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

Carretero-González, R.; Caplan, Ronald M.

doi:10.5642/cguetd/52

Cited by 9 publications

(13 citation statements)

References 100 publications

(160 reference statements)

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“…Tsubota et al [21] solved the GPE in 2D to simulate vortex lattice in rotating superfluids, while Kasamatsu et al [22] solved the GPE in 3D and observed vortex tubes with lattice formation. Zuccher et al [23] analyzed the quantum vortex reconnection, while Caplan et al [24] explored vortex ring dynamics. This work adopts a novel superfluid model [6], which covers the entire velocity range and incorporates the previous models as its non-relativistic limit.…”

Section: Related Workmentioning

confidence: 99%

Towards High-Quality Visualization of Superfluid Vortices

Guo¹,

Liu²,

Xiong³

et al. 2018

IEEE Trans. Visual. Comput. Graphics

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Superfluidity is a special state of matter exhibiting macroscopic quantum phenomena and acting like a fluid with zero viscosity. In such a state, superfluid vortices exist as phase singularities of the model equation with unique distributions. This paper presents novel techniques to aid the visual understanding of superfluid vortices based on the state-of-the-art non-linear Klein-Gordon equation, which evolves a complex scalar field, giving rise to special vortex lattice/ring structures with dynamic vortex formation, reconnection, and Kelvin waves, etc. By formulating a numerical model with theoretical physicists in superfluid research, we obtain high-quality superfluid flow data sets without noise-like waves, suitable for vortex visualization. By further exploring superfluid vortex properties, we develop a new vortex identification and visualization method: a novel mechanism with velocity circulation to overcome phase singularity and an orthogonal-plane strategy to avoid ambiguity. Hence, our visualizations can help reveal various superfluid vortex structures and enable domain experts for related visual analysis, such as the steady vortex lattice/ring structures, dynamic vortex string interactions with reconnections and energy radiations, where the famous Kelvin waves and decaying vortex tangle were clearly observed. These visualizations have assisted physicists to verify the superfluid model, and further explore its dynamic behavior more intuitively.

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Section: Related Workmentioning

confidence: 99%

Towards High-Quality Visualization of Superfluid Vortices

Guo¹,

Liu²,

Xiong³

et al. 2018

IEEE Trans. Visual. Comput. Graphics

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“…5, while the unique forms of the Gershgorin disk centers and radii for A ′ are shown in Table 7. The stability bounds are the same as in 191,190,189,174,173,172,156,155,138,36,21,20,6,5,4, −9, −10, −11, −12} .…”

Section: Fourth-order Central Differencementioning

confidence: 99%

Numerical stability of explicit Runge–Kutta finite-difference schemes for the nonlinear Schrödinger equation

Caplan¹,

Carretero-González²

2013

Applied Numerical Mathematics

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Linearized numerical stability bounds for solving the nonlinear time-dependent Schrödinger equation (NLSE) using explicit finite-differencing are shown. The bounds are computed for the fourth-order Runge-Kutta scheme in time and both second-order and fourth-order central differencing in space. Results are given for Dirichlet, modulus-squared Dirichlet, Laplacian-zero, and periodic boundary conditions for one, two, and three dimensions. Our approach is to use standard Runge-Kutta linear stability theory, treating the nonlinearity of the NLSE as a constant. The required bounds on the eigenvalues of the scheme matrices are found analytically when possible, and otherwise estimated using the Gershgorin circle theorem.

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“…These driver scripts contain all the code necessary to reproduce the results computed in this paper (as well as those in the author's dissertation [31]). This includes the initial conditions (vortices, vortex rings, etc.…”

Section: The Nlsemagic Code Packagementioning

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

Cited by 9 publications

References 100 publications

Towards High-Quality Visualization of Superfluid Vortices

Towards High-Quality Visualization of Superfluid Vortices

Numerical stability of explicit Runge–Kutta finite-difference schemes for the nonlinear Schrödinger equation

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

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