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

Joseph-Marie PLEWA; Olivier DUCASSE; Philippe DESSANTE; Carolyn JACOBS; Olivier EICHWALD; Nicolas RENON; Mohammed YOUSFI

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

Plasma Science and Technology > 2016 > 18(5): 538-543. > DOI: 10.1088/1009-0630/18/5/16

Joseph-Marie PLEWA, Olivier DUCASSE, Philippe DESSANTE, Carolyn JACOBS, Olivier EICHWALD, Nicolas RENON, Mohammed YOUSFI. Benchmarks of 3D Laplace Equation Solvers in a Cubic Configuration for Streamer Simulation[J]. Plasma Science and Technology, 2016, 18(5): 538-543. DOI: 10.1088/1009-0630/18/5/16

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

1 Universit´e de Toulouse, UPS, INPT, LAPLACE (Laboratoire Plasma et Conversion d’Energie) Toulouse Cedex 9 F-31062, France 2 Group of Electrical Engineering-Paris (GeePs), UMR 8507 CNRS, CentraleSupelec, Universite Paris-Sud—UPMC, 11 rue Joliot-Curie, Plateau de Moulon, 91192 Gif-sur-Yvette Cedex F-91192, France 3 CALMIP, Universit´e de Toulouse-CNRS-INPT-INSA-UPS, UMS 3667, France 4 CNRS, LAPLACE, Toulouse F-31062, France

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Received Date: September 08, 2015

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Abstract

Abstract

The aim of this paper is to test a developed SOR R&B method using the Chebyshev accelerator algorithm to solve the Laplace equation in a cubic 3D configuration. Comparisons are made in terms of precision and computing time with other elliptic equation solvers proposed in the open source LIS library. The first results, obtained by using a single core on a HPC, show that the developed SOR R&B method is efficient when the spectral radius needed for the Chebyshev acceleration is carefully pre-estimated. Preliminary results obtained with a parallelized code using the MPI library are also discussed when the calculation is distributed over one hundred cores.
- numerical methods for elliptic equations,
- high performance computing,
- 3D streamer simulation,
- SOR,
- IDR,
- BiCGSTAB

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References

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