Maximally-fast coarsening algorithms

TL;DR

This paper introduces maximally-fast, stable, and accurate numerical algorithms for conserved coarsening systems that allow for increasing time-steps, outperforming traditional fixed-timestep methods in efficiency and accuracy.

Contribution

The authors develop and demonstrate the first maximally-fast algorithms for conserved coarsening systems, enabling unconditionally stable simulations with increasing time-steps.

Findings

Error scales as the square root of A, allowing arbitrary accuracy.

Maximally-fast algorithms outperform fixed-timestep Euler in efficiency.

Algorithms are stable and accurate with a growing natural time-step.

Abstract

We present maximally-fast numerical algorithms for conserved coarsening systems that are stable and accurate with a growing natural time-step $\Delta t=A t_s^{2/3}$. For non-conserved systems, only effectively finite timesteps are accessible for similar unconditionally stable algorithms. We compare the scaling structure obtained from our maximally-fast conserved systems directly against the standard fixed-timestep Euler algorithm, and find that the error scales as $\sqrt{A}$ -- so arbitrary accuracy can be achieved.