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OGS
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OGS
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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.
1.11.0