C programs for solving the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap

TL;DR

This paper provides C language implementations of algorithms for solving the time-dependent Gross-Pitaevskii equation in various trap geometries, including parallelized versions for efficient multi-core computation, enhancing simulation speed and flexibility.

Contribution

The authors developed and optimized C programs, including threaded versions, for solving the Gross-Pitaevskii equation in multiple dimensions and trap configurations, based on previously published Fortran codes.

Findings

Almost linear speedup with multi-core parallelization

Significant reduction in execution times on modern CPUs

Validated accuracy of the C implementations

Abstract

We present C programming language versions of earlier published Fortran programs (Muruganandam and Adhikari, Comput. Phys. Commun. 180 (2009) 1888) for calculating both stationary and non-stationary solutions of the time-dependent Gross-Pitaevskii (GP) equation. The GP equation describes the properties of dilute Bose-Einstein condensates at ultra-cold temperatures. C versions of programs use the same algorithms as the Fortran ones, involving real- and imaginary-time propagation based on a split-step Crank-Nicolson method. In a one-space-variable form of the GP equation, we consider the one-dimensional, two-dimensional, circularly-symmetric, and the three-dimensional spherically-symmetric harmonic-oscillator traps. In the two-space-variable form, we consider the GP equation in two-dimensional anisotropic and three-dimensional axially-symmetric traps. The fully-anisotropic three-dimensional GP equation is also considered. In addition to these twelve programs, for six algorithms that involve two and three space variables, we have also developed threaded (OpenMP parallelized) programs, which allow numerical simulations to use all available CPU cores on a computer. All 18 programs are optimized and accompanied by makefiles for several popular C compilers. We present typical results for scalability of threaded codes and demonstrate almost linear speedup obtained with the new programs, allowing a decrease in execution times by an order of magnitude on modern multi-core computers.