NLSEmagic: Nonlinear Schr?dinger equation multi-dimensional Matlab-based GPU-accelerated integrators using compact high-order schemes

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• 作者：R.M. Caplan ; ^{sumseq@gmail.com} ; ^{caplanr@predsci.com} ;
• 关键词：Nonlinear Schrö ; dinger equation ; Bose&ndash ; Einstein condensates ; GPU ; GPGPU ; Explicit finite difference schemes
• 刊名：Computer Physics Communications
• 出版年：2013
• 出版时间：April, 2013
• 年：2013
• 卷：184
• 期：4
• 页码：1250-1271
• 全文大小：1063 K

文摘

We present a simple to use, yet powerful code package called NLSEmagic to numerically integrate the nonlinear Schr?dinger equation in one, two, and three dimensions. NLSEmagic is a high-order finite-difference code package which utilizes graphic processing unit (GPU) parallel architectures. The codes running on the GPU are many times faster than their serial counterparts, and are much cheaper to run than on standard parallel clusters. The codes are developed with usability and portability in mind, and therefore are written to interface with MATLAB utilizing custom GPU-enabled C codes with the MEX-compiler interface. The packages are freely distributed, including user manuals and set-up files.

Program summary

Program title: NLSEmagic

Catalogue identifier: AEOJ_v1_0

Program summary URL:

Program obtainable from: CPC Program Library, Queen¡¯s University, Belfast, N. Ireland

Licensing provisions: Standard CPC licence,

No. of lines in distributed program, including test data, etc.: 124453

No. of bytes in distributed program, including test data, etc.: 4728604

Distribution format: tar.gz

Programming language: C, CUDA, MATLAB.

Computer: PC, MAC.

Operating system: Windows, MacOS, Linux.

Has the code been vectorized or parallelized?: Yes.

Number of processors used: Single CPU, number of GPU processors dependent on chosen GPU card (max is currently 3072 cores on GeForce GTX 690).

Supplementary material: Setup guide, Installation guide.

RAM: Highly dependent on dimensionality and grid size. For typical medium-large problem size in three dimensions, 4GB is sufficient.

Keywords: Nonlinear Schr?odinger Equation, GPU, high-order finite difference, Bose-Einstien condensates.

Classification: 4.3, 7.7.

Nature of problem:

Integrate solutions of the time-dependent one-, two-, and three-dimensional cubic nonlinear Schr?dinger equation.

Solution method:

The integrators utilize a fully-explicit fourth-order Runge-Kutta scheme in time and both second- and fourth-order differencing in space. The integrators are written to run on NVIDIA GPUs and are interfaced with MATLAB including built-in visualization and analysis tools.

Restrictions:

The main restriction for the GPU integrators is the amount of RAM on the GPU as the code is currently only designed for running on a single GPU.

Unusual features:

Ability to visualize real-time simulations through the interaction of MATLAB and the compiled GPU integrators.

Additional comments:

Setup guide and Installation guide provided. Program has a dedicated web site at .

Running time:

A three-dimensional run with a grid dimension of 87¡Á87¡Á203 for 3360 time steps (100 non-dimensional time units) takes about one and a half minutes on a GeForce GTX 580 GPU card.