixers in atmospheric general circulation models. Numerical Techniques for Global Atmospheric Models. 2011; Berlin Heidelberg: Springer–Verlag. 381– 493. -
. An explicit time-difference scheme with an Adams–Bashforth predictor and a trapezoidal corrector. Mon. Weather Rev. 2012; 140: 307– 322. -
, , . Unsteady analytical solutions of the spherical shallow water equations. J. Comput. Phys. 2005; 210: 535– 553. -
, . Comparative performance of exponential, implicit, and explicit integrators for stiff systems of ODEs. J. Comput. Appl. Math. 2013; 241: 45– 67. -
, . A Review of Exponential Integrators for First Order Semi-Linear Problems. 2005. Technical Report 2/2005, Department of Mathematical Sciences, NorwegianUniversity of Science and Technology, N-7491 Trondheim, Norway. -
, . Nineteen dubious ways to compute the exponential of a matrix, twenty–five years later. SIAM Rev. 2003; 45: 3– 49. -
, . The mass-conservative cell-integrated semi-Lagrangian advection scheme on the sphere. Mon. Weather Rev. 2002; 130: 649– 667. -
. Exponential Integrators for the Incompressible Navier–Stokes Equations. 2003; Blacksburg, VA: Virginia Polytechnic Institute and State University. 101. PhD Thesis. -
, . Algorithm 919: a Krylov subspace algorithm for evaluating the ϕ-functions appearing in exponential integrators. ACM Trans. Math. Software. 2012; 38( 3 ): 1– 19. -
. Numerical solution of the reaction-advection-diffusion equation on the sphere. J. Comput. Phys. 2006; 213: 358– 390. -
. On numerical solution of the shallow water equations with chemical reactions on icosahedral geodesic grid. J. Comput. Phys. 2011; 230: 1956– 1991. -
, , , , . Experiments with different discretizations for the shallow-water equations on a sphere. Q. J. Roy. Meteorol. Soc. 2012; 138: 989– 1003. -
. Iterative Methods for Sparse Linear Systems. 2003; SIAM, Philadelphia. -
. Efficient integration of large stiff systems of ODEs with exponential propagation iterative (EPI) methods. J. Comput. Phys. 2006; 213: 748– 776. -
, , . New adaptive exponential propagation iterative methods of Runge–Kutta type. SIAM J. Sci. Comput. 2012; 34: A2650– A2669. -
. An iterative solution method for solving f(a)x=b using Krylov subspace information obtained for the symmetric positive definite matrix a. J. Comput. Appl. Math. 1987; 18: 249– 263. -
, , , , . A standard test set for numerical approximation to the Shallow Water equations in spherical geometry. J. Comp. Phys. 1992; 102: 211– 224.
DOI: https://doi.org/10.3402/tellusa.v65i0.20898 | Journal eISSN: 3035-9554
Language: English
Page range: 20898 - 20898
Submitted on: Mar 19, 2013
Accepted on: Nov 6, 2013
Published on: Dec 1, 2013
Published by: Stockholm University Press
In partnership with: Paradigm Publishing Services
Keywords:
© 2013 Colm Clancy, Janusz A. Pudykiewicz, published by Stockholm University Press
This work is licensed under the Creative Commons Attribution 4.0 License.