Accelerating the Fourier split operator method via graphics processing units

DOI10.1016/j.cpc.2011.07.003zbMath1261.65101arXiv1012.3911OpenAlexW1988175256MaRDI QIDQ1943057

Heiko Bauke, Christoph H. Keitel

Publication date: 15 March 2013

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.3911

zbMATH Keywords

numerical examplesfast Fourier transformSchrödinger equationDirac equationgraphics processing unitGPU computingFourier split operator method

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Numerical methods for discrete and fast Fourier transforms (65T50) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items

Krylov subspace methods for the Dirac equation ⋮ Optimized spatial matrix representations of quantum Hamiltonians ⋮ Split-operator technique for propagating phase space functions: exploring chaotic, dissipative and relativistic dynamics ⋮ A GPU parallelized spectral method for elliptic equations in rectangular domains ⋮ Solution of relativistic quantum optics problems using clusters of graphical processing units ⋮ A split-step numerical method for the time-dependent Dirac equation in 3-D axisymmetric geometry ⋮ Numerical solution of the time-dependent Dirac equation in coordinate space without fermion-doubling ⋮ A matrix-exponential decomposition based time-domain method for calculating the defect states of scalar waves in two-dimensional periodic structures ⋮ A stability analysis of a real space split operator method for the Klein-Gordon equation ⋮ A simple pseudospectral method for the computation of the time-dependent Dirac equation with perfectly matched layers ⋮ Computational performance of simple and efficient sequential and parallel Dirac equation solvers ⋮ A new framework of GPU-accelerated spectral solvers: collocation and Galerkin methods for systems of coupled elliptic equations ⋮ An OpenCL implementation for the solution of the time-dependent Schrödinger equation on GPUs and CPUs ⋮ Pseudospectral computational methods for the time-dependent Dirac equation in static curved spaces

Uses Software

• FFTW
• OpenCL
• Dirac++

Cites Work

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