NLSEmagic: Nonlinear Schrödinger Equation Multidimensional Matlab-based GPU-accelerated Integrators using Compact High-order Schemes

Abstract

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 GPU-enabled C codes with the MEX-compiler interface. The packages are freely distributed, including user manuals and set-up files.

37 pages, 13 figures

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Cited by in corpus (14)

• Computational methods for the dynamics of the nonlinear Schrodinger/Gross-Pitaevskii equations
• Fortran and C programs for the time-dependent dipolar Gross-Pitaevskii equation in an anisotropic trap
• Computation of Ground States of the Gross-Pitaevskii Functional via Riemannian Optimization
• OpenMP Fortran and C programs for solving the time-dependent Gross-Pitaevskii equation in an anisotropic trap
• Faraday waves in collisionally inhomogeneous Bose-Einstein condensates
• A finite-element toolbox for the stationary Gross-Pitaevskii equation with rotation
• Scattering and leapfrogging of vortex rings in a superfluid
• A Modulus-Squared Dirichlet Boundary Condition for Time-Dependent Complex Partial Differential Equations and its Application to the Nonlinear Schrödinger Equation
• Quantum turbulence simulations using the Gross-Pitaevskii equation: high-performance computing and new numerical benchmarks
• CUDA-based optical parametric oscillator simulator
• GPU-accelerated solutions of the nonlinear Schrödinger equation for simulating 2D spinor BECs
• A Two-Step High-Order Compact Scheme for the Laplacian Operator and its Implementation in an Explicit Method for Integrating the Nonlinear Schrödinger Equation
• Numerical Stability of Explicit Runge-Kutta Finite-Difference Schemes for the Nonlinear Schrödinger Equation
• BRAHMS: A cross-platform graphical toolkit for (3+1)D simulation of three-wave mixing in ${\chi }^{(2)}$ nonlinear media, with GPU and CPU backends