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Shaoqiang Tang - Department of Mechanics, Peking University, Beijing, China
Friday, July 26, 2013 - 10:00am to 11:00am
In this talk, we introduce several accurate boundary treatments for concurrent multiscale simulations, as well as atomic dynamics calculations. The time history kernel treatment is exact for linear lattices. Yet the time convolution is costly, and the exact kernel functions are usually not easy to obtain. We illustrate the delicacy of the kernel functions for a square lattice. Local boundary conditions, including the velocity interfacial conditions and the matching boundary conditions, are developed by approximating a one-way wave differential operator and the dispersion relation, respectively. They alleviate considerably the numerical costs, and may be readily extended to handle multi-dimensional nonlinear lattices. Numerical examples are presented. We further describe a class of accurate boundary conditions for the harmonic lattice designed by matching the time history kernel functions. They take a linear form similar to the matching boundary conditions, yet with more sophisticated derivation and accordingly higher accuracy. All above boundary treatments may be generalized to two-way boundary conditions for treating both incoming and outgoing waves. In addition, we illustrate numerical results with these boundary treatments in a finite difference approach for accurate and efficient multiscale simulations.
Graduating from Hong Kong University of Science and Technology in 1995, Prof. Shaoqiang Tang has been a faculty member in Mechanics Department of Peking University since 1997. His research activities focus on computational mechanics and applied mathematics, including concurrent multiscale methods, quantum effects in semiconductor charge transport, dynamic phase transitions, and nonlinear waves. Prof. Tang serves in Chinese Society of Computational Physics, Chinese Society of Theoretical and Applied Mechanics, and International Chinese Association for Computational Mechanics. He is Associate-Chief-Editor of Mechanics in Engineering, and founding associate editor of Advances in Applied Mathematics and Mechanics. He is currently the deputy director of the Peking University Center for Applied Physics and Technology, and director of Key Laboratory of High Energy Density Physics Simulations, Ministry of Education, China.