Namespace for exact solution for Poisson equation with "sharp step". More...

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

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

void	get_exact_gradient (const Vector< double > &x, Vector< double > &dudx)
	Exact gradient as a Vector. More...

Variables
double	Alpha =100.0
	Parameter for steepness of "step". More...

Detailed Description

Namespace for exact solution for Poisson equation with "sharp step".

Function Documentation

◆ get_exact_gradient()

void ArcTanSolnForPoisson::get_exact_gradient	(	const Vector< double > &	x,
		Vector< double > &	dudx
	)

Exact gradient as a Vector.

  {
   dudx[0] = Alpha/(1.0+(Alpha*(x[0]-0.5))*(Alpha*(x[0]-0.5)));
  }

References TanhSolnForAdvectionDiffusion::Alpha, and plotDoE::x.

◆ get_exact_u()

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

Exact solution as a Vector.

  {
   u[0] = atan(Alpha*(x[0]-0.5));
  }

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

Referenced by RefineableOneDPoissonProblem< ELEMENT >::actions_before_newton_solve(), PRefineableOneDPoissonProblem< ELEMENT >::actions_before_newton_solve(), RefineableOneDPoissonProblem< ELEMENT >::doc_solution(), and PRefineableOneDPoissonProblem< ELEMENT >::doc_solution().

◆ get_source()

void ArcTanSolnForPoisson::get_source	(	const Vector< double > &	x,
		double &	source
	)

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

  {
   // Cache tan( atan(Alpha*(x[0]-0.5)) ) term
   double tan_term = tan( atan(Alpha*(x[0]-0.5)) );
   
   // Compute source function
   source = -(2.0 * Alpha*Alpha * tan_term) /
    ( (1.0 + tan_term*tan_term)*(1.0 + tan_term*tan_term) );
  }

References Alpha, Eigen::bfloat16_impl::atan(), TestProblem::source(), Eigen::bfloat16_impl::tan(), and plotDoE::x.

Referenced by main().

Variable Documentation

◆ Alpha

double ArcTanSolnForPoisson::Alpha =100.0

Parameter for steepness of "step".

Referenced by get_exact_u(), get_source(), and main().

Functions