Solves the spin-orbit nuclear potential problem. More...

#include <madness/mra/mra.h>
#include <madness/mra/vmra.h>
#include <madness/mra/operator.h>
#include <madness/constants.h>

Include dependency graph for vnucso.cc:

Typedefs
typedef Vector< double, 3 >	coordT

typedef std::shared_ptr < FunctionFunctorInterface < double, 3 > >	real_functorT

typedef std::shared_ptr < FunctionFunctorInterface < double_complex, 3 > >	complex_functorT

typedef Function< double, 3 >	real_functionT

typedef Function < double_complex, 3 >	complex_functionT

typedef FunctionFactory < double, 3 >	real_factoryT

typedef FunctionFactory < double_complex, 3 >	complex_factoryT

typedef SeparatedConvolution < double, 3 >	operatorT

typedef std::shared_ptr < operatorT >	poperatorT

Functions
void	moments (World &world, const std::vector< complex_functionT > &u, const std::vector< complex_functionT > &v)

void	gaxpy1 (World &world, const double_complex alpha, std::vector< complex_functionT > &a, const double_complex beta, const std::vector< complex_functionT > &b, bool fence=true)

std::vector< poperatorT >	make_bsh_operators (World &world, const Tensor< double > &evals, double tol)

Tensor< double_complex >	hamiltonian_matrix (World &world, const std::vector< complex_functionT > &u, const std::vector< complex_functionT > &v, const std::vector< complex_functionT > &Vu, const std::vector< complex_functionT > &Vv, const std::vector< complex_functionT > du[3], const std::vector< complex_functionT > dv[3])

void	apply_potential (World &world, const real_functionT &V0, const real_functionT &V0x, const real_functionT &V0y, const real_functionT &V0z, const std::vector< complex_functionT > &u, const std::vector< complex_functionT > &v, std::vector< complex_functionT > &Vu, std::vector< complex_functionT > &Vv, std::vector< complex_functionT > du[3], std::vector< complex_functionT > dv[3], bool doso)

void	normalize2 (World &world, std::vector< complex_functionT > &u, std::vector< complex_functionT > &v)

void	doit (World &world)

int	main (int argc, char **argv)

Variables
const double	L = 120.0

const double	zeta = 7.5

const double	R1 = 2.0

const double	R2 = 2.0

const double	a1 = 1.0

const double	a2 = 1.0

const double	reduced = 0.04825964488415279478

const double	V1 = -50.0*reduced

const double	V2 = -50.0*reduced

const double	lambda_correct = 0.0026608048208104861/reduced

Detailed Description

Solves the spin-orbit nuclear potential problem.

Solves the Hartree-Fock equation for the 2-cosh potential with spin-orbit in Nuclear Density Functional Theory witough assumption on spatial symmetry.

Points of interest.

Forming a Hamiltonian and a Fock matrix
Forming and solving a generalized eigensystem problem using LAPACK
Refining the representation of real and complex functions
Vectors of functions and operators, inner-product, gaxpy
Application of the Helmholtz bound-state Green function as vector of operators and functions
Projection and change of representation of functions from multiwavelets of degree k to k+1

The source is here.

This is a more involved example than the Hydrogen and Helium. This example couples the traditional diagonalization approach with that of the integral equation approach. The details are described in: G. I. Fann , J. Pei, R. J. Harrison1, J. Jia, J. Hill1 , M. Ou, W. Nazarewicz, W. A. Shelton and N. Schunck, "Fast multiresolution methods for density functional theory in nuclear physics," Journal of Physics, 180 (2009) 012080.

Typedef Documentation

typedef FunctionFactory<double_complex,3> complex_factoryT

typedef Function<double_complex,3> complex_functionT

typedef std::shared_ptr< FunctionFunctorInterface<double_complex,3> > complex_functorT

typedef Vector<double,3> coordT

typedef SeparatedConvolution<double,3> operatorT

typedef std::shared_ptr<operatorT> poperatorT

typedef FunctionFactory<double,3> real_factoryT

typedef Function<double,3> real_functionT

typedef std::shared_ptr< FunctionFunctorInterface<double,3> > real_functorT

Function Documentation

void apply_potential	(	World &	world,
		const real_functionT &	V0,
		const real_functionT &	V0x,
		const real_functionT &	V0y,
		const real_functionT &	V0z,
		const std::vector< complex_functionT > &	u,
		const std::vector< complex_functionT > &	v,
		std::vector< complex_functionT > &	Vu,
		std::vector< complex_functionT > &	Vv,
		std::vector< complex_functionT >	du[3],
		std::vector< complex_functionT >	dv[3],
		bool	doso
	)

References madness::apply(), madness::gaxpy(), I(), madness::mul(), one(), madness::reconstruct(), and madness::Function< T, NDIM >::reconstruct().

Referenced by doit().

void doit ( World & world )

References madness::add(), madness::apply(), apply_potential(), c, e1(), madness::WorldGopInterface::fence(), madness::World::gop, hamiltonian_matrix(), k, L, make_bsh_operators(), madness::matrix_inner(), max, moments(), madness::norm2s(), normalize2(), madness::print(), madness::project(), madness::World::rank(), madness::reconstruct(), reduced, madness::FunctionDefaults< NDIM >::set_autorefine(), madness::FunctionDefaults< NDIM >::set_cubic_cell(), madness::FunctionDefaults< NDIM >::set_initial_level(), madness::FunctionDefaults< NDIM >::set_k(), madness::FunctionDefaults< NDIM >::set_refine(), madness::FunctionDefaults< NDIM >::set_thresh(), madness::FunctionDefaults< NDIM >::set_truncate_mode(), sqrt(), madness::sygv(), thresh, madness::transform(), madness::truncate(), V(), madness::wall_time(), and zeta.

Referenced by main().

void gaxpy1	(	World &	world,
		const double_complex	alpha,
		std::vector< complex_functionT > &	a,
		const double_complex	beta,
		const std::vector< complex_functionT > &	b,
		bool	fence = `true`
	)

References madness::WorldGopInterface::fence(), and madness::World::gop.

Tensor<double_complex> hamiltonian_matrix	(	World &	world,
		const std::vector< complex_functionT > &	u,
		const std::vector< complex_functionT > &	v,
		const std::vector< complex_functionT > &	Vu,
		const std::vector< complex_functionT > &	Vv,
		const std::vector< complex_functionT >	du[3],
		const std::vector< complex_functionT >	dv[3]
	)