Class PenaltyBarrierU_quadratic_bis¶
Defined in File PenaltyBarrierU.cc
Inheritance Relationships¶
Base Type¶
public Mechatronix::PenaltyBarrierU_base(Class PenaltyBarrierU_base)
Class Documentation¶
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class
Mechatronix::PenaltyBarrierU_quadratic_bis: public Mechatronix::PenaltyBarrierU_base¶
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Piecewise quadratic penalty.
Public Functions
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inline explicit
PenaltyBarrierU_quadratic_bis(string const &name)¶
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Construct the penalty.
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inline virtual void
setup(real_type epsilon, real_type tolerance) override¶
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Initialize the penalty internal parameters based on the values of \( h \) and \( \epsilon \)
The following values are precomputed for the penalty.
\[ H=1-h,\qquad A_0=\frac{1}{h},\qquad A_1 = \frac{\epsilon}{H^2}, \qquad A_2 = \frac{2\epsilon}{H}, \qquad A_3 = \frac{1-A_1}{h^2}+A_1, \qquad A_4 = \frac{2}{h}\left(1-A_1\right)+ A_2 \]- Parameters
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epsilon – value \( \epsilon \)
tolerance – value \( h \)
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inline virtual real_type
eval(real_type x) const override¶
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Compute penalty value
\[\begin{split} p(x) = \begin{cases} 1+(2\,A_0(x+1)-A_4)(x+1) & x < -1 \\[1em] \epsilon + ( A_3(x+H) - A_2)(x+H) & x \in [-1,-1+h] \\[1em] A_1\, x^2 & x \in [-H,H] \\[1em] \epsilon + ( A_3(x-H) + A2)(x-H) & x \in [H,1] \\[1em] 1 + ( 2A_0 (x-1) + A_4 )(x-1) & x>1 \end{cases} \end{split}\]where the values
\[ H=1-h,\qquad A_0=\frac{1}{h},\qquad A_1 = \frac{\epsilon}{H^2}, \qquad A_2 = \frac{2\epsilon}{H}, \qquad A_3 = \frac{1-A_1}{h^2}+A_1, \qquad A_4 = \frac{2}{h}\left(1-A_1\right)+ A_2 \]are precomputed after a call of method
setup.
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inline explicit
