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CONCURRENT MULTISCALE METHODS FOR CRYSTALLINE SOLIDS
Shaoqiang Tang 한국산업응용수학회 2006 한국산업응용수학회 학술대회 논문집 Vol.1 No.2
In this talk, we shall discuss three concurrent multiscale methods, namely, the bridging scale method (BSM), the pseudo-spectral multiscale method (PMM), and a finite difference approach (FDA). These methods share the same idea of a sharp domain decomposition. The first two methods adopt a time history treatment for interfacial conditions, yet with two different ways in the displacement decomposition. The finite difference approach adopts a velocity interfacial condition instead, which is local in time and hence allows treating solids with relatively strong nonlinearity and large deformation. Numerical results have demonstrated the efficiency and accuracy for these methods.
Stability of matching boundary conditions for diatomic chain and square lattice
Ji, Songsong,Tang, Shaoqiang Techno-Press 2018 Coupled systems mechanics Vol.7 No.3
Stability of MBC1, a specific matching boundary condition, is proved for atomic simulations of a diatomic chain. The boundary condition and the Newton equations that govern the atomic dynamics form a coupled system. Energy functions that decay along with time are constructed for both the boundary with the same type atoms and the one with different type atoms. For a nonlinear chain, MBC1 is also shown stable. Numerical verifications are presented. Moreover, MBC1 is proved to be stable for a two dimensional square lattice.
Heat jet approach for finite temperature atomic simulations of two-dimensional square lattice
Liu, Baiyili,Tang, Shaoqiang 테크노프레스 2016 Multiscale and multiphysics mechanics Vol.1 No.3
We propose a heat jet approach for a two-dimensional square lattice with nearest neighbouring harmonic interaction. First, we design a two-way matching boundary condition that linearly relates the displacement and velocity at atoms near the boundary, and a suitable input in terms of given incoming wave modes. Then a phonon representation for finite temperature lattice motion is adopted. The proposed approach is simple and compact. Numerical tests validate the effectiveness of the boundary condition in reflection suppression for outgoing waves. It maintains target temperature for the lattice, with expected kinetic energy distribution and heat flux. Moreover, its linear nature facilitates reliable finite temperature atomic simulations with a correct description for non-thermal motions.
Heat jet approach for finite temperature atomic simulations of two-dimensional square lattice
Liu, Baiyili,Tang, Shaoqiang Techno-Press 2016 Coupled systems mechanics Vol.5 No.4
We propose a heat jet approach for a two-dimensional square lattice with nearest neighbouring harmonic interaction. First, we design a two-way matching boundary condition that linearly relates the displacement and velocity at atoms near the boundary, and a suitable input in terms of given incoming wave modes. Then a phonon representation for finite temperature lattice motion is adopted. The proposed approach is simple and compact. Numerical tests validate the effectiveness of the boundary condition in reflection suppression for outgoing waves. It maintains target temperature for the lattice, with expected kinetic energy distribution and heat flux. Moreover, its linear nature facilitates reliable finite temperature atomic simulations with a correct description for non-thermal motions.