Creates and solves the discretised Hodge Laplacian source problems and the Dirac operator source Problem for a given list of levels and values of k and compares the two solutions. More...

#include </home/nico/bildung/SemVI/thesis/lehrfempp/projects/hldo_sphere/experiments/hodge_and_dirac/hodge_and_dirac_experiment.h>

Public Member Functions
	HodgeAndDiracExperiment (std::function< complex(const Eigen::Matrix< double, 3, 1 > &)> f_zero_dirac, std::function< Eigen::Matrix< complex, 3, 1 >(const Eigen::Matrix< double, 3, 1 > &)> f_one_dirac, std::function< complex(const Eigen::Matrix< double, 3, 1 > &)> f_two_dirac, std::function< complex(const Eigen::Matrix< double, 3, 1 > &)> f_zero, std::function< Eigen::Matrix< complex, 3, 1 >(const Eigen::Matrix< double, 3, 1 > &)> f_one, std::function< complex(const Eigen::Matrix< double, 3, 1 > &)> f_two, double &k, std::string name)
	Constructor setting all the functions and the reference k. More...

void	Compute (std::vector< unsigned > refinement_levels, std::vector< double > ks)
	Solves the Hodge Laplacian and the Dirac operator source problems for the tensor product of passed refinement levels and ks. More...

Private Attributes
std::function< complex(const Eigen::Matrix< double, 3, 1 > &)>	f_zero_

std::function< Eigen::Matrix< complex, 3, 1 >(const Eigen::Matrix< double, 3, 1 > &)>	f_one_

std::function< complex(const Eigen::Matrix< double, 3, 1 > &)>	f_two_

std::function< complex(const Eigen::Matrix< double, 3, 1 > &)>	f_zero_dirac_

std::function< Eigen::Matrix< complex, 3, 1 >(const Eigen::Matrix< double, 3, 1 > &)>	f_one_dirac_

std::function< complex(const Eigen::Matrix< double, 3, 1 > &)>	f_two_dirac_

double &	k_

std::string	name_

Detailed Description

Creates and solves the discretised Hodge Laplacian source problems and the Dirac operator source Problem for a given list of levels and values of k and compares the two solutions.

In order to make this work, the load functions for the Dirac operator and Hodge Laplacians must be appropriately chosen

\[ D\, \vec{u} + \imath\, k \, \vec{u} = \vec{f} \\ \Delta\, \vec{u} + k^2\, \vec{u} = D\, \vec{f} - \imath k \, \vec{f} \]

Details about the experiments can be found in the thesis Hodge-Laplacians and Dirac Operators on the Surface of the 3-Sphere chapter 6.

Definition at line 51 of file hodge_and_dirac_experiment.h.

Constructor & Destructor Documentation

◆ HodgeAndDiracExperiment()

projects::hldo_sphere::experiments::HodgeAndDiracExperiment::HodgeAndDiracExperiment	(	std::function< complex(const Eigen::Matrix< double, 3, 1 > &)>	f_zero_dirac,
		std::function< Eigen::Matrix< complex, 3, 1 >(const Eigen::Matrix< double, 3, 1 > &)>	f_one_dirac,
		std::function< complex(const Eigen::Matrix< double, 3, 1 > &)>	f_two_dirac,
		std::function< complex(const Eigen::Matrix< double, 3, 1 > &)>	f_zero,
		std::function< Eigen::Matrix< complex, 3, 1 >(const Eigen::Matrix< double, 3, 1 > &)>	f_one,
		std::function< complex(const Eigen::Matrix< double, 3, 1 > &)>	f_two,
		double &	k,
		std::string	name
	)

inline

Constructor setting all the functions and the reference k.

Parameters

f_zero	load function to the analytical solution of (D + ik) u_zero
f_one	load function to the analytical solution (D + ik) u_one
f_two	load function to the analytical solution (D + ik) u_two
f_zero_dirac	load function equivalent to (D - ik) f_zero
f_one_dirac	load function equivalent to (D - ik) f_one
f_two_dirac	load function equivalent to (D - ik) f_two
k	reference used in all the functions such that changes of k affect the functions
name	identifier of the example (cretes a folder with this name for the results)

Definition at line 69 of file hodge_and_dirac_experiment.h.

Member Function Documentation

◆ Compute()

void projects::hldo_sphere::experiments::HodgeAndDiracExperiment::Compute	(	std::vector< unsigned >	refinement_levels,
		std::vector< double >	ks
	)

inline

Solves the Hodge Laplacian and the Dirac operator source problems for the tensor product of passed refinement levels and ks.

Parameters

refinement_levels	integer list containing all the levels
ks	list of all ks to be used

Definition at line 99 of file hodge_and_dirac_experiment.h.

Member Data Documentation

◆ f_one_

std::function<Eigen::Matrix<complex, 3, 1>( const Eigen::Matrix<double, 3, 1> &)> projects::hldo_sphere::experiments::HodgeAndDiracExperiment::f_one_

private

Definition at line 260 of file hodge_and_dirac_experiment.h.

Referenced by Compute().

◆ f_one_dirac_

std::function<Eigen::Matrix<complex, 3, 1>( const Eigen::Matrix<double, 3, 1> &)> projects::hldo_sphere::experiments::HodgeAndDiracExperiment::f_one_dirac_

private

Definition at line 265 of file hodge_and_dirac_experiment.h.

Referenced by Compute().