Lecture 12: Recent Advances in Time Integration Methods and How They Can Enable Exascale Simulations
Physical systems models, exascale, power grid, multiphysics, renewable energy, time integration, splitting methods, time integration methods, integrators, sequential time stepping, multirate, multigrid, algorithm
To prepare for exascale systems, scientific simulations are growing in physical realism and thus complexity. This increase often results in additional and changing time scales. Time integration methods are critical to efficient solution of these multiphysics systems. Yet, many large-scale applications have not fully embraced modern time integration methods nor efficient software implementations. Hence, achieving temporal accuracy with new and complex simulations has proved challenging. We will overview recent advances in time integration methods, including additive IMEX methods, multirate methods, and parallel-in-time approaches, expected to help realize the potential of exascale systems on multiphysics simulations. Efficient execution of these methods relies, in turn, on efficient algebraic solvers, and we will discuss the relationships between integrators and solvers. In addition, an effective time integration approach is not complete without efficient software, and we will discuss effective software design approaches for time integrators and their uses in application codes. Lastly, examples demonstrating some of these new methods and their implementations will be presented.
This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. LLNL-ABS- 819501.
Woodward, C. S. (2021). Lecture 12: Recent Advances in Time Integration Methods and How They Can Enable Exascale Simulations. Mathematical Sciences Spring Lecture Series. Retrieved from https://scholarworks.uark.edu/mascsls/11
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