Co-authors: Atsushi Suzuki (1), Jean-Marc Sac-Epée (2) and Ionut Danaila (3)

(1) Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris, France.

(2) Institut Elie Cartan de Lorraine, Université de Lorraine, Metz, France.

(3) Laboratoire de mathématiques Raphaël Salem, Université de Rouen, France.

The purpose of this paper is to introduce a new robust, efficient and scalable  code: GPS (Gross-Pitaevskii Solver). GPS computes stationary and time-dependent solutions of the Gross-Pitaevskii Equation (GPE) coming from the modelling of ultracold quantum gases: Bose-Einstein Condensates (BEC), quantum turbulence. The understanding of BEC is nowadays one of the most active area in quantum physics. In order to obtain highly accurate solutions, two spectral-like discretizations (Fourier spectral and compact 6th order finite differences) of mathematical operators are implemented in GPS.

We have parallelized the code via a two-level communication scheme using MPI across nodes and OpenMP within nodes. GPS has been tested on several high performance architectures (SGI UV2000, IBM BG/Q, IBM IdataPlex) with good scalability up to 80 000 cores [1].

We first focus on the scalabilty of the code. We present strong and weak scalability tests with $512^3$, $1024^3$ and $2048^3$ grid points, and up to 20,000 MPI processes. Secondly, the capabilities of GPS are highlighted by simulating some experimental configurations requiring very high spatial resolutions (giant vortex, BEC in optical lattices, multi-component BEC).

This work was partially supported by the French ANR ANR-12-MONU-0007 BECASIM (Modèles Numériques call).

We acknowledge that the results of this research have been achieved using the GENCI Research Infrastructure resource Turing based in Orsay, France at the Institut du Développement et des Ressources en Informatique Scientifique (IDRIS/CNRS).

References:
[1] P. Parnaudeau, A. Suzuki, J-M. Sac-Epée, GPS: an efficient and spectrally accurate code for computing Gross-Pitaevskii Equation , Poster of the ISC15, 2015. 

Co-authors: Atsushi Suzuki (Université Pierre et Marie Curie), Jean-Marc Sac-Epée (Université de Lorraine) and Ionut Danaila (Université de Rouen).