Graphics processor unit (GPU) acceleration of finite-difference time-domain (FDTD) algorithm

Krakiwsky, S.E.; Turner, L.E.; Okoniewski, M.

doi:10.1109/iscas.2004.1329513

Cited by 25 publications

(26 citation statements)

References 6 publications

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“…7.3 and 7.4, in higher dimensions, this issue is somewhat minimized due to the added number of points in the second-order Laplacian stencil (the speedup reduction is lowered from 27% in one dimension to 16% in three dimensions in single precision, and from 45% to 0% in double precision). 4. Since there is no analytical solution to the dark vortex, and moreover, since we are using only an approximation of the true solution, we cannot record the error of the runs.…”

Section: One-dimensional Speedup Resultsmentioning

confidence: 99%

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

Caplan

2013

Computer Physics Communications

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We present a simple to use, yet powerful code package called NLSEmagic to numerically integrate the nonlinear Schrödinger 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 GPUenabled C codes with the MEX-compiler interface. The packages are freely distributed, including user manuals and set-up files. The integrators utilize a fully-explicit fourth-order Runge-Kutta scheme in time and both second-and fourthorder 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:Program has a dedicated web site at www.nlsemagic.com. Running time:A three-dimensional run with a grid dimension of 87x87x203 for 3360 time steps (100 non-dimensional time units) takes about one and a half minutes on a GeForce GTX 580 GPU card.

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Section: One-dimensional Speedup Resultsmentioning

confidence: 99%

“…GPUs have been used for various finite-difference PDE integrator codes with good results [4][5][6][7][8][9]. In Ref.…”

Section: Introductionmentioning

confidence: 99%

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

Caplan

2013

Computer Physics Communications

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“…The discrete method of the core-shooting numerical simulation program is finite difference. Krakiwsky et al studied the finite difference time domain method with a GPU parallelization method, and good performance of GPU parallelization method has been proved in the improvement of computing efficiency and reliable simulation results [14,15] . In the casting field, simulation studies based on GPU have achieved some breakthroughs in the solidification process [16,17] , but the core shooting process is close to an isothermal process while the studies about the core shooting process are relatively limited.…”

mentioning

confidence: 99%

“…A parallel program was developed to simulate a relatively simple test-piece, and the algorithm was improved in the process. In the GPU parallelization method, data delay and model capability of parallelization have a great influence on the improvement of computing efficiency [10][11][12][13][14][15] .…”

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confidence: 99%

GPU based numerical simulation of core shooting process

Zhang

et al. 2017

China Foundry

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“…GPUs have been used for various finite-difference scheme codes with good results [73][74][75][76][77][78]. In Ref.…”

Section: Code Parallelism With Graphics Processing Unitsmentioning

confidence: 99%

Study of Vortex Ring Dynamics in the Nonlinear Schrödinger Equation Utilizing GPU-Accelerated High-Order Compact Numerical Integrators

Carretero-González

Caplan

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We numerically study the dynamics and interactions of vortex rings in the nonlinear Schrödinger equation (NLSE). Single ring dynamics for both bright and dark vortex rings are explored including their traverse velocity, stability, and perturbations resulting in quadrupole oscillations. Multi-ring dynamics of dark vortex rings are investigated, including scattering and merging of two colliding rings, leapfrogging interactions of co-traveling rings, as well as co-moving steady-state multi-ring ensembles.Simulations of choreographed multi-ring setups are also performed, leading to intriguing interaction dynamics.Due to the inherent lack of a closed form solution for vortex rings and the dimensionality where they live, efficient numerical methods to integrate the NLSE have to be developed in order to perform the extensive number of required simulations. To facilitate this, compact high-order numerical schemes for the spatial derivatives are developed which include a new semi-compact modulus-squared Dirichlet boundary condition. The schemes are combined with a fourth-order Runge-Kutta time-stepping scheme in order to keep the overall method fully explicit. To ensure efficient use of the schemes, a stability analysis is performed to find bounds on the largest usable time step-size as a function of the spatial step-size.The numerical methods are implemented into codes which are run on NVIDIA graphic processing unit (GPU) parallel architectures. The codes running on the GPU are shown to be many times faster than their serial counterparts. The codes are developed with future usability in mind, and therefore are written to interface with MATLAB utilizing custom GPU-enabled C codes with a MEX-compiler interface. The codes are combined into a software package called NLSEmagic which is freely distributed on a dedicated website allowing reproducibility of the simulations presented in the study.vi

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Graphics processor unit (GPU) acceleration of finite-difference time-domain (FDTD) algorithm

Cited by 25 publications

References 6 publications

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

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

GPU based numerical simulation of core shooting process

Study of Vortex Ring Dynamics in the Nonlinear Schrödinger Equation Utilizing GPU-Accelerated High-Order Compact Numerical Integrators

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