Parallel energy stable phase field simulations of Ni-based alloys system

TL;DR

This paper develops a parallel, energy-stable numerical method for simulating Ni-based alloy phase fields, enabling large-scale, efficient computations while preserving physical laws.

Contribution

It introduces a semi-implicit scheme with adaptive time stepping and a domain decomposition parallel solver for Ni-based alloy phase field simulations, ensuring stability and scalability.

Findings

Algorithm is energy stable with large time steps

Method is highly scalable to thousands of processor cores

Numerical experiments confirm stability and efficiency

Abstract

In this paper, we investigate numerical methods for solving Nickel-based phase field system related to free energy, including the elastic energy and logarithmic type functionals. To address the challenge posed by the particular free energy functional, we propose a semi-implicit scheme based on the discrete variational derivative method, which is unconditionally energy stable and maintains the energy dissipation law and the mass conservation law. Due to the good stability of the semi-implicit scheme, the adaptive time step strategy is adopted, which can flexibly control the time step according to the dynamic evolution of the problem. A domain decomposition based, parallel Newton--Krylov--Schwarz method is introduced to solve the nonlinear algebraic system constructed by the discretization at each time step. Numerical experiments show that the proposed algorithm is energy stable with large time steps, and highly scalable to six thousand processor cores.