Benchmarks of 3D Laplace Equation Solvers in a Cubic Configuration for Streamer Simulation

Plewa, Jérémie-Marie; Ducasse, Olivier; Dessante, Philippe; Jacobs, Carolyn; Eichwald, Olivier; Renon, Nicolas; Yousfi, Mohammed

doi:10.1088/1009-0630/18/5/16

Cited by 1 publication

(2 citation statements)

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“…A first investigation was already done for the comparison of the efficiency of elliptic equation methods in solving the 3D Laplace equation in a stationary problem and using high performance computing [36]. In the present section, this preliminary work is extended to a dynamical problem consisting of the propagation of a representative space charge density of a monofilament streamer.…”

Section: Study Of the Efficiency Of Numerical Methods For Solving Ell...mentioning

confidence: 99%

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3D streamers simulation in a pin to plane configuration using massively parallel computing

Plewa

Eichwald

Ducasse

et al. 2018

J. Phys. D: Appl. Phys.

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This paper concerns the 3D simulation of corona discharge using high performance computing (HPC) managed with the message passing interface (MPI) library. In the field of finite volume methods applied on non-adaptive mesh grids and in the case of a specific 3D dynamic benchmark test devoted to streamer studies, the great efficiency of the iterative R&B SOR and BiCGSTAB methods versus the direct MUMPS method was clearly demonstrated in solving the Poisson equation using HPC resources. The optimization of the parallelization and the resulting scalability was undertaken as a function of the HPC architecture for a number of mesh cells ranging from 8 to 512 million and a number of cores ranging from 20 to 1600. The R&B SOR method remains at least about four times faster than the BiCGSTAB method and requires significantly less memory for all tested situations. The R&B SOR method was then implemented in a 3D MPI parallelized code that solves the classical first order model of an atmospheric pressure corona discharge in air. The 3D code capabilities were tested by following the development of one, two and four coplanar streamers generated by initial plasma spots for 6 ns. The preliminary results obtained allowed us to follow in detail the formation of the tree structure of a corona discharge and the effects of the mutual interactions between the streamers in terms of streamer velocity, trajectory and diameter. The computing time for 64 million of mesh cells distributed over 1000 cores using the MPI procedures is about 30 min ns −1 , regardless of the number of streamers.

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Section: Study Of the Efficiency Of Numerical Methods For Solving Ell...mentioning

confidence: 99%

“…The crucial part of the SOR algorithm is the optimal choice of the ω value. A high convergence acceleration is obtained only in a fairly narrow window around the correct value of ω [36]. In our case, the over relaxation parameter is calculated with the Chebyshev acceleration procedure [39].…”

Section: Appendix a A Brief Description Of The Chosen Solversmentioning

confidence: 99%