A Comparison of Fourier Spectral Iterative Perturbation Method and Finite Element Method in Solving Phase-Field Equilibrium Equations (Communications in Computational Physics, 2018)
This paper systematically compares the numerical implementation and computationalcost between the Fourier spectral iterative perturbation method (FSIPM)and the finite element method (FEM) in solving partial differential equilibrium equationswith inhomogeneous material coefficients and eigenfields (e.g., stress-free strainand spontaneous electric polarization) involved in phase-field models. Four benchmarknumerical examples, including inhomogeneous elastic, electrostatic, and steady-stateheat conduction problems demonstrate that (1) the FSIPM rigorously requiresuniform hexahedral (3D) and quadrilateral (2D) mesh and periodic boundary conditionsfor numerical implementation while the FEM permits arbitrary mesh and boundaryconditions; (2) the FSIPM solutions are comparable to their FEM counterparts, andboth of them agree with the analytic solutions, (3) the FSIPM is much faster in solvingequilibrium equations than the FEM to achieve the accurate solutions, thus exhibitinga greater potential for large-scale 3D computations.