An efficient multi-modes Monte Carlo homogenization
method for random materials
报告人: 黄记祖副研究员(中科院数学与系统科学研究院计算数学所)
报告时间：2022年4月15日（周五）下午3：00-4：00
报告地点：腾讯会议726-126-932
邀请人: 马强
摘要: In this talk, we propose and analyze a new stochastic homogenization method for diffusion equations with random and fast oscillatory coefficients. In the proposed method, the homogenized solutions are sought through a two-stage procedure. In the first stage, the original oscillatory diffusion equation is approximated, for each fixed random sample \omega, by a spatially homogenized diffusion equation with piecewise constant coefficients, resulting in a random diffusion equation. In the second stage, the esulting random diffusion equation is approximated and computed by using an efficient multi-modes Monte Carlo method which only requires to solve a diffusion equation with a constant diffusion coefficient and a random right-hand side. The main advantage of the proposed method is that it separates the computational difficulty caused by the spatial fast oscillation of the solution and that caused by the randomness of the solution, so they can be overcome separately using different strategies. The convergence of the solution of the spatially homogenized equation (from the first stage) to the solution of the original random diffusion equation is established and the optimal rate of convergence is also obtained for the proposed multi-modes Monte Carlo method. Numerical experiments on some benchmark test problems for random composite materials are also presented to gauge the efficiency and accuracy of the proposed two-stage stochastic homogenization method.
专家简介：黄记祖, 现任中国科学院数学与系统科学研究院副研究员。2004年毕业于湖南大学，获学士学位。2012年在中国科学院数学与系统科学研究院获理学博士学位，导师：曹礼群研究员。2012年9月到2013年2月，访问美国University of Colorado Boulder计算机系系主任蔡小川教授。2012年7月到2014年7月，在中国科学院软件研究所从事博士后研究工作，2014年7月，入职中国科学院数学与系统科学研究院，主要研究领域为多尺度模型和并行算法。迄今为止，在 Multiscale Model. & Simul.、SIAM S J. Sci. Comput.、J. Compu. Phys.、Comput. Phys. Commun.等国际知名期刊独立或者与其合作者发表学术论文20多篇。
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