A domain decomposition method for pseudo-spectral electromagnetic simulations of plasmas

Vay, Jean‐Luc; Haber, I.; Godfrey, Brendan B.

doi:10.1016/j.jcp.2013.03.010

Cited by 116 publications

(140 citation statements)

References 13 publications

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“…The finite-difference electromagnetic solver has been extended to support arbitrary order of accuracy (through the use of larger stencils). The PSTD and PSATD solvers were also implemented and a new paradigm for parallelizing spectral solvers was introduced, using the fundamental property of finite speed of light with Maxwell's equation to enable usage of local Fast Fourier Transform on each compute node [15]. The new parallelization method removes the difficulty of scaling global FFTs to very large number of cores.…”

Section: Novel Methodsmentioning

confidence: 99%

Summary report of working group 2: Computations for accelerator physics

Vay¹,

Arefiev²

2016

AIP Conference Proceedings

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Section: Novel Methodsmentioning

confidence: 99%

Summary report of working group 2: Computations for accelerator physics

Vay¹,

Arefiev²

2016

AIP Conference Proceedings

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“…Despite their accuracy, such methods have however hardly been used during the last two decades in PIC codes due to their low scalability to 10, 000s of cores at best, which is not enough to take advantage of petascale supercomputers architectures required for 3D modeling. To break this barrier a pioneering grid decomposition technique [16] was recently proposed for very high-order/pseudo-spectral solvers that was first validated by an extensive analytical work [17] and then implemented and benchmarked in our high performance WARP+PXR PIC code [18,19].…”

Section: B Main Challenges In the Numerical Modeling Of Doppler Harmmentioning

confidence: 99%

Pseudospectral Maxwell solvers for an accurate modeling of Doppler harmonic generation on plasma mirrors with particle-in-cell codes

et al. 2017

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With the advent of PetaWatt (PW) class lasers, the very large laser intensities attainable on-target should enable the production of intense high-order Doppler harmonics from relativistic laser-plasma mirrors interactions. At present, the modeling of these harmonics with Particle-In-Cell (PIC) codes is extremely challenging as it implies an accurate description of tens to hundreds of harmonic orders on a a broad range of angles. In particular, we show here that due to the numerical dispersion of waves they induce in vacuum, standard Finite Difference Time Domain (FDTD) Maxwell solvers employed in most PIC codes can induce a spurious angular deviation of harmonic beams potentially degrading simulation results. This effect was extensively studied and a simple toy-model based on Snell-Descartes law was developed that allows us to finely predict the angular deviation of harmonics depending on the spatio-temporal resolution and the Maxwell solver used in the simulations. Our model demonstrates that the mitigation of this numerical artifact with FDTD solvers mandates very high spatio-temporal resolution preventing doing realistic 3D simulations even on the largest computers available at the time of writing. We finally show that non-dispersive pseudo-spectral analytical time domain solvers can considerably reduce the spatio-temporal resolution required to mitigate this spurious deviation and should enable in the near future 3D accurate modeling on supercomputers in a realistic time-to-solution.

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“…Moreover, for a wide class of equations, their spectral counterparts can be integrated in time analytically, so that the accuracy of the fields dynamics modeling does not directly depend on the simulations temporal resolution 12 . This is known as the pseudo-spectral analytical time domain (PSATD) method, and it was shown to produce no numerical dispersion of electromagnetic fields associated with the tem-poral and spatial resolutions in PIC 14 . Here we develop the PSATD PIC considering that the model geometry has a certain level of cylindrical symmetry, which allows to replace the three-dimensional Cartesian geometry with a series of cylindrical models with different symmetries, e.g.…”

Section: Introductionmentioning

confidence: 99%

Laser-plasma interactions with a Fourier-Bessel particle-in-cell method

2016

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A new spectral particle-in-cell (PIC) method for plasma modeling is presented and discussed. In the proposed scheme, the Fourier-Bessel transform is used to translate the Maxwell equations to the quasi-cylindrical spectral domain. In this domain, the equations are solved analytically in time, and the spatial derivatives are approximated with high accuracy. In contrast to the finite-difference time domain (FDTD) methods that are commonly used in PIC, the developed method does not produce numerical dispersion, and does not involve grid staggering for the electric and magnetic fields. These features are especially valuable in modeling the wakefield acceleration of particles in plasmas. The proposed algorithm is implemented in the code PLARES-PIC, and the test simulations of laser plasma interactions are compared to the ones done with the quasi-cylindrical FDTD PIC code CALDER-CIRC.

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A domain decomposition method for pseudo-spectral electromagnetic simulations of plasmas

Cited by 116 publications

References 13 publications

Summary report of working group 2: Computations for accelerator physics

Summary report of working group 2: Computations for accelerator physics

Pseudospectral Maxwell solvers for an accurate modeling of Doppler harmonic generation on plasma mirrors with particle-in-cell codes

Laser-plasma interactions with a Fourier-Bessel particle-in-cell method

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