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// ---------------------------------------------------------------------
//
// Copyright (C) 2000 - 2016 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.
//
// ---------------------------------------------------------------------
#include <deal.II/base/point.h>
#include <deal.II/base/function_derivative.h>
#include <deal.II/lac/vector.h>
#include <cmath>
DEAL_II_NAMESPACE_OPEN
template <int dim>
FunctionDerivative<dim>::FunctionDerivative (const Function<dim> &f,
const Point<dim> &dir,
const double h)
:
AutoDerivativeFunction<dim> (h, f.n_components, f.get_time()),
f(f),
h(h),
incr(1, h *dir)
{
set_formula();
}
template <int dim>
FunctionDerivative<dim>::FunctionDerivative (const Function<dim> &f,
const std::vector<Point<dim> > &dir,
const double h)
:
AutoDerivativeFunction<dim> (h, f.n_components, f.get_time()),
f(f),
h(h),
incr(dir.size())
{
for (unsigned int i=0; i<incr.size (); ++i)
incr[i] = h*dir[i];
set_formula();
}
template <int dim>
void
FunctionDerivative<dim>::set_formula (typename AutoDerivativeFunction<dim>::DifferenceFormula form)
{
// go through all known formulas, reject ones we don't know about
// and don't handle in the member functions of this class
switch (form)
{
case AutoDerivativeFunction<dim>::Euler:
case AutoDerivativeFunction<dim>::UpwindEuler:
case AutoDerivativeFunction<dim>::FourthOrder:
break;
default:
Assert(false, ExcMessage("The argument passed to this function does not "
"match any known difference formula."));
}
formula = form;
}
template <int dim>
void
FunctionDerivative<dim>::set_h (const double new_h)
{
for (unsigned int i=0; i<incr.size (); ++i)
incr[i] *= new_h/h;
h = new_h;
}
template <int dim>
double
FunctionDerivative<dim>::value (const Point<dim> &p,
const unsigned int component) const
{
Assert (incr.size() == 1,
ExcMessage ("FunctionDerivative was not initialized for constant direction"));
switch (formula)
{
case AutoDerivativeFunction<dim>::Euler:
return (f.value(p+incr[0], component)-f.value(p-incr[0], component))/(2*h);
case AutoDerivativeFunction<dim>::UpwindEuler:
return (f.value(p, component)-f.value(p-incr[0], component))/h;
case AutoDerivativeFunction<dim>::FourthOrder:
return (-f.value(p+2*incr[0], component) + 8*f.value(p+incr[0], component)
-8*f.value(p-incr[0], component) + f.value(p-2*incr[0], component))/(12*h);
default:
Assert(false, ExcNotImplemented());
}
return 0.;
}
template <int dim>
void
FunctionDerivative<dim>::vector_value (
const Point<dim> &p,
Vector<double> &result) const
{
Assert (incr.size() == 1,
ExcMessage ("FunctionDerivative was not initialized for constant direction"));
Vector<double> aux(result.size());
// Formulas are the same as in
// value, but here we have to use
// Vector arithmetic
switch (formula)
{
case AutoDerivativeFunction<dim>::Euler:
f.vector_value(p+incr[0], result);
f.vector_value(p-incr[0], aux);
result.sadd(1./(2*h), -1./(2*h), aux);
return;
case AutoDerivativeFunction<dim>::UpwindEuler:
f.vector_value(p, result);
f.vector_value(p-incr[0], aux);
result.sadd(1./h, -1./h, aux);
return;
case AutoDerivativeFunction<dim>::FourthOrder:
f.vector_value(p-2*incr[0], result);
f.vector_value(p+2*incr[0], aux);
result.add(-1., aux);
f.vector_value(p-incr[0], aux);
result.add(-8., aux);
f.vector_value(p+incr[0], aux);
result.add(8., aux);
result/=(12.*h);
return;
default:
Assert(false, ExcNotImplemented());
}
}
template <int dim>
void
FunctionDerivative<dim>::value_list (const std::vector<Point<dim> > &points,
std::vector<double> &values,
const unsigned int component) const
{
const unsigned int n = points.size();
const bool variable_direction = (incr.size() == 1) ? false : true;
if (variable_direction)
Assert (incr.size() == points.size(),
ExcDimensionMismatch(incr.size(), points.size()));
// Vector of auxiliary values
std::vector<double> aux(n);
// Vector of auxiliary points
std::vector<Point<dim> > paux(n);
// Use the same formulas as in
// value, but with vector
// arithmetic
switch (formula)
{
case AutoDerivativeFunction<dim>::Euler:
for (unsigned int i=0; i<n; ++i)
paux[i] = points[i]+incr[(variable_direction) ? i : 0U];
f.value_list(paux, values, component);
for (unsigned int i=0; i<n; ++i)
paux[i] = points[i]-incr[(variable_direction) ? i : 0U];
f.value_list(paux, aux, component);
for (unsigned int i=0; i<n; ++i)
values[i] = (values[i]-aux[i])/(2*h);
return;
case AutoDerivativeFunction<dim>::UpwindEuler:
f.value_list(points, values, component);
for (unsigned int i=0; i<n; ++i)
paux[i] = points[i]-incr[(variable_direction) ? i : 0U];
f.value_list(paux, aux, component);
for (unsigned int i=0; i<n; ++i)
values[i] = (values[i]-aux[i])/h;
return;
case AutoDerivativeFunction<dim>::FourthOrder:
for (unsigned int i=0; i<n; ++i)
paux[i] = points[i]-2*incr[(variable_direction) ? i : 0U];
f.value_list(paux, values, component);
for (unsigned int i=0; i<n; ++i)
paux[i] = points[i]+2*incr[(variable_direction) ? i : 0U];
f.value_list(paux, aux, component);
for (unsigned int i=0; i<n; ++i)
values[i] -= aux[i];
for (unsigned int i=0; i<n; ++i)
paux[i] = points[i]+incr[(variable_direction) ? i : 0U];
f.value_list(paux, aux, component);
for (unsigned int i=0; i<n; ++i)
values[i] += 8.*aux[i];
for (unsigned int i=0; i<n; ++i)
paux[i] = points[i]-incr[(variable_direction) ? i : 0U];
f.value_list(paux, aux, component);
for (unsigned int i=0; i<n; ++i)
values[i] = (values[i] - 8.*aux[i])/(12*h);
return;
default:
Assert(false, ExcNotImplemented());
}
}
template <int dim>
std::size_t
FunctionDerivative<dim>::memory_consumption () const
{
// only simple data elements, so
// use sizeof operator
return sizeof (*this);
}
// explicit instantiations
template class FunctionDerivative<1>;
template class FunctionDerivative<2>;
template class FunctionDerivative<3>;
DEAL_II_NAMESPACE_CLOSE
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