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A Comparison of Fourier Spectral Iterative Perturbation Method and Finite Element Method in Solving Phase-Field Equilibrium Equations

Published online by Cambridge University Press:  27 March 2017

Pengcheng Song
Affiliation:
Science and Technology on Reactor Fuel and Materials Laboratory, Nuclear Power Institute of China, Chengdu 610041, China Key Laboratory for Advanced Materials of Ministry of Education, Department of Materials Science and Engineering, Tsinghua University, Beijing 100084, China Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802, USA
Tiannan Yang
Affiliation:
Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802, USA
Yanzhou Ji
Affiliation:
Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802, USA
Zhuo Wang
Affiliation:
Department of Mechanical Engineering, Mississippi State University, MS 39762, USA
Zhigang Yang
Affiliation:
Key Laboratory for Advanced Materials of Ministry of Education, Department of Materials Science and Engineering, Tsinghua University, Beijing 100084, China
Longqing Chen
Affiliation:
Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802, USA
Lei Chen
Affiliation:
Department of Mechanical Engineering, Mississippi State University, MS 39762, USA
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Abstract

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 eigen-fields (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.

Type
Research Article
Copyright
Copyright © Global-Science Press 2017 

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Footnotes

The authors contribute equally.

References

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