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// $Id: function_derivative.h 30036 2013-07-18 16:55:32Z maier $
//
// Copyright (C) 2000 - 2013 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, redistribute
// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE at
// the top level of the deal.II distribution.
//
// ---------------------------------------------------------------------
#ifndef __deal2__function_derivative_h
#define __deal2__function_derivative_h
#include <deal.II/base/config.h>
#include <deal.II/base/exceptions.h>
#include <deal.II/base/function.h>
#include <deal.II/base/auto_derivative_function.h>
DEAL_II_NAMESPACE_OPEN
/**
* Derivative of a function object. The value access functions of
* this class return the directional derivative of a function with
* respect to a direction provided on construction. If <tt>b</tt> is the
* vector, the derivative <tt>b . grad f</tt> is computed. This derivative
* is evaluated directly, not by computing the gradient of <tt>f</tt> and
* its scalar product with <tt>b</tt>.
*
* The derivative is computed numerically, using one of the provided
* difference formulas (see <tt>set_formula</tt> for available
* schemes). Experimenting with <tt>h</tt> and the difference scheme may be
* necessary to obtain sufficient results.
*
* @ingroup functions
* @author Guido Kanschat, 2000
*/
template <int dim>
class FunctionDerivative : public AutoDerivativeFunction<dim>
{
public:
/**
* Constructor. Provided are the
* functions to compute
* derivatives of, the direction
* vector of the differentiation
* and the step size <tt>h</tt> of the
* difference formula.
*/
FunctionDerivative (const Function<dim> &f,
const Point<dim> &direction,
const double h = 1.e-6);
/**
* Constructor. Provided are the
* functions to compute
* derivatives of and the
* direction vector of the
* differentiation in each
* quadrature point and the
* difference step size.
*
* This is the constructor for a
* variable velocity field. Most
* probably, a new object of
* <tt>FunctionDerivative</tt> has to
* be constructed for each set of
* quadrature points.
*
* The number of quadrature point
* must still be the same, when
* values are accessed.
*/
FunctionDerivative (const Function<dim> &f,
const std::vector<Point<dim> > &direction,
const double h = 1.e-6);
/**
* Choose the difference formula.
* This is set to the default in
* the constructor.
*
* Formulas implemented right now
* are first order backward Euler
* (<tt>UpwindEuler</tt>), second
* order symmetric Euler
* (<tt>Euler</tt>) and a symmetric
* fourth order formula
* (<tt>FourthOrder</tt>).
*/
void set_formula (typename AutoDerivativeFunction<dim>::DifferenceFormula formula
= AutoDerivativeFunction<dim>::Euler);
/**
* Change the base step size of
* the difference formula
*/
void set_h (const double h);
virtual double value (const Point<dim> &p,
const unsigned int component = 0) const;
virtual void vector_value(const Point<dim> &p,
Vector<double> &value) const;
virtual void value_list (const std::vector<Point<dim> > &points,
std::vector<double> &values,
const unsigned int component = 0) const;
/**
* Determine an estimate for
* the memory consumption (in
* bytes) of this
* object. Since sometimes
* the size of objects can
* not be determined exactly
* (for example: what is the
* memory consumption of an
* STL <tt>std::map</tt> type with a
* certain number of
* elements?), this is only
* an estimate. however often
* quite close to the true
* value.
*/
std::size_t memory_consumption () const;
/** @addtogroup Exceptions
* @{ */
/**
* Exception.
*/
DeclException0(ExcInvalidFormula);
//@}
private:
/**
* Function for differentiation.
*/
const Function<dim> &f;
/**
* Step size of the difference
* formula.
*/
double h;
/**
* Difference formula.
*/
typename AutoDerivativeFunction<dim>::DifferenceFormula formula;
/**
* Helper object. Contains the
* increment vector for the
* formula.
*/
std::vector<Point<dim> > incr;
};
DEAL_II_NAMESPACE_CLOSE
#endif
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