On architecture and performance of adaptive mesh refinement in an electrostatics Particle-In-Cell code

Frey, Matthias; Adelmann, Andreas; Locans, Uldis

doi:10.1016/j.cpc.2019.106912

Cited by 8 publications

(9 citation statements)

References 30 publications

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“…For the time integration we use the leap frog method and for the Poisson equation we use the second order cell-centered finite difference method as in [38,39] with single level and without any spatial adaptivity. For solving the linear system arising from the discretized Poisson equation we use the smoothed aggregation algebraic multigrid (SAAMG) from the second generation Trilinos MueLu library [40].…”

Section: Numerical Resultsmentioning

confidence: 99%

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Sparse Grids based Adaptive Noise Reduction strategy for Particle-In-Cell schemes

Muralikrishnan,

Cerfon,

Frey

et al. 2020

Preprint

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We propose a sparse grids based adaptive noise reduction strategy for electrostatic particle-in-cell (PIC) simulations. Our approach is based on the key idea of relying on sparse grids instead of a regular grid in order to increase the number of particles per cell for the same total number of particles, as first introduced in [1]. Adopting a new filtering perspective for this idea, we construct the algorithm so that it can be easily integrated into high performance largescale PIC code bases. Unlike the physical and Fourier domain filters typically used in PIC codes, our approach automatically adapts to mesh size, number of particles per cell, smoothness of the density profile and the initial sampling technique. Thanks to the truncated combination technique [2, 3, 4], we can reduce the larger grid-based error of the standard sparse grids approach for non-aligned and non-smooth functions. We propose a heuristic based on formal error analysis for selecting the optimal truncation parameter at each time step, and develop a natural framework to minimize the total error in sparse PIC simulations. We demonstrate its efficiency and performance by means of two test cases: the diocotron instability in two dimensions, and the three-dimensional electron dynamics in a Penning trap. Our run time performance studies indicate that our new scheme can provide significant speedup and memory reduction as compared to regular PIC for achieving comparable accuracy in the charge density deposition.

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Section: Numerical Resultsmentioning

confidence: 99%

“…The stopping tolerance for the iterative solver is set as 10 −10 multiplied by the infinity norm of the right hand side. More details on the solver can be found in [39]. The code is written on top of a C++ miniapp based on the particle accelerator library OPAL [27] and box structured adaptive mesh refinement library AMReX [41].…”

Section: Numerical Resultsmentioning

confidence: 99%

Sparse Grids based Adaptive Noise Reduction strategy for Particle-In-Cell schemes

Muralikrishnan,

Cerfon,

Frey

et al. 2020

Preprint

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“…1b). In order to resolve these effects, the open source beam dynamics code OPAL [12] got recently enhanced with AMR capabilities [13] which adds more complexity to the numerical model. The influence of the AMR solver parameter settings on the statistical measures of the particle bunches is yet unknown and a too conservative AMR regrid frequency worsens the time-to-solution.…”

Section: H +mentioning

confidence: 99%

“…While the resolution is basically controlled by the maximum number of AMR levels, the refinement policy affects its location. As described in [13] the OPAL library provides several refinement criteria such as the charge density per grid point, the potential as well as the electric field. the effect of the threshold λ ∈ [0, 1] of the electrostatic potential refinement policy, where a grid cell (i, j, k) on a level l is refined if…”

Section: High Intensity Cyclotronsmentioning

confidence: 99%

“…In this paper we study the sensitivity of adaptive mesh refinement (AMR) and multi bunch [10,11] parameters in Particle-In-Cell (PIC) simulations of high intensity cyclotrons where we use the new AMR capabilities of OPAL (Object Oriented Parallel Accelerator Library) [12] as presented in [13]. We further explore the sensitivity of a rf electron gun model with respect to the number of macro particles, the energy binning and the time step.…”

Section: Introductionmentioning

confidence: 99%

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Global Sensitivity Analysis on Numerical Solver Parameters of Particle-In-Cell Models in Particle Accelerator Systems

Frey,

Adelmann

2020

Preprint

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Every computer model depends on numerical input parameters that are chosen according to mostly conservative but rigorous numerical or empirical estimates. These parameters could for example be the step size for time integrators, a seed for pseudo-random number generators, a threshold or the number of grid points to discretize a computational domain. In case a numerical model is enhanced with new algorithms and modelling techniques the numerical influence on the quantities of interest, the running time as well as the accuracy is often initially unknown.Usually parameters are chosen on a trial-and-error basis neglecting the computational cost versus accuracy aspects. As a consequence the cost per simulation might be unnecessarily high which wastes computing resources. Hence, it is essential to identify the most critical numerical parameters and to analyze systematically their effect on the result in order to minimize the timeto-solution without losing significantly on accuracy. Relevant parameters are identified by global sensitivity studies where Sobol' indices are common measures. These sensitivities are obtained by surrogate models based on polynomial chaos expansion.In this paper, we first introduce the general methods for uncertainty quantification. We then demonstrate their use on numerical solver parameters to reduce the computational costs and discuss further model improvements based on the sensitivity analysis. The sensitivities are evaluated for neighbouring bunch simulations of the existing PSI Injector II and PSI Ring as well as the proposed DAEδALUS Injector cyclotron and simulations of the rf electron gun of the

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Expansion of a finite-size photoplasma in an electrostatic field with M-type electrode configuration using a novel adaptive mesh 2D-PIC code

Singh

Sridhar

Maiti

2023

Current Applied Physics

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On architecture and performance of adaptive mesh refinement in an electrostatics Particle-In-Cell code

Cited by 8 publications

References 30 publications

Sparse Grids based Adaptive Noise Reduction strategy for Particle-In-Cell schemes

Sparse Grids based Adaptive Noise Reduction strategy for Particle-In-Cell schemes

Global Sensitivity Analysis on Numerical Solver Parameters of Particle-In-Cell Models in Particle Accelerator Systems

Expansion of a finite-size photoplasma in an electrostatic field with M-type electrode configuration using a novel adaptive mesh 2D-PIC code

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