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

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.Prehminary results obtained with a parallelized code using the MPI library are also discussed when the calculation is distributed over one hundred cores.