Exponential integrators for non-linear diffusion

TL;DR

This paper compares exponential integrators with traditional methods for solving RMHD systems, showing initial results that suggest exponential integrators can be a more efficient alternative.

Contribution

It provides a preliminary comparison demonstrating the potential efficiency benefits of exponential integrators over traditional schemes in RMHD simulations.

Findings

Exponential integrators show promising efficiency in RMHD.

Initial results favor exponential integrators over diagonally implicit Runge-Kutta methods.

Further research is needed to confirm these findings.

Abstract

The goal of this project is to compare the performance of exponential time integrators with traditional methods such as diagonally implicit Runge-Kutta methods in the context of solving the system of reduced magnetohydrodynamics (RMHD). In this report, we present initial results of a proof of concept study that shows that exponential integrators can be an efficient alternative to traditional integration schemes.