Convection experiments with the exponential time integration scheme

[1]  N. Higham The Scaling and Squaring Method for the Matrix Exponential Revisited , 2005, SIAM J. Matrix Anal. Appl..

[2]  D. Lilly On the numerical simulation of buoyant convection , 1962 .

[3]  Francis X. Giraldo,et al.  Current and Emerging Time-Integration Strategies in Global Numerical Weather and Climate Prediction , 2019 .

[4]  Guillaume Houzeaux,et al.  A Review of Element-Based Galerkin Methods for Numerical Weather Prediction: Finite Elements, Spectral Elements, and Discontinuous Galerkin , 2015 .

[5]  Colm Clancy,et al.  On the use of exponential time integration methods in atmospheric models , 2013 .

[7]  Gordey Goyman,et al.  Parallel Efficiency of Time-Integration Strategies for the Next Generation Global Weather Prediction Model , 2020, RuSCDays.

[8]  Mayya Tokman,et al.  Efficient integration of large stiff systems of ODEs with exponential propagation iterative (EPI) methods , 2006, J. Comput. Phys..

[9]  Paul A. Ullrich,et al.  A high-order staggered finite-element vertical discretization for non-hydrostatic atmospheric models , 2016 .

[10]  Max Gunzburger,et al.  Exponential time differencing for mimetic multilayer ocean models , 2019, J. Comput. Phys..

[11]  N. Žagar,et al.  A high‐accuracy global prognostic model for the simulation of Rossby and gravity wave dynamics , 2021, Quarterly Journal of the Royal Meteorological Society.

[12]  A method for relaxing the Courant-Friedrich-Levy condition in time-explicit schemes , 2005 .

[13]  Vu Thai Luan,et al.  Further development of efficient and accurate time integration schemes for meteorological models , 2018, J. Comput. Phys..

[14]  J. M. Keiser,et al.  A New Class of Time Discretization Schemes for the Solution of Nonlinear PDEs , 1998 .

[15]  Martin Schreiber,et al.  Exponential integrators with parallel-in-time rational approximations for the shallow-water equations on the rotating sphere , 2019, Parallel Comput..

[16]  D. Durran Numerical Methods for Fluid Dynamics , 2010 .

[17]  P. Lynch,et al.  Improving the Laplace transform integration method , 2016 .

[18]  Fabrice Falissard Genuinely multi-dimensional explicit and implicit generalized Shapiro filters for weather forecasting, computational fluid dynamics and aeroacoustics , 2013, J. Comput. Phys..

[19]  Jitse Niesen,et al.  Algorithm 919: A Krylov Subspace Algorithm for Evaluating the ϕ-Functions Appearing in Exponential Integrators , 2009, TOMS.

[20]  Y. Saad Analysis of some Krylov subspace approximations to the matrix exponential operator , 1992 .

[21]  J. D. Lawson Generalized Runge-Kutta Processes for Stable Systems with Large Lipschitz Constants , 1967 .

[22]  S. Cox,et al.  Exponential Time Differencing for Stiff Systems , 2002 .

[23]  V. Shashkin,et al.  Semi-Lagrangian exponential time-integration method for the shallow water equations on the cubed sphere grid , 2020, Russian Journal of Numerical Analysis and Mathematical Modelling.

[24]  David A. Pope An exponential method of numerical integration of ordinary differential equations , 1963, CACM.

[25]  Louis J. Wicker,et al.  Numerical solutions of a non‐linear density current: A benchmark solution and comparisons , 1993 .

[26]  Janusz A. Pudykiewicz,et al.  An efficient exponential time integration method for the numerical solution of the shallow water equations on the sphere , 2016, J. Comput. Phys..

[27]  M. Tapp,et al.  A non‐hydrostatic mesoscale model , 1976 .

[28]  Numerical analyses of exponential time‐differencing schemes for the solution of atmospheric models , 2021, Quarterly Journal of the Royal Meteorological Society.

[29]  Roger B. Sidje,et al.  Expokit: a software package for computing matrix exponentials , 1998, TOMS.

[30]  Marlis Hochbruck,et al.  Explicit Exponential Runge-Kutta Methods for Semilinear Parabolic Problems , 2005, SIAM J. Numer. Anal..

[31]  Lili Ju,et al.  An exponential time-integrator scheme for steady and unsteady inviscid flows , 2018, J. Comput. Phys..