Fast and Stable Schemes for Phase Fields Models

TL;DR

This paper introduces new stabilized semi-implicit time marching schemes for phase field models like Allen-Cahn and Cahn-Hilliard, achieving faster computations while maintaining stability and accuracy in high-order finite difference discretizations.

Contribution

The paper presents novel stabilized semi-implicit schemes with sparse pre-conditioners for phase field models, improving computational efficiency and stability in high-order discretizations.

Findings

Significant CPU time reduction in simulations.

Effective application to pattern dynamics.

Successful use in image processing tasks.

Abstract

We propose and analyse new stabilized time marching schemes for Phase Fields model such as Allen-Cahn and Cahn-Hillard equations, when discretized in space with high order finite differences compact schemes. The stabilization applies to semi-implicit schemes for which the linear part is simplified using sparse pre-conditioners. The new methods allow to significant obtain a gain of CPU time. The numerical illustrations we give concern applications on pattern dynamics and on image processing (inpainting, segmentation) in two and three dimension cases.