 |
OGS
|
This class gives an adaptive algorithm whose time step control is evolutionary PID controller. With an definition of relative solution change e_n=\frac{\|u^{n+1}-u^n\|}{\|u^{n+1}\|}, the algorithm gives a time step size estimation as
h_{n+1} = \left(\frac{e_{n-1}}{e_n}\right)^{k_P} \left(\frac{TOL}{e_n}\right)^{k_I} \left(\frac{e^2_{n-1}}{e_n e_{n-2}}\right)^{k_D}
where k_P=0.075, k_I=0.175, k_D=0.01 are empirical PID parameters.
In the computation, e_n is calculated firstly. If e_n>TOL, the current time step is rejected and repeated with a new time step size of h=\frac{TOL}{e_n} h_n.
Limits of the time step size are given as
h_{\mbox{min}} \leq h_{n+1} \leq h_{\mbox{max}}, l \leq \frac{h_{n+1}}{h_n} \leq L
Similar algorithm can be found in [1] .
No additional info.
