Exponential Integrators for Phase-Field Equations using Pseudo-spectral Methods: A Python Implementation

TL;DR

This paper presents a Python implementation of exponential integrators combined with pseudo-spectral methods for solving phase-field equations, demonstrating improved accuracy and efficiency over traditional methods in modeling complex physical phenomena.

Contribution

The paper introduces a novel Python framework integrating exponential integrators with pseudo-spectral techniques for phase-field equations, highlighting their advantages over existing methods.

Findings

ETD methods outperform IMEX Euler in accuracy

Pseudo-spectral techniques enhance computational efficiency

The implementation effectively models phase-field dynamics

Abstract

In this paper, we implement exponential integrators, specifically Integrating Factor (IF) and Exponential Time Differencing (ETD) methods, using pseudo-spectral techniques to solve phase-field equations within a Python framework. These exponential integrators have showcased robust performance and accuracy when addressing stiff nonlinear partial differential equations. We compare these integrators to the well-known implicit-explicit (IMEX) Euler integrators used in phase-field modeling. The synergy between pseudo-spectral techniques and exponential integrators yields significant benefits for modeling intricate systems governed by phase-field dynamics, such as solidification processes and pattern formation. Our comprehensive Python implementation illustrates the effectiveness of this combined approach in solving phase-field model equations. The results obtained from this implementation highlight the accuracy and computational advantages of the ETD method compared to other numerical techniques.