Namespace for exact solution for Poisson equation. More...

Functions
void	get_exact_u (const Vector< double > &x, Vector< double > &u)
	Exact solution as a Vector. More...

void	source_function (const Vector< double > &x, double &source)
	Source function required to make the solution above an exact solution. More...

void	prescribed_flux_on_fixed_x_boundary (const Vector< double > &x, double &flux)
	Flux required by the exact solution on a boundary on which x is fixed. More...

Variables
double	Alpha =4.0
	Parameter for steepness of "step". More...

double	TanPhi =1.0
	Parameter for angle Phi of "step". More...

Detailed Description

Namespace for exact solution for Poisson equation.

/////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////////// ///////////////////////////////////////////////////////////////////////

Function Documentation

◆ get_exact_u()

void SolnForPoisson::get_exact_u	(	const Vector< double > &	x,
		Vector< double > &	u
	)

Exact solution as a Vector.

  {
   u[0]=tanh(1.0-Alpha*(TanPhi*x[0]-x[1]));
  }

References Alpha, Eigen::bfloat16_impl::tanh(), TanPhi, and plotDoE::x.

Referenced by FluxPoissonMGProblem< ELEMENT, MESH >::doc_solution().

◆ prescribed_flux_on_fixed_x_boundary()

void SolnForPoisson::prescribed_flux_on_fixed_x_boundary	(	const Vector< double > &	x,
		double &	flux
	)

Flux required by the exact solution on a boundary on which x is fixed.

  {
   // The outer unit normal to the boundary is (1,0)
   double N[2] = {1.0,0.0};
   
   // The flux in terms of the normal is
   flux = -(1.0-pow(tanh(-1.0+Alpha*(TanPhi*x[0]-x[1])),2.0))*
    Alpha*TanPhi*N[0]+(1.0-pow(tanh(-1.0+Alpha*(TanPhi*x[0]-x[1])),2.0))*
    Alpha*N[1];
  } 

References Alpha, ProblemParameters::flux(), N, Eigen::bfloat16_impl::pow(), Eigen::bfloat16_impl::tanh(), TanPhi, and plotDoE::x.

Referenced by FluxPoissonMGProblem< ELEMENT, MESH >::create_flux_elements().

◆ source_function()

void SolnForPoisson::source_function	(	const Vector< double > &	x,
		double &	source
	)

Source function required to make the solution above an exact solution.

  {
   source = 2.0*tanh(-1.0+Alpha*(TanPhi*x[0]-x[1]))*
    (1.0-pow(tanh(-1.0+Alpha*(TanPhi*x[0]-x[1])),2.0))*
    Alpha*Alpha*TanPhi*TanPhi+2.0*tanh(-1.0+Alpha*(TanPhi*x[0]-x[1]))*
    (1.0-pow(tanh(-1.0+Alpha*(TanPhi*x[0]-x[1])),2.0))*Alpha*Alpha;
  }