Functions.cc

// @sect3{Functions.cc}
// In this file we keep right hand side function, Dirichlet boundary
// conditions and solution to our Poisson equation problem.  Since
// these classes and functions have been discussed extensively in
// the deal.ii tutorials we won't discuss them any further.
#include <deal.II/base/function.h>
#include <deal.II/base/tensor_function.h>
#include <deal.II/lac/vector.h>
#include <cmath>

using namespace dealii;

template <int dim>
class RightHandSide : public Function<dim>
{
public:
    RightHandSide() : Function<dim>(1)
    {}

    virtual double value(const Point<dim> &p,
                         const unsigned int component = 0 ) const;
};

template <int dim>
class DirichletBoundaryValues : public Function<dim>
{
public:
    DirichletBoundaryValues() : Function<dim>(1)
    {}

    virtual double value(const Point<dim> &p,
                         const unsigned int component = 0 ) const;
};

template<int dim>
class TrueSolution : public Function<dim>
{
public:
    TrueSolution() : Function<dim>(dim+1)
    {}

    virtual void vector_value(const Point<dim> & p,
                              Vector<double> &valuess) const;
};

template <int dim>
double
RightHandSide<dim>::
value(const Point<dim> &p,
      const unsigned int ) const
{
    const double x = p[0];
    const double y = p[1];
    return 4*M_PI*M_PI*(cos(2*M_PI*y) - sin(2*M_PI*x));

}

template <int dim>
double
DirichletBoundaryValues<dim>::
value(const Point<dim> &p,
      const unsigned int ) const
{
    const double x = p[0];
    const double y = p[1];
    return cos(2*M_PI*y) -sin(2*M_PI*x) - x;
}


template <int dim>
void
TrueSolution<dim>::
vector_value(const Point<dim> &p,
             Vector<double> &values) const
{
    Assert(values.size() == dim+1,
           ExcDimensionMismatch(values.size(), dim+1) );

    double x = p[0];
    double y = p[1];

    values(0) = 1 + 2*M_PI*cos(2*M_PI*x);
    values(1) = 2*M_PI*sin(2*M_PI*y);

    values(2) = cos(2*M_PI*y) - sin(2*M_PI*x) - x;
}