Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8902564 | Applied Numerical Mathematics | 2018 | 23 Pages |
Abstract
In this paper, we propose a step size selection strategy that adaptively reduces the computational cost (per unit time step) as the simulation progresses, constraint by the tolerance specified. We show that the proposed approach yields significant improvements in performance for a range of problems (diffusion-advection equation, Burgers' equation with a reaction term, porous media equation, viscous Burgers' equation, Allen-Cahn equation, and the two-dimensional Brusselator system). While traditional step size controllers have emphasized a smooth sequence of time step sizes, we emphasize the exploration of different step sizes which necessitates relatively rapid changes in the step size.
Related Topics
Physical Sciences and Engineering
Mathematics
Computational Mathematics
Authors
Lukas Einkemmer,