publication . Article . Preprint . Other literature type . 2019

Parallel time integrator for linearized SWE on rotating sphere

Schreiber, Martin; Loft, Richard;
Open Access
  • Published: 01 Mar 2019 Journal: Numerical Linear Algebra with Applications, volume 26, page e2220 (issn: 1070-5325, Copyright policy)
  • Publisher: Wiley
Abstract
With the stagnation of processor core performance, further reductions in the time-to-solution for geophysical fluid problems are becoming increasingly difficult with standard time integrators. Parallel-in-time exposes and exploits additional parallelism in the time dimension which is inherently sequential in traditional methods. The rational approximation of exponential integrators (REXI) method allows taking arbitrarily long time steps based on a sum over a number of decoupled complex PDEs that can be solved independently massively parallel. Hence REXI is assumed to be well suited for modern massively parallel super computers which are currently trending. To da...
Subjects
free text keywords: Supercomputer, Spherical harmonics, Massively parallel, Mathematics, Shallow water equations, Mathematical analysis, Integrator, Physics - Computational Physics, Computer Science - Performance
36 references, page 1 of 3

1. Dennard RH, Rideout V, Bassous E, Leblanc A. Design of ion-implanted mosfet's with very small physical dimensions. Solid-State Circuits, IEEE Journal of 1974; 9(5):256-268. [OpenAIRE]

2. Gander MJ. 50 years of time parallel time integration. Multiple Shooting and Time Domain Decomposition, Carraro T, Geiger M, Korkel S, Rannacher R (eds.). Springer-Verlag, 2015.

3. Haut T, Babb T, Martinsson P, Wingate B. A high-order time-parallel scheme for solving wave propagation problems via the direct construction of an approximate time-evolution operator. IMA Journal of Numerical Analysis 2015; . [OpenAIRE]

4. Schreiber M, Peixoto PS, Haut T, Wingate B. Beyond spatial scalability limitations with a massively parallel method for linear oscillatory problems. The International Journal of High Performance Computing Applications 2017; .

5. Hochbruck M, Ostermann A. Exponential integrators. Acta Numerica 2010; 19:209-286. [OpenAIRE]

6. Kasahara A. Numerical integration of the global barotropic primitive equations with hough harmonic expansions. Journal of the Atmospheric Sciences 1977; 34(5):687-701.

7. Wang H, Boyd JP, Akmaev RA. On computation of hough functions. Geoscientific Model Development 2016; 9(4):1477.

8. Robert A. The integration of a spectral model of the atmosphere by the implicit method. Proc. WMO/IUGG Symposium on NWP, Tokyo, Japan Meteorological Agency, vol. 7, 1969; 19-24.

9. Hack JJ, Jakob R. Description of a global shallow water model based on the spectral transform method. National Center for Atmospheric Research, 1992. [OpenAIRE]

10. Ritchie H. Application of the semi-lagrangian method to a spectral model of the shallow water equations. Monthly Weather Review 1988; 116(8):1587-1598.

11. Wood N, Staniforth A, White A, Allen T, Diamantakis M, Gross M, Melvin T, Smith C, Vosper S, Zerroukat M, et al.. An inherently mass-conserving semi-implicit semi-lagrangian discretization of the deep-atmosphere global non-hydrostatic equations. Quarterly Journal of the Royal Meteorological Society 2014; 140(682):1505-1520. [OpenAIRE]

12. Barros S, Dent D, Isaksen L, Robinson G, Mozdzynski G, Wollenweber F. The IFS model: A parallel production weather code. Parallel Computing 1995; 21(10):1621 - 1638. Climate and weather modeling.

13. Moler C, Van Loan C. Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later. SIAM review 2003; 45(1):3-49.

14. Garcia F, Bonaventura L, Net M, Sa´nchez J. Exponential versus imex high-order time integrators for thermal convection in rotating spherical shells. Journal of Computational Physics 2014; 264:41-54.

15. Clancy C, Lynch P. Laplace transform integration of the shallow-water equations. part i: Eulerian formulation and kelvin waves. Quarterly Journal of the Royal Meteorological Society 2011; 137(656):792-799.

36 references, page 1 of 3
Abstract
With the stagnation of processor core performance, further reductions in the time-to-solution for geophysical fluid problems are becoming increasingly difficult with standard time integrators. Parallel-in-time exposes and exploits additional parallelism in the time dimension which is inherently sequential in traditional methods. The rational approximation of exponential integrators (REXI) method allows taking arbitrarily long time steps based on a sum over a number of decoupled complex PDEs that can be solved independently massively parallel. Hence REXI is assumed to be well suited for modern massively parallel super computers which are currently trending. To da...
Subjects
free text keywords: Supercomputer, Spherical harmonics, Massively parallel, Mathematics, Shallow water equations, Mathematical analysis, Integrator, Physics - Computational Physics, Computer Science - Performance
36 references, page 1 of 3

1. Dennard RH, Rideout V, Bassous E, Leblanc A. Design of ion-implanted mosfet's with very small physical dimensions. Solid-State Circuits, IEEE Journal of 1974; 9(5):256-268. [OpenAIRE]

2. Gander MJ. 50 years of time parallel time integration. Multiple Shooting and Time Domain Decomposition, Carraro T, Geiger M, Korkel S, Rannacher R (eds.). Springer-Verlag, 2015.

3. Haut T, Babb T, Martinsson P, Wingate B. A high-order time-parallel scheme for solving wave propagation problems via the direct construction of an approximate time-evolution operator. IMA Journal of Numerical Analysis 2015; . [OpenAIRE]

4. Schreiber M, Peixoto PS, Haut T, Wingate B. Beyond spatial scalability limitations with a massively parallel method for linear oscillatory problems. The International Journal of High Performance Computing Applications 2017; .

5. Hochbruck M, Ostermann A. Exponential integrators. Acta Numerica 2010; 19:209-286. [OpenAIRE]

6. Kasahara A. Numerical integration of the global barotropic primitive equations with hough harmonic expansions. Journal of the Atmospheric Sciences 1977; 34(5):687-701.

7. Wang H, Boyd JP, Akmaev RA. On computation of hough functions. Geoscientific Model Development 2016; 9(4):1477.

8. Robert A. The integration of a spectral model of the atmosphere by the implicit method. Proc. WMO/IUGG Symposium on NWP, Tokyo, Japan Meteorological Agency, vol. 7, 1969; 19-24.

9. Hack JJ, Jakob R. Description of a global shallow water model based on the spectral transform method. National Center for Atmospheric Research, 1992. [OpenAIRE]

10. Ritchie H. Application of the semi-lagrangian method to a spectral model of the shallow water equations. Monthly Weather Review 1988; 116(8):1587-1598.

11. Wood N, Staniforth A, White A, Allen T, Diamantakis M, Gross M, Melvin T, Smith C, Vosper S, Zerroukat M, et al.. An inherently mass-conserving semi-implicit semi-lagrangian discretization of the deep-atmosphere global non-hydrostatic equations. Quarterly Journal of the Royal Meteorological Society 2014; 140(682):1505-1520. [OpenAIRE]

12. Barros S, Dent D, Isaksen L, Robinson G, Mozdzynski G, Wollenweber F. The IFS model: A parallel production weather code. Parallel Computing 1995; 21(10):1621 - 1638. Climate and weather modeling.

13. Moler C, Van Loan C. Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later. SIAM review 2003; 45(1):3-49.

14. Garcia F, Bonaventura L, Net M, Sa´nchez J. Exponential versus imex high-order time integrators for thermal convection in rotating spherical shells. Journal of Computational Physics 2014; 264:41-54.

15. Clancy C, Lynch P. Laplace transform integration of the shallow-water equations. part i: Eulerian formulation and kelvin waves. Quarterly Journal of the Royal Meteorological Society 2011; 137(656):792-799.

36 references, page 1 of 3
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publication . Article . Preprint . Other literature type . 2019

Parallel time integrator for linearized SWE on rotating sphere

Schreiber, Martin; Loft, Richard;