Applications of semi-implicit Fourier-spectral method to phase field equations

Chen, Lei; Shen, Jie

doi:10.1016/s0010-4655(97)00115-x

Cited by 1,039 publications

(609 citation statements)

References 15 publications

Supporting

Mentioning

594

Contrasting

Unclassified

Order By: Relevance

“…The semi-implicit Fourierspectral method [27] is used to solve the TDGL equation. All the simulations start from an initial paraelectric state with random noise perturbations for the local polarization.…”

Section: Modelmentioning

confidence: 99%

Piezoelectric enhancement of(PbTiO3)m/(BaTiO3)nferroelectric superlattices through domai

Hong

et al. 2014

Phys. Rev. B

View full text Add to dashboard Cite

show abstract

Section: Modelmentioning

confidence: 99%

Piezoelectric enhancement of(PbTiO3)m/(BaTiO3)nferroelectric superlattices through domai

Hong

et al. 2014

Phys. Rev. B

View full text Add to dashboard Cite

show abstract

“…From the early stage of decomposition at the film surface, the decomposed phases have a tendency to align along <100> directions. For a cubic alloy with negative elastic anisotropy, <100> directions are elastically soft directions and morphological alignment along those directions reduces the elastic energy [18]. As the B-rich domain coarsens, the morphology not only shows a strong <100> alignment in the xy-plane, but also shows a layered structure along the z-direction.…”

Section: Resultsmentioning

confidence: 99%

“…The above equation can be efficiently solved using a semiimplicit method [17,18]. More precisely, (15) where and ∆t * is the time step for integration.…”

Section: -D Simulation Of the Spinodal Decompositionmentioning

confidence: 99%

Three-dimensional phase-field modeling of spinodal decomposition in constrained films

Seol

et al. 2003

Met. Mater. Int.

View full text Add to dashboard Cite

The morphological evolution during spinodal decomposition in binary alloy thin films elastically constrained by substrates is studied. Elastic solutions, derived for both elastically isotropic and anisotropic thin films subject to mixed stress-free and constraint boundary conditions, are employed in a three-dimensional phasefield model to investigate the effect of coherency strain and substrate constraint on microstructural evolution. The temporal evolution of the Cahn-Hilliard equation under thin film boundary conditions is solved with a semi-implicit Fourier-spectral method. The phase separation with coherency strain in an elastically anisotropic film shows the behavior of surface-directed spinodal decomposition driven by the elastic energy effect. Negative elastic anisotropy in the cubic alloy causes the alignment of the phases along <100> elastically soft directions.

show abstract

“…Spectral methods, which were widely used in the ®eld of¯uid dynamics [6], o ered us an accurate and e cient alternative to solve partial di erential equations. Recently, Chen and Shen [7] used a semi-implicit Fourier spectral method for solving the time-dependent Ginzburg±Landau and Cahn±Hilliard equations. They showed that the semi-implicit Fourier spectral method is signi®-cantly more e cient and accurate than a conventional explicit ®nite di erence method.…”

Section: Methodsmentioning

confidence: 99%

“…For example, the thickness of the grain boundary d should be determined from the di use-interface ®eld variable pro®le [7]. Fig.…”

Section: Grain Boundary DI Usionmentioning

confidence: 99%

Microstructure dependence of diffusional transport

Zhu

Chen

Shen

et al. 2001

Computational Materials Science

Self Cite

View full text Add to dashboard Cite

A simple and e ective numerical method is proposed for simulating the temporal di usive mass transport process through a microstructure with arbitrary complexity described by a phase-®eld approach. The mass di usion through a given microstructure is modeled by a di usion equation with a variable di usion coe cient, which is solved by an e cient and accurate semi-implicit spectral method. It is shown that it is possible to extract the e ective di usion coe cient for any given microstructure from the temporal concentration pro®les. The method is used to simulate the grain boundary di usion in a single-phase polycrystalline grain structure and the heterogeneous di usion in a twophase microstructure with di erent di usion coe cient in each phase. Results are compared with existing analytical theories and computer simulations. Ó

show abstract

Applications of semi-implicit Fourier-spectral method to phase field equations

Cited by 1,039 publications

References 15 publications

Piezoelectric enhancement of(PbTiO3)m/(BaTiO3)nferroelectric superlattices through domai

Piezoelectric enhancement of(PbTiO3)m/(BaTiO3)nferroelectric superlattices through domai

Three-dimensional phase-field modeling of spinodal decomposition in constrained films

Microstructure dependence of diffusional transport

Contact Info

Product

Resources

About