fGPE — A Fast Gross–Pitaevskii Equation Solver

version: 0.3

fGPE is a high-performance solver for the Gross–Pitaevskii equation (GPE), designed for fast and accurate simulation of Bose–Einstein condensates.

The solver can be extended to user-specific Hamiltonians that include e.g. dipolar interactions of soft-core potential.

• ⚡ High-performance GPE integration using optimized numerical schemes
• 🧮 Supports imaginary-time evolution and real-time dynamics
• 📦 Modular architecture for extending potentials
• 📈 Stable for long-time simulations thanks to RK4 integration algorithm.
• 🔧 Easy configuration via input files

The stationary solution of a given problem is found by minimizing the energy of a system defined with user-defined (or predefined) energy density functional ( \mathcal{E} ).

The solver integrates the time-dependent Gross–Pitaevskii equation:

$$ i\hbar \frac{\partial \psi}{\partial t} = \left( -\frac{\hbar^2}{2m} \nabla^2 + V(\mathbf{r}) + g|\psi|^2 \right)\psi $$

Includes options for:

• Harmonic, box, or custom potentials
• Interaction strengths
• Normalized wavefunctions
• 1D, 2D, or 3D domains (depending on your implementation)

• CUDA version > 11

• Imaginary-time evolution:

make
./gpe input.txt

• Real-time evolution:

make
./gpe rinput.txt