Nonconstant Dirichlet BC (04-bc-dirichlet)¶

Let us keep the equation from the previous example P01/03-poisson,

(1) $-\mbox{div}(\lambda \nabla u) - C_{src} = 0,$

but the boundary conditions will be modified to

$u(x, y) = Ax + By + C$

where $A$ , $B$ and $C$ are real constants.

Subclassing EssentialBoundaryCondition¶

This is done by defining a descendant of the EssentialBoundaryCondition class:

class CustomDirichletCondition : public EssentialBoundaryCondition<double>
{
public:
  CustomDirichletCondition(Hermes::vector<std::string> markers, double A, double B, double C);

  virtual EssentialBoundaryCondition<double>::EssentialBCValueType get_value_type() const;

  virtual double value(double x, double y, double n_x, double n_y, double t_x, double t_y) const;

  protected:
    double A, B, C;
};

The methods are defined in the file definitions.cpp as follows:

CustomDirichletCondition::CustomDirichletCondition(Hermes::vector<std::string> markers,
                                                   double A, double B, double C)
  : EssentialBoundaryCondition<double>(markers), A(A), B(B), C(C)
{
}

EssentialBoundaryCondition<double>::EssentialBCValueType CustomDirichletCondition::get_value_type() const
{
  return EssentialBoundaryCondition<double>::BC_FUNCTION;
}

double CustomDirichletCondition::value(double x, double y, double n_x, double n_y,
                                       double t_x, double t_y) const
{
  return A*x + B*y + C;
}

The custom boundary condition class is used as follows:

// Initialize boundary conditions.
CustomDirichletCondition bc_essential(Hermes::vector<std::string>("Bottom", "Inner", "Outer", "Left"),
                                      BDY_A_PARAM, BDY_B_PARAM, BDY_C_PARAM);
EssentialBCs<double> bcs(&bc_essential);