example_01.cpp File Reference

Minimize the Gross-Pitaevskii functional and demonstrate the effect of choice of function space of the Gradient on convergence. More...

#include "example_01.hpp"
#include "ROL_ConstraintStatusTest.hpp"
#include "ROL_CompositeStep.hpp"

Go to the source code of this file.

Functions
int	main (int argc, char **argv)

Detailed Description

Minimize the Gross-Pitaevskii functional and demonstrate the effect of choice of function space of the Gradient on convergence.

Minimize the one-dimensional Gross-Pitaevskii (GP) energy functional

\[ J[\psi] = \int \frac{1}{2} |\nabla\psi|^2 + V(x)|\psi|^2 +g|\psi|^4 \,\mathrm{d}x \]

Subject to the equality constraint that the particle density be normalized.

\[ e(\psi) = \int |\psi|^2\,\mathrm{d}x - 1 = 0 \]

For simplicity, we will assume the wavefunction \(\psi\) to be real-valued, the potential function \( V(x)\geq 0\), the computational domain is the interval \([0,1]\), and that \(\psi(0)=\psi(1)=0\). We also discretize the problem using second-order centered finite differences on a uniform grid.

\[ \psi''(x_i) \approx = \frac{\psi(x_{i-1})-2\psi(x_i)+\psi(x_{i+1})}{\Delta x^2} \]

Author

Greg von Winckel

Date

Mon Dec 1 12:55:12 MST 2014

Definition in file gross-pitaevskii/example_01.cpp.

Function Documentation

main()

int main	(	int	argc,
		char **	argv )

Definition at line 42 of file gross-pitaevskii/example_01.cpp.