Fully implicit time stepping can be efficient on parallel computers
KAUST DepartmentApplied Mathematics and Computational Science Program
Extreme Computing Research Center
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Online Publication Date2019-07-18
Print Publication Date2019-06
Permanent link to this recordhttp://hdl.handle.net/10754/656811
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AbstractBenchmarks in high performance computing often involve a single component used in the full solution of a computational problem, such as the solution of a linear system of equations. In many cases, the choice of algorithm, which can determine the components used, is also important when solving a full problem. Numerical evidence suggests that for the Taylor-Green vortex problem at a Reynolds number of 1600, a second order implicit midpoint rule method can require less computational time than the often used linearly implicit Carpenter-Kennedy method for solving the equations of incompressible fluid dynamics for moderate levels of accuracy at the beginning of the flow evolution. The primary reason is that even though the implicit midpoint rule is fully implicit, it can use a small number of iterations per time step, and thus require less computational work per time step than the Carpenter-Kennedy method. For the same number of timesteps, the Carpenter-Kennedy method is more accurate since it uses a higher order timestepping method.
SponsorsWe thank the reviewers for their constructive comments, and Koen Hillewaert and David Ketcheson for helpful advice. We thank the participants of the 2013 HiOCFD workshop  for feedback on an earlier version of this work that enabled greater examination of the numerical results. BKM thanks Arieh Iserles for pointing out the geometric properties of the implicit midpoint rule and Charles Doering, José Gracia, Hans Johnston, Ning Li, Peter Van Keken, Divakar Viswanath and Jared Whitehead for helpful discussion. BKM was partially supported by HPC Europa 3 (INFRAIA-2016-1-730897).