A Test Set for an Adaptive Moving Grid PDE Solver with Time-Dependent Adaptivity

Abstract

We have tested a moving grid method with time-dependent adaptivity parameter on a wide variety of test problems. The real-time calculated adaptivity parameter makes the method more robust, removing the need to re-scale problems to fit the solver. When compared to the best results for a fixed adaptivity parameter in our computational efficiency measurements, this increased robustness more than compensates for the small decrease in performance. Finally, tests on a small subset of our test problems show that we can further improve results for models whose solution components differed by several orders of magnitude by calculating separate adaptivity parameters for each component.