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

Functions
double	scalar_soln (const Vector< double > &x)
	Scalar solution. More...

double	scalar_source (const Vector< double > &x)
	Scalar source. More...

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

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

Variables
double	Alpha =5.0
	Parameter for steepness of "step". More...

double	TanPhi =1.0
	Parameter for angle Phi of "step" (45 degrees) More...

double	Beta =1.0
	Interaction parameter. More...

Detailed Description

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

Function Documentation

◆ get_exact_u()

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

Exact solution as a Vector.

  {
   double u_scalar=scalar_soln(x);
   for (unsigned i=0;i<N_FIELD;i++)
    {
     u[i]=double(i+1)*u_scalar;
    }
  }

References i, N_FIELD, scalar_soln(), and plotDoE::x.

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

◆ scalar_soln()

double TanhSolnForMultiPoisson::scalar_soln ( const Vector< double > & x )

Scalar solution.

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

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

Referenced by get_exact_u(), and source_function().

◆ scalar_source()

double TanhSolnForMultiPoisson::scalar_source ( const Vector< double > & x )

Scalar source.

  {
   return 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;
  }

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

Referenced by source_function().

◆ source_function()

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

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

  {
   double scalar_f=scalar_source(x);
   double scalar_u=scalar_soln(x);
   for (unsigned i=0;i<N_FIELD;i++)
    {
     source[i] = double(i+1)*scalar_f;
     for (unsigned k=0;k<N_FIELD;k++)
      {
       source[i]+=Beta*double(k+1)*scalar_u;
      }
     source[i]*=double(i+1);
    }
  }