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Class implementing cubic splines. More...
#include <opm/common/Exceptions.hpp>#include <opm/material/common/TridiagonalMatrix.hpp>#include <opm/material/common/PolynomialUtils.hpp>#include <iosfwd>#include <vector>Go to the source code of this file.
Classes | |
| class | Opm::Spline< Scalar > |
| Class implementing cubic splines. More... | |
| struct | Opm::Spline< Scalar >::ComparatorX_ |
| Helper class needed to sort the input sampling points. More... | |
Namespaces | |
| namespace | Opm |
| This class implements a small container which holds the transmissibility mulitpliers for all the faces in the grid. | |
Class implementing cubic splines.
This class supports full, natural, periodic and monotonic cubic splines.
Full a splines 



for any given boundary slopes 

Natural splines which are defined by

For periodic splines of splines the slopes at the boundaries are identical:

Finally, there are monotonic splines which guarantee that the curve is confined by its sampling points, i.e.,
![\[
y_i \leq s(x) \leq y_{i+1} \quad \text{for} x_i \leq x \leq x_{i+1} \;.
\]](form_29.png)
For more information on monotonic splines, see http://en.wikipedia.org/wiki/Monotone_cubic_interpolation
Full, natural and periodic splines are continuous in their first and second derivatives, i.e.,
![\[
s \in \mathcal{C}^2
\]](form_30.png)
holds for such splines. Monotonic splines are only continuous up to their first derivative, i.e., for these only
![\[
s \in \mathcal{C}^1
\]](form_31.png)
is true.