Close Search Advanced
Journals
Resources
About Us
Open Access

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

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

Year:    2017

Communications in Computational Physics, Vol. 21 (2017), Iss. 5 : pp. 1325–1349

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 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.

Submit Article

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2016-0114

Communications in Computational Physics, Vol. 21 (2017), Iss. 5 : pp. 1325–1349

Published online:    2017-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    25

Keywords:   

  1. Mesoscale modeling and semi-analytical approach for the microstructure-aware effective thermal conductivity of porous polygranular materials

    Song, Younggil | Heo, Tae Wook

    Computational Materials Science, Vol. 235 (2024), Iss. P.112808

    https://doi.org/10.1016/j.commatsci.2024.112808 [Citations: 0]

  2. Machine learning unifies flexibility and efficiency of spinodal structure generation for stochastic biomaterial design

    Wang, Zhuo | Dabaja, Rana | Chen, Lei | Banu, Mihaela

    Scientific Reports, Vol. 13 (2023), Iss. 1

    https://doi.org/10.1038/s41598-023-31677-7 [Citations: 7]

  3. Efficient local energy dissipation preserving algorithms for the Cahn–Hilliard equation

    Mu, Zhenguo | Gong, Yuezheng | Cai, Wenjun | Wang, Yushun

    Journal of Computational Physics, Vol. 374 (2018), Iss. P.654

    https://doi.org/10.1016/j.jcp.2018.08.004 [Citations: 8]

  4. Emergence of non-trivial polar topologies hidden in singular stress field in SrTiO3: topological strain-field engineering

    Shimada, Takahiro | Wang, Yu | Hamaguchi, Takayuki | Kasai, Kohta | Masuda, Kairi | Van Lich, Le | Xu, Tao | Wang, Jie | Hirakata, Hiroyuki

    Journal of Physics: Condensed Matter, Vol. 33 (2021), Iss. 50 P.505301

    https://doi.org/10.1088/1361-648X/ac28c1 [Citations: 11]

  5. A family of second-order energy-stable schemes for Cahn–Hilliard type equations

    Yang, Zhiguo | Lin, Lianlei | Dong, Suchuan

    Journal of Computational Physics, Vol. 383 (2019), Iss. P.24

    https://doi.org/10.1016/j.jcp.2019.01.014 [Citations: 34]

  6. Enhancement of effective thermal conductivity of rGO/Mg nanocomposite packed beds

    Kim, Dong-min | Han, Dong Ju | Heo, Tae Wook | Kang, ShinYoung | Wood, Brandon C. | Lee, Jungchul | Cho, Eun Seon | Lee, Bong Jae

    International Journal of Heat and Mass Transfer, Vol. 192 (2022), Iss. P.122891

    https://doi.org/10.1016/j.ijheatmasstransfer.2022.122891 [Citations: 9]

  7. Phase field model for electric-thermal coupled discharge breakdown of polyimide nanocomposites under high frequency electrical stress

    HAN 韩, Zhiyun 智云 | LI 李, Qingmin 庆民 | LI 李, Junke 俊科 | WANG 王, Mengxi 梦溪 | REN 任, Hanwen 瀚文 | ZOU 邹, Liang 亮

    Plasma Science and Technology, Vol. 26 (2024), Iss. 2 P.025505

    https://doi.org/10.1088/2058-6272/ad0d49 [Citations: 1]

  8. Ferroelectric nanoscale logic gates by mixed dislocations in SrTiO3

    Masuda, Kairi | Shimada, Takahiro | Kitamura, Takayuki

    Physical Review B, Vol. 104 (2021), Iss. 5

    https://doi.org/10.1103/PhysRevB.104.054104 [Citations: 1]

  9. Microstructural effects on effective piezoelectric responses of textured PMN-PT ceramics

    Ming, Chen | Yang, Tiannan | Luan, Kun | Chen, Lei | Wang, Liang | Zeng, Jiangtao | Li, Yongxiang | Zhang, Wenqing | Chen, Long-Qing

    Acta Materialia, Vol. 145 (2018), Iss. P.62

    https://doi.org/10.1016/j.actamat.2017.11.043 [Citations: 28]

  10. Formation of polarization needle-like domain and its unusual switching in compositionally graded ferroelectric thin films: an improved phase field model

    Van Lich, Le | Dinh, Van-Hai

    RSC Advances, Vol. 9 (2019), Iss. 13 P.7575

    https://doi.org/10.1039/C8RA10614B [Citations: 17]

  11. Microstructural impacts on ionic conductivity of oxide solid electrolytes from a combined atomistic-mesoscale approach

    Heo, Tae Wook | Grieder, Andrew | Wang, Bo | Wood, Marissa | Hsu, Tim | Akhade, Sneha A. | Wan, Liwen F. | Chen, Long-Qing | Adelstein, Nicole | Wood, Brandon C.

    npj Computational Materials, Vol. 7 (2021), Iss. 1

    https://doi.org/10.1038/s41524-021-00681-8 [Citations: 36]

  12. Switching the chirality of a ferroelectric vortex in designed nanostructures by a homogeneous electric field

    Van Lich, Le | Shimada, Takahiro | Wang, Jie | Dinh, Van-Hai | Bui, Tinh Quoc | Kitamura, Takayuki

    Physical Review B, Vol. 96 (2017), Iss. 13

    https://doi.org/10.1103/PhysRevB.96.134119 [Citations: 41]

  13. Finite strain crystal plasticity-phase field modeling of twin, dislocation, and grain boundary interaction in hexagonal materials

    Liu, Chuanlai | Roters, Franz | Raabe, Dierk

    Acta Materialia, Vol. 242 (2023), Iss. P.118444

    https://doi.org/10.1016/j.actamat.2022.118444 [Citations: 28]

  14. Dynamical topology in ferroelectric nanostructures by 12[11¯0](110) dislocations in SrTiO3

    Masuda, Kairi | Shimada, Takahiro | Kitamura, Takayuki

    Physical Review B, Vol. 103 (2021), Iss. 5

    https://doi.org/10.1103/PhysRevB.103.054114 [Citations: 2]

  15. Accelerating large-scale phase-field simulations with GPU

    Shi, Xiaoming | Huang, Houbing | Cao, Guoping | Ma, Xingqiao

    AIP Advances, Vol. 7 (2017), Iss. 10

    https://doi.org/10.1063/1.5003709 [Citations: 14]

  16. An efficient space-time phase field discretization for ferroelectrics

    Lich, Le Van | Bui, Tinh Quoc | Nguyen, Thanh-Tung | Wang, Jie | Nguyen, Trong-Giang | Dinh, Van-Hai

    Modelling and Simulation in Materials Science and Engineering, Vol. 28 (2020), Iss. 2 P.025005

    https://doi.org/10.1088/1361-651X/ab620a [Citations: 2]

  17. Machine-learning-assisted deciphering of microstructural effects on ionic transport in composite materials: A case study of Li7La3Zr2O12-LiCoO2

    Feng, Longsheng | Wang, Bo | Kim, Kwangnam | Wan, Liwen F. | Wood, Brandon C. | Heo, Tae Wook

    Energy Storage Materials, Vol. 73 (2024), Iss. P.103776

    https://doi.org/10.1016/j.ensm.2024.103776 [Citations: 1]