# An efficient and accurate MPI based parallel simulator for streamer discharges in three dimensions

## TL;DR

This paper introduces a new MPI-based parallel simulator for 3D streamer discharges that combines a semi-implicit scheme and a multigrid solver, achieving high efficiency and accuracy for large-scale simulations.

## Contribution

It presents a novel semi-implicit scheme and a multigrid preconditioned solver integrated into an MPI framework for efficient 3D streamer discharge simulation.

## Key findings

- The semi-implicit scheme relaxes dielectric relaxation time restrictions.
- The multigrid solver requires no more than 4 iterations for convergence.
- The parallel code scales efficiently up to 2560 cores on large meshes.

## Abstract

In this paper, we propose an efficient and accurate message-passing interface (MPI)-based parallel simulator for streamer discharges in three dimensions using the fluid model. First, we propose a new second-order semi-implicit scheme for the temporal discretization of the model that relaxes the dielectric relaxation time restriction. Moreover, it requires solving the Poisson-type equation only once at each time step, while the classical second-order explicit scheme typically needs to do twice. Second, we introduce a geometric multigrid preconditioned FGMRES solver that dramatically improves the efficiency of solving the Poisson-type equation with either constant or variable coefficients. We show numerically that no more than 4 iterations are required for the Poisson solver to converge to a relative residual of $10^{-8}$ during streamer simulations; the FGMRES solver is much faster than R&B SOR and other Krylov subspace solvers. Last but not least, all the methods are implemented using MPI. The parallel efficiency of the code and the fast algorithmic performances are demonstrated by a series of numerical experiments using up to 2560 cores on the Tianhe2-JK clusters. For applications, we study a double-headed streamer discharge as well as the interaction between two streamers, using up to 10.7 billion mesh cells.