@Article{CiCP-21-1325,
author = {Pengcheng Song, Tiannan Yang, Yanzhou Ji, Zhuo Wang, Zhigang Yang, Longqing Chen and Lei Chen},
title = {A Comparison of Fourier Spectral Iterative Perturbation Method and Finite Element Method in Solving Phase-Field Equilibrium Equations},
journal = {Communications in Computational Physics},
year = {2018},
volume = {21},
number = {5},
pages = {1325--1349},
abstract = {<p style="text-align: justify;">This paper systematically compares the numerical implementation and computational
cost between the Fourier spectral iterative perturbation method (FSIPM)
and the finite element method (FEM) in solving partial differential equilibrium equations
with inhomogeneous material coefficients and eigenfields (e.g., stress-free strain
and spontaneous electric polarization) involved in phase-field models. Four benchmark
numerical examples, including inhomogeneous elastic, electrostatic, and steady-state
heat conduction problems demonstrate that (1) the FSIPM rigorously requires
uniform hexahedral (3D) and quadrilateral (2D) mesh and periodic boundary conditions
for numerical implementation while the FEM permits arbitrary mesh and boundary
conditions; (2) the FSIPM solutions are comparable to their FEM counterparts, and
both of them agree with the analytic solutions, (3) the FSIPM is much faster in solving
equilibrium equations than the FEM to achieve the accurate solutions, thus exhibiting
a greater potential for large-scale 3D computations.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2016-0114},
url = {http://global-sci.org/intro/article_detail/cicp/11281.html}
}