Gross-Pitaevskii-FDM

For details about code, refer documentation page

• Overview
  • Equation
  • Physics
• Installation
  • Dependencies
  • Build
• Execution
  • Generate configuration file
  • Execute single condition
  • Execute multiple conditions with MPI
  • Save data
  • Visualization
• Example results

Overview

Equation

The time-dependent Gross-Pitaevskii equation is $$𝑖ℏ \frac{𝜕Ψ(𝒓, 𝑡)}{𝜕𝑡}=(−\frac{ ℏ^2}{2𝑚} ∇^2+𝑉(𝒓)+𝑔 |Ψ(𝒓,𝑡)|^2 )Ψ(𝒓, 𝑡)$$ g parameter is correlated to interactions of particles.
In this project, the equation is solved numerically with various initial condition, potential values, and g values in a parallel manner.

Physics

Bose-Einstein condensate(BEC) is a state of matter of a dilute gas of bosons cooled to temperatures very close to absolute zero.
Under such conditions, bosons condensate to the same ground state.
The Gross-Pitaevskii equation is an approximation model of BEC.
In Hartree-Fock approximation, many body equation is turned to one body equation. Also, in the partial-wave analysis, scattering process between each bosons are approximated by the s-wave scattering.

Installation

Dependencies

• C++ 17
• Cmake version >= 3.5
• MPICH2
• Nvidia CUDA toolkit version == 11.7
• gtest

Build

The build configuration is created with CMake.
To create build configuration in this project, create a build directory in the project directory.
Then, in the build directory, use cmake command to create build configuraiton as below.

mkdir build 
cd build 
cmake ..

To build, execute:

make

Check that if the two programs are generated.

GrossPitaevskiiFDM_run  
GrossPitaevskiiFDM_tst   

GrossPitaevskiiFDM_run is the main program and GrossPitaevskiiFDM_tst is the test program.
You can use GrossPitaevskiiFDM_tst to test the code and debug.
The test program should be run with MPI.

mpiexec -np 2 ./GrossPitaevskiiFDM_tst

Execution

Generate configuration file

In the inputs directory, there are three example configuration files.

benchmarking.inp
example_single.inp
example_sweep.inp

If you want to run the codes in a single condition(initial condition, potential, parameter g), use example_single.inp as a template.
There are following parameters to set.

• Main Configuration
• Domain Configuration
• Initial Condition Configuration
• Equation Configuration
• Solver Configuration

For the details, refer to the code description.
Especially, if you want to use GPU to accelerate the execution, set parallel as true and set cuda_device = {device number} in Solver Configuration.
For example,

  parallel = true
   ...
  cuda_device = 0 

Execute single condition

To execute the program, in the build directory run ./GrossPitaevskiiFDM_run with the generated configurated file.

{PATH_TO_PROGRAM}/GrossPitaevskiiFDM_run {PATH_TO_INPUT_CONFIGURATION}.inp

For example,

./build/GrossPitaevskiiFDM_run ./inputs/example_single.inp

Execute multiple conditions with MPI

To execute the program, in the build directory run ./GrossPitaevskiiFDM_run with the generated configurated file. If you want to execute the program with various condition parallely, use MPI.
You have to run the program with mpiexec and set the {PROCESSOR_NUMBER} which is the number of processors that you want to use.

mpiexec -np {PROCESSOR_NUMBER} {PATH_TO_PROGRAM}/GrossPitaevskiiFDM_run {PATH_TO_INPUT_CONFIGURATION}.inp

For example,

mpiexec -np 4 ./build/GrossPitaevskiiFDM_run ./inputs/example_sweep.inp

Save data

If you run the code with save_info=true, it creates new folder under results directory.
Time log is included in folder name. Also, if you run parallely, the folder name contains the rank of the processor executed the program.
If you want to manage folder name, give the string parameter that contains folder name in solve method in solver class.
For example, in results directory, following directory is created.

'2022-06-09-17-29-26_Crank_Nicolson_parallel_MPI&CUDA_0'

In the directory, txt file is generated for each time step. It contains the spatial grid info and wave function values(real and imaginary).

Visualization

Generated output file could be directly loaded by ParaView. By using Filters>Alphabetical>Table to Points and Filters>Alphabetical>Delaunary 2D successively, you could visualize the result data in 2D heatmap without any scripting.

Example results

1. Below GIF is result from .inputs/swing.inp.

2. Below GIF is result from .inputs/asym_init.inp.