I shall discuss a new hybrid numerical method for multiscale partial differential equations, which simultaneously captures the global macroscopic information and resolves the local microscopic events over regions of relatively small size. The idea comes from an earlier work of Nitsche in 1970s. The method couples concurrently the microscopic coefficients in the region of interest with the homogenized coefficients elsewhere. The cost of the method is comparable to the heterogeneous multiscale method proposed by E and Engquist in 2003, while being able to recover microscopic information of the solution. The convergence of the method is proved for problems with bounded and measurable coefficients, while the rate of convergence is established for problems with rapidly oscillating periodic or almost-periodic coefficients. Extensive numerical results are reported to show the efficiency and accuracy of the proposed method. This is a joint work with S.Q. Song.

明平兵，中科院数学与系统科学研究院研究员，并担任科学与工程计算国家重点实验室副主任。主要从事固体多尺度建模、模拟及多尺度算法的研究。他预测了石墨烯的理想强度并在Cauchy-Born法则的数学理论、拟连续体方法的稳定性方面有较为系统的工作。他在JAMS, CPAM, ARMA, PRB, SINUM, Math. Comp. Numer. Math, MMS, JMPS 等国际著名学术期刊上发表学术论文五十余篇。他曾应邀在SCADE2009，The SIAM Mathematics Aspects of Materials Science 2016等会议上作大会报告。他于2014年获得国家杰出青年基金并于2019年入选第四批国家“万人计划”中青年科技创新领军人才计划。