MADNESS: siam_example.cc File Reference

MADNESS 0.10.1

examples

A simple example of solving PDEs with MADNESS. More...

#include <madness/mra/mra.h>
#include <madness/constants.h>
#include <madness/mra/nonlinsol.h>

Include dependency graph for siam_example.cc:

Classes
class	DSphere
	Functor representing the log-derivative of $\epsilon$ along an axis. More...

Functions
int	main (int argc, char **argv)
	Main function. Project the functions and solve the PDE.

double	rho_function (const coord_3d &r)
	Function that provides the charge density, $\rho$ .

Variables
const double	eps_ext =10.0
	Exterior dielectric.

const double	eps_int = 1.0
	Interior dielectric.

const double	R = 2.0
	Radius of sphere.

const double	sigma = 0.1
	Surface "width".

const double	xi = 100.0
	Exponent for delta function approx.

Detailed Description

A simple example of solving PDEs with MADNESS.

This example solves Poisson's equation for a system with an inhomogeneous dielectric constant,

$\nabla \cdot{} \left[ \epsilon(\vec{r}) \nabla u(\vec{r}) \right] = - 4 \pi \rho(\vec{r}).$

$\epsilon(\vec{r}) = \epsilon_\mathrm{int}$ for $|\vec{r}| < R$ and $\epsilon(\vec{r}) = \epsilon_\mathrm{ext}$ for $|\vec{r}| > R.$ The PDE is converted to a fixed point iteration using the Green's function for the Laplacian (with free-space boundary conditions) and then solved using a fixed point iteration.

Other objectives are to demonstrate the use of functors when projecting MADNESS functions.

Function Documentation

◆ main()

int main	(	int	argc,
		char **	argv
	)

Main function. Project the functions and solve the PDE.

Parameters

[in]	argc	The number of command-line arguments.
[in]	argv	The command-line arguments.

Returns: Exit status.

References SafeMPI::COMM_WORLD, madness::CoulombOperator(), e(), eps_ext, eps_int, madness::finalize(), madness::initialize(), lo, madness::norm2(), op(), madness::constants::pi, madness::plot_line(), madness::print(), rho_function(), madness::FunctionDefaults< NDIM >::set_cubic_cell(), madness::FunctionDefaults< NDIM >::set_initial_level(), madness::FunctionDefaults< NDIM >::set_k(), madness::FunctionDefaults< NDIM >::set_thresh(), madness::FunctionDefaults< NDIM >::set_truncate_on_project(), madness::startup(), madness::Function< T, NDIM >::trace(), madness::truncate(), and u().

◆ rho_function()

double rho_function ( const coord_3d & r )

Function that provides the charge density, $\rho$ .

Parameters

[in] r The coordinate at which to evaluate the function.

Returns: The value of $\rho$ at the point.

References madness::constants::pi, pow(), and xi.

Referenced by main().

Variable Documentation

◆ eps_ext

const double eps_ext =10.0

Exterior dielectric.

Referenced by main().

◆ eps_int

const double eps_int = 1.0

Interior dielectric.

Referenced by main().

◆ R

const double R = 2.0

Radius of sphere.

◆ sigma

const double sigma = 0.1

Surface "width".

◆ xi

const double xi = 100.0

Exponent for delta function approx.

Referenced by madness::Nemo::compute_all_cphf(), madness::PNO::compute_cispd_correction_es(), madness::PNO::compute_cispd_correction_gs(), madness::PNO::compute_cispd_f12_correction_es(), madness::PNO::compute_cispd_f12_correction_gs(), madness::F12Potentials::compute_cispd_f12_energies(), madness::PNO::compute_cispd_fluctuation_matrix(), madness::PNO::compute_cispd_fluctuation_potential(), madness::response_space::copy(), madness::Molecule::core_derivative(), madness::CorePotentialManager::core_derivative(), madness::Molecule::core_potential_derivative(), madness::create_response_matrix(), madness::FunctionImpl< T, NDIM >::eval(), madness::CorePotential::eval_derivative(), madness::CoreOrbital::eval_derivative(), madness::FunctionImpl< T, NDIM >::eval_local_only(), madness::CoreOrbital::eval_radial_derivative(), madness::FunctionImpl< T, NDIM >::evaldepthpt(), madness::FunctionImpl< T, NDIM >::evalR(), madness::PNO::grow_rank(), madness::Nemo::hessian(), madness::PNO::initialize_pairs(), madness::Nemo::make_incomplete_hessian_response_part(), madness::TDHF::make_potentials(), madness::make_radius(), molresponseExchange(), madness::MomentFunctor::operator()(), madness::CorePotentialManager::potential_derivative(), rho_function(), madness::NuclearCorrelationFactor::smoothed_unitvec(), madness::Nemo::solve_cphf(), sympgrad4(), madness::to_conjugate_X_space(), madness::TDHF::transform(), and madness::transposeResponseMatrix().