Numerical efficiency of explicit time integrators for phase-field models

TL;DR

This paper compares explicit time integrators for phase-field models, demonstrating significant speedups while maintaining accuracy, and provides benchmarks with exact solutions to evaluate error contributions.

Contribution

It introduces adapted explicit integrators for phase-field models with constraints and benchmarks them using exact sharp interface solutions.

Findings

Speedups of 4 to 114 times over forward Euler

Explicit schemes can be both fast and accurate

Benchmarks with exact solutions enable error analysis

Abstract

Phase-field simulations are a practical but also expensive tool to calculate microstructural evolution. This work aims to compare explicit time integrators for a broad class of phase-field models involving coupling between the phase-field and concentration. Particular integrators are adapted to constraints on the phase-field as well as storage scheme implications. Reproducible benchmarks are defined with a focus on having exact sharp interface solutions, allowing for identification of dominant error terms. Speedups of 4 to 114 over the classic forward Euler integrator are achievable while still using a fully explicit scheme without appreciable accuracy loss. Application examples include final stage sintering with pores slowing down grain growth as they move and merge over time.