Exponential integrators with parallel-in-time rational approximations for the shallow-water equations on the rotating sphere
- Published: 01 Jul 2019
- Publisher: Elsevier BV
[1] H. Sutter, The free lunch is over: A fundamental turn toward concurrency in software, Dr. Dobb's journal 30 (3) (2005) 202{210.
[2] ECMWF, Ecmwf strategy 2016-2025, the strengh of a common goal (2016). [OpenAIRE]
[3] M. O ce, Met o ce science strategy: 2016-2021 delivering science with impact (2016).
[4] C. Moler, C. Van Loan, Nineteen dubious ways to compute the exponential of a matrix, twenty- ve years later, SIAM review 45 (1) (2003) 3{49.
[5] M. Hochbruck, A. Ostermann, Exponential integrators, Acta Numerica 19.
[6] J. D. Lawson, Generalized runge-kutta processes for stable systems with large lipschitz constants, SIAM Journal on Numerical Analysis 4 (3) (1967) 372{380. [OpenAIRE]
[7] M. Hochbruck, C. Lubich, H. Selhofer, Exponential integrators for large systems of di erential equations, SIAM Journal on Scienti c Computing 19 (5).
[8] S. Cox, P. Matthews, Exponential time di erencing for sti systems, Journal of Computational Physics 176 (2) (2002) 430 { 455.
[9] M. Tokman, E cient integration of large sti systems of odes with exponential propagation iterative (epi) methods, Journal of Comp. Physics 213 (2).
[10] M. Tokman, A new class of exponential propagation iterative methods of runge{kutta type (epirk), Journal of Comp. Physics 230 (24) (2011) 8762{ 8778. [OpenAIRE]
[11] C. Clancy, P. Lynch, Laplace transform integration of the SWE. Part I: Eulerian form. and Kelvin waves, Quarterly Journal of the RMS 137 (656) (2011) 792{799.
[12] J. Niesen, W. M. Wright, Algorithm 919: A Krylov Subspace Algorithm for Evaluating the -Functions Appearing in Exponential Integrators, ACM Trans. Math. Softw. 38 (3) (2012) 22:1{22:19. doi:10.1145/2168773. 2168781. URL http://doi.acm.org/10.1145/2168773.2168781
[13] C. Clancy, J. A. Pudykiewicz, On the use of exponential time integration methods in atmospheric models, Tellus A 65 (2013) 1{16. [OpenAIRE]
[14] L. Bonaventura, Local exponential methods: a domain decomposition approach to exponential time integration of pdes, CoRR abs/1505.02248. URL http://arxiv.org/abs/1505.02248
[15] F. Garcia, L. Bonaventura, M. Net, J. Sanchez, Exp. versus IMEX highorder time int. for thermal conv. in rot. spherical shells, J. of Comp. Physics 264.
[1] H. Sutter, The free lunch is over: A fundamental turn toward concurrency in software, Dr. Dobb's journal 30 (3) (2005) 202{210.
[2] ECMWF, Ecmwf strategy 2016-2025, the strengh of a common goal (2016). [OpenAIRE]
[3] M. O ce, Met o ce science strategy: 2016-2021 delivering science with impact (2016).
[4] C. Moler, C. Van Loan, Nineteen dubious ways to compute the exponential of a matrix, twenty- ve years later, SIAM review 45 (1) (2003) 3{49.
[5] M. Hochbruck, A. Ostermann, Exponential integrators, Acta Numerica 19.
[6] J. D. Lawson, Generalized runge-kutta processes for stable systems with large lipschitz constants, SIAM Journal on Numerical Analysis 4 (3) (1967) 372{380. [OpenAIRE]
[7] M. Hochbruck, C. Lubich, H. Selhofer, Exponential integrators for large systems of di erential equations, SIAM Journal on Scienti c Computing 19 (5).
[8] S. Cox, P. Matthews, Exponential time di erencing for sti systems, Journal of Computational Physics 176 (2) (2002) 430 { 455.
[9] M. Tokman, E cient integration of large sti systems of odes with exponential propagation iterative (epi) methods, Journal of Comp. Physics 213 (2).
[10] M. Tokman, A new class of exponential propagation iterative methods of runge{kutta type (epirk), Journal of Comp. Physics 230 (24) (2011) 8762{ 8778. [OpenAIRE]
[11] C. Clancy, P. Lynch, Laplace transform integration of the SWE. Part I: Eulerian form. and Kelvin waves, Quarterly Journal of the RMS 137 (656) (2011) 792{799.
[12] J. Niesen, W. M. Wright, Algorithm 919: A Krylov Subspace Algorithm for Evaluating the -Functions Appearing in Exponential Integrators, ACM Trans. Math. Softw. 38 (3) (2012) 22:1{22:19. doi:10.1145/2168773. 2168781. URL http://doi.acm.org/10.1145/2168773.2168781
[13] C. Clancy, J. A. Pudykiewicz, On the use of exponential time integration methods in atmospheric models, Tellus A 65 (2013) 1{16. [OpenAIRE]
[14] L. Bonaventura, Local exponential methods: a domain decomposition approach to exponential time integration of pdes, CoRR abs/1505.02248. URL http://arxiv.org/abs/1505.02248
[15] F. Garcia, L. Bonaventura, M. Net, J. Sanchez, Exp. versus IMEX highorder time int. for thermal conv. in rot. spherical shells, J. of Comp. Physics 264.
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