Loading...
Searching...
No Matches
Spline.hpp File Reference

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.

## Detailed Description

Class implementing cubic splines.

This class supports full, natural, periodic and monotonic cubic splines.

Full a splines are splines which, given sampling points , fulfill the following conditions

for any given boundary slopes and .

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.,

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.,

holds for such splines. Monotonic splines are only continuous up to their first derivative, i.e., for these only

is true.