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8-07天元基金几何与随机分析及其应用交叉讲座之131【陶默雷】

报告人: Molei Tao  Georgia Institute of Technology
  
时间: 2018年8月7日 上午 10:30-11:30 

地点: 管理科研楼 1218

摘要:

Symplectic integrators preserve the phase-space volume and have favorable performances in long time simulations. Methods for an explicit symplectic integration have been extensively studied for separable Hamiltonians (i.e., H(q,p)=K(p)+V(q)), and they correspond to both accuracy and efficiency. However, nonseparable Hamiltonians also model important problems, such as non-Newtonian mechanics and nearly integrable systems in action-angle coordinates. Unfortunately, implicit methods had been the only available symplectic approach for general nonseparable systems.

This talk will describe a recent result that constructs explicit and arbitrary high-order symplectic integrators for arbitrary Hamiltonians. These integrators are based on a mechanical restraint that binds two copies of phase space together. Based on backward error analysis, KAM theory, and some additional multiscale analysis, a pleasant error bound is established for integrable systems, and demonstrated on a conceptual example and the Schwarzschild geodesics problem. For nonintegrable systems, some numerical experiments with the nonlinear Schr\"odinger equation will be discussed.

 

  科大主页 | 国家数学与交叉科学中心(合肥) | 中科院吴文俊数学重点实验室 |
中科院数学与系统科学研究院 | 北京国际数学研究中心 | 安徽省数学会