knowledgebase_921 How does COMSOL Multiphysics determine the time-step size

dior

底下连结是官网的knowledge base，一个有关time step control的问题....

有没有哪位朋友是会员~能帮忙贴出来看一下吗?

我一直通不过会员申请>"<

http://www.comsol.com/support/knowledgebase/921/

非常谢谢大家!!

jinxiaoli_1981

Solution Number: 921
Title: Time-step control
Platform: All Platforms
Applies to: All Products
Versions: 3.3, 3.4
Created: August 20, 2003
Last Modified: January 23, 2009
Categories: Solver
Keywords:  

Problem Description
How does COMSOL Multiphysics determine the time-step size?

Solution
In all of the COMSOL Multiphysics solvers for time-dependent problems, the time step is determined by local error estimates. Since the time methods are implicit, the accuracy is the only limiting factor for the time-step determination. You can specify limits (max/min) for this time-step control.

The local error can be estimated by taking time steps with two different methods and then using Richardson extrapolation to determine the dominating error term in the truncation error expansion. The local error is the error from one local time step by the time method. The global error, which is what you really want to control, is not just the sum of the local errors. The global error can both be larger and smaller than the sum of all the local errors, depending on the sensitivity of the underlying problem (the propagated data errors). Nevertheless, the global error is estimated based upon these local error estimates by taking the sum. Standard text books on numerical methods for ODEs cover this.

If the error tolerances, relative or absolute, are not met, the local time step is disqualified and a new smaller time step is chosen. For example, if the solution explodes at some point in a simulation, to fulfill the absolute error tolerance, the time step has to be taken smaller and smaller, causing the solver to stop.

For the above reasons, the tolerance parameters should be used with caution for problems with a lot of dynamics, like oscillations and wave dynamics. It is also a good practice to investigate the influence of the tolerance parameters on the solution, by redoing the simulations with new tolerance parameters.