Finite difference approach for multiscale computations of atomic chain at finite temperature

• Published in: Computers & mathematics with applications (1987) Vol. 110; pp. 77 - 90
• Main Authors: Zhang, Lei, Tang, Shaoqiang, Liu, Baiyili
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 15.03.2022; Elsevier BV
• Subjects: Atomic simulation; Boundary condition; Boundary conditions; Differential equations; Domains; Finite difference method; Finite temperature; Heat jet approach; Heat sources; Interpolation; Molecular dynamics; Morse potential; Multiscale analysis; Multiscale method; Operators (mathematics); Temperature control; Boundary condition; Multiscale method; Finite temperature; Heat jet approach; Atomic simulation
• ISSN: 0898-1221; 1873-7668
• DOI: 10.1016/j.camwa.2022.01.035

In this paper, we propose a finite temperature multiscale method for simulating complex dynamics with different spatial scales accurately and efficiently. We separate the domain into an MD (Molecular Dynamics) subdomain and an MC (MacrosCopic) subdomain, with a handshaking subdomain between two scales. We cast the coarse grid over the whole domain using a matching differential operator approach. We reassign the coarse grid displacement in the MD subdomain with an average of the MD solution. Using a spectral decomposition in a handshaking subdomain, we split the displacement of atoms into its mean and fluctuation parts. The mean part is reassigned by the coarse grid linear interpolation, which is the main technique to realize information exchange from the coarse grid to fine grid consistently. A two-way artificial boundary condition is proposed for eliminating boundary reflections and injecting heat sources. With the two-way boundary condition, we design the heat jet approach and combine with the handshaking subdomain, which is used to implement temperature control in crystalline solids. Numerical tests of linear lattice and non-linear lattice with Morse potential in one space dimension illustrate the accuracy and effectiveness of resolving information exchange between the two scales subject to thermal fluctuations at a given temperature.